diff --git a/CMakeLists.txt b/CMakeLists.txt index 566badf4c..ef7d36d3f 100644 --- a/CMakeLists.txt +++ b/CMakeLists.txt @@ -47,6 +47,7 @@ find_package(Qt5Widgets REQUIRED) set(CMAKE_AUTOMOC ON) find_package(glog REQUIRED) find_package(Ipelib REQUIRED) +find_package(Eigen3 3.4 REQUIRED NO_MODULE) # ## SOURCES ### diff --git a/README.md b/README.md index 0ffce58e1..f6417eb29 100644 --- a/README.md +++ b/README.md @@ -7,7 +7,7 @@ CartoCrow is a framework that simplifies the implementation of algorithms in cartographic visualization. It allows researchers to experiment with these algorithms and use them to generate maps. The framework behind CartoCrow can be used to run other cartography algorithms online. CartoCrow consists of a C++ library (this repository) which provides a set of command-line applications, and a web interface (see [cartocrow-web](https://github.com/tue-alga/cartocrow-web)) which allows end users to generate maps in a user-friendly way. -> [!WARNING] +> [!WARNING] > CartoCrow is still a **work in progress** and should not be considered stable yet. This repository consists of the following subdirectories: @@ -115,7 +115,7 @@ The remaining dependencies need to be built manually. * in `src/ipelib/ipeplatform.cpp` and `src/ipelib/ipebitmap_win.cpp`, add an `#include `; * in `src/ipelib/ipeplatform.cpp`, in `Platform::runLatex()`, replace `wcmd.data()` by `&wcmd[0]`; * in `src/ipelib/ipeplatform.cpp`, in `String::w()`, replace `result.data()` by `&result[0]`. - + Then, to compile: ```sh cd src @@ -135,6 +135,15 @@ On Ubuntu, most dependencies can be obtained from the repository: ```sh sudo apt install build-essential cmake sudo apt install libcgal-dev nlohmann-json3-dev qtbase5-dev +sudo apt install libeigen3-dev +``` + +If Eigen [cannot be found](https://stackoverflow.com/q/23284473) during compilation, you might need to run: + +```sh +cd /usr/include +sudo ln -s eigen3/Eigen Eigen + ``` The remaining dependencies need to be built manually. diff --git a/cartocrow/CMakeLists.txt b/cartocrow/CMakeLists.txt index 8d8b5b5e2..1b3796e6c 100644 --- a/cartocrow/CMakeLists.txt +++ b/cartocrow/CMakeLists.txt @@ -15,6 +15,7 @@ add_subdirectory(renderer) add_subdirectory(necklace_map) add_subdirectory(simplification) add_subdirectory(flow_map) +add_subdirectory(mosaic_cartogram) add_subdirectory(isoline_simplification) add_library(cartocrow_lib INTERFACE) @@ -25,14 +26,10 @@ target_link_libraries( necklace_map flow_map simplification + mosaic_cartogram ) -install( - TARGETS cartocrow_lib - EXPORT ${CARTOCROW_EXPORT_TARGETS} - LIBRARY DESTINATION ${CMAKE_INSTALL_LIBRARY_DIR} - INCLUDES DESTINATION ${CMAKE_INSTALL_SOURCE_DIR} -) +cartocrow_install_module(cartocrow_lib) install( EXPORT ${CARTOCROW_EXPORT_TARGETS} FILE "${CARTOCROW_EXPORT_TARGETS}.cmake" diff --git a/cartocrow/core/CMakeLists.txt b/cartocrow/core/CMakeLists.txt index 2f3dd609a..cd7db98bd 100644 --- a/cartocrow/core/CMakeLists.txt +++ b/cartocrow/core/CMakeLists.txt @@ -1,5 +1,6 @@ set(SOURCES core.cpp + ellipse.cpp ipe_reader.cpp region_arrangement.cpp region_map.cpp @@ -9,6 +10,7 @@ set(SOURCES set(HEADERS centroid.h core.h + ellipse.h ipe_reader.h region_arrangement.h region_map.h @@ -18,7 +20,7 @@ set(HEADERS add_library(core ${SOURCES}) target_link_libraries(core - PUBLIC Ipe::ipelib + PUBLIC Eigen3::Eigen Ipe::ipelib PRIVATE glog::glog ) diff --git a/cartocrow/core/centroid.h b/cartocrow/core/centroid.h index 0caf02da6..640810ea5 100644 --- a/cartocrow/core/centroid.h +++ b/cartocrow/core/centroid.h @@ -23,6 +23,7 @@ Created by tvl (t.vanlankveld@esciencecenter.nl) on 05-12-2019 #define CARTOCROW_CORE_POLYGON_H #include "core.h" +#include "region_arrangement.h" #include #include @@ -89,6 +90,17 @@ template Point centroid(const PolygonSet& polygon) { return CGAL::ORIGIN + sum / areaSum; } +/// Computes the centroid of the given face. +inline Point centroid(RegionArrangement::Face_const_handle f) { + Polygon polygon; + auto circ = f->outer_ccb(); + auto curr = circ; + do { + polygon.push_back(curr->target()->point()); + } while (++curr != circ); + return centroid(polygon); +} + } // namespace cartocrow #endif //CARTOCROW_CORE_POLYGON_H diff --git a/cartocrow/core/core.cpp b/cartocrow/core/core.cpp index 375e25bda..c52224960 100644 --- a/cartocrow/core/core.cpp +++ b/cartocrow/core/core.cpp @@ -20,10 +20,32 @@ Created by tvl (t.vanlankveld@esciencecenter.nl) on 05-12-2019 */ #include "core.h" +#include +#include #include namespace cartocrow { +Color Color::shaded(double f) const { + f = std::clamp(f, 0.0, 2.0); + if (f < 1) { + // darken (shade) + return { + (int) std::round(r * f), + (int) std::round(g * f), + (int) std::round(b * f) + }; + } else { + // lighten (tint) + f -= 1; + return { + (int) std::round(r + (255 - r) * f), + (int) std::round(g + (255 - g) * f), + (int) std::round(b + (255 - b) * f), + }; + } +} + Number wrapAngle(Number alpha, Number beta) { return wrap(alpha, beta, beta + M_2xPI); } diff --git a/cartocrow/core/core.h b/cartocrow/core/core.h index e45af1df0..9dd227da9 100644 --- a/cartocrow/core/core.h +++ b/cartocrow/core/core.h @@ -162,6 +162,14 @@ Polyline approximate(const Polyline& p) { return result; } +/// Returns the area of a polygon with holes. +/// TODO: move to more logical place +template Number area(PolygonWithHoles polygon) { + Number a = polygon.outer_boundary().area(); + for (const auto &h : polygon.holes()) a -= h.area(); + return a; // = outer area minus area of each hole +} + /// An RGB color. Used for storing the color of elements to be drawn. struct Color { /// Red component (integer 0-255). @@ -170,6 +178,10 @@ struct Color { int g; /// Blue component (integer 0-255). int b; + + /// Returns a new color that is darker (\f$0 \le f < 1\f$) or lighter + /// (\f$1 < f \le 2\f$). + Color shaded(double f) const; }; /// Wraps the given number \f$n\f$ to the interval \f$[a, b)\f$. diff --git a/cartocrow/core/ellipse.cpp b/cartocrow/core/ellipse.cpp new file mode 100644 index 000000000..d0fe237a1 --- /dev/null +++ b/cartocrow/core/ellipse.cpp @@ -0,0 +1,262 @@ +#include "ellipse.h" + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + +#include "../core/centroid.h" + +namespace cartocrow { + +bool isZero(double x) { + return std::abs(x) < 1e-10; +} + +Eigen::Matrix3d Ellipse::Parameters::matrix() const { + // multiply matrices left to right: translation, rotation, scaling + const double cos = std::cos(angle); + const double sin = std::sin(angle); + return Eigen::Matrix3d { + { cos*a, -sin*b, x0 }, + { sin*a, cos*b, y0 }, + { 0, 0, 1 } + }; +} + +// TODO: only enable checks in debug builds? +Ellipse::Ellipse(double a, double b, double c, double d, double e, double f) + : A(a), B(b), C(c), D(d), E(e), F(f) { + if (!std::isfinite(a) || !std::isfinite(b) || !std::isfinite(c) || + !std::isfinite(d) || !std::isfinite(e) || !std::isfinite(f)) { + throw std::invalid_argument("The coefficients cannot be infinite or NaN"); + } + + // see Lawrence (1972), page 63 + const double min = 4*A*C - B*B; + const double det = min * F - A*E*E + (B*E - C*D) * D; + if (det == 0) { + throw std::invalid_argument("The conic cannot be degenerate"); + } + if (min <= 0) { + throw std::invalid_argument("The conic cannot be a hyperbola or parabola"); + } + if (A*det >= 0) { + throw std::invalid_argument("The ellipse cannot be imaginary"); + } +} + +double Ellipse::angle() const { + // substitute x -> x cos(t) - y sin(t) and y -> x sin(t) + y cos(t) + // and solve for t such that coefficient of xy is 0 + if (isZero(A - C)) return std::numbers::pi / 2; + return .5 * std::atan(B / (A-C)); +} + +Point Ellipse::center() const { + // solve system { dQ/dx = 0, dQ/dy = 0 } for x,y + const double x = (2*C*D - B*E) / (B*B - 4*A*C); + return { x, -(B*x + E) / (2*C) }; +} + +Ellipse Ellipse::normalizeSign() const { + if (A > 0) return *this; // note: sgn(A) = sgn(C) + return { -A, -B, -C, -D, -E, -F }; +} + +Ellipse::Parameters Ellipse::parameters() const { + Parameters p = translateToOrigin().parameters(); + const Point c = center(); + p.x0 = c.x(), p.y0 = c.y(); + return p; +} + +Ellipse Ellipse::stretch(double cx, double cy) const { + // substitute x -> cx x and y -> cy y and compute new coefficients + return { A*cx*cx, B*cx*cy, C*cy*cy, D*cx, E*cy, F }; +} + +Ellipse Ellipse::translate(double dx, double dy) const { + // substitute x -> x-dx and y -> y-dy and compute new coefficients + return { + A, B, C, + D - 2*A*dx - B*dy, + E - 2*C*dy - B*dx, + (A*dx - D) * dx + (B*dx + C*dy - E) * dy + F + }; +} + +Ellipse Ellipse::translateTo(double x, double y) const { + const Point c = center(); + return translate(x - c.x(), y - c.y()); +} + +EllipseAtOrigin Ellipse::translateToOrigin() const { + const Point c = center(); + const double x0 = c.x(), y0 = c.y(); + return { + A, B, C, + (A*x0 + D) * x0 + (B*x0 + C*y0 + E) * y0 + F + }; +} + +std::ostream& operator<<(std::ostream &os, const Ellipse &e) { + const std::array coefficients = e.coefficients(); + static const std::vector variables = { "x²", "xy", "y²", "x", "y", "" }; + + bool first = true; + for (int i = 0; i < coefficients.size(); i++) { + double c = coefficients[i]; + const std::string &v = variables[i]; + + if (!c) continue; + if (!first) { + os << (c > 0 ? " + " : " - "); + c = std::abs(c); + } + if (c != 1 || v.empty()) os << c; + os << v; + + first = false; + } + return os << " = 0"; +} + +std::string Ellipse::toString(int precision) const { + std::stringstream ss; + ss << std::setprecision(precision) << *this; + return ss.str(); +} + +template Ellipse Ellipse::fit(const Polygon &polygon) { + const auto n = polygon.size(); + + // if the polygon is too small, we simply return a circle with the same area and centroid + if (n < 6) { + const EllipseAtOrigin circle(1, 0, 1, -CGAL::to_double(polygon.area()) / std::numbers::pi); + return circle.translate(approximate(centroid(polygon)) - CGAL::ORIGIN); + } + + // TODO: linearly space points on boundary instead of taking vertices, which biases the ellipse towards "detailed corners" + Eigen::ArrayX2d boundary(n, 2); + for (int i = 0; i < n; i++) { + const Point &p = polygon.vertex(i); + boundary(i, 0) = CGAL::to_double(p.x()); + boundary(i, 1) = CGAL::to_double(p.y()); + } + return fit(boundary); +} + +// instantiate template function for Exact and Inexact +template Ellipse Ellipse::fit(const Polygon &polygon); +template Ellipse Ellipse::fit(const Polygon &polygon); + +// based on Fitzgibbon et al. (1999) +// TODO: implement improvements by Harker et al. (2008)? +Ellipse leastSquares(const Eigen::ArrayX2d &boundary) { + const int n = boundary.rows(); + if (n < 6) throw std::invalid_argument("To fit an ellipse you need at least 6 points"); + + const Eigen::ArrayXd xs = boundary.col(0); + const Eigen::ArrayXd ys = boundary.col(1); + + // design matrix (n×6) + Eigen::MatrixXd D(n, 6); + D << xs*xs, xs*ys, ys*ys, xs, ys, Eigen::VectorXd::Ones(n); + + // scatter matrix (6×6) + const Eigen::MatrixXd S = D.transpose() * D; + + // constraint matrix (6×6) + Eigen::MatrixXd C = Eigen::MatrixXd::Zero(6, 6); + C(0, 2) = 2; + C(1, 1) = -1; + C(2, 0) = 2; + + // Compute the one positive eigenvalue and corresponding eigenvector. Due to numerical instabi- + // lity, there are often other positive eigenvalues that are very close to 0. We ignore these by + // taking the largest. + // TODO: What should happen with zero, infinite, or imaginary eigenvalues? + // TODO: This could produce nonsense (e.g., see Halíř & Flusser, 1998). + const Eigen::EigenSolver evSolver(S.inverse() * C); + const Eigen::Vector evs = evSolver.eigenvalues().real(); + const int i = std::max_element(evs.begin(), evs.end()) - evs.begin(); + const Eigen::Vector u = evSolver.eigenvectors().col(i).real(); + + // ellipse coefficients + const Eigen::Vector a = u / std::sqrt(u.transpose() * C * u); + return { a[0], a[1], a[2], a[3], a[4], a[5] }; +} + +Ellipse Ellipse::fit(const Eigen::ArrayX2d &boundary) { + Eigen::ArrayX2d ps = boundary; + + // normalize the points: subtract mean and divide by standard deviation + // this improves numerical stability during fitting + const Eigen::Array mean = ps.colwise().mean(); + ps.rowwise() -= mean; + const Eigen::Array invStd = std::sqrt(ps.rows()) / ps.colwise().norm(); + ps.rowwise() *= invStd; + + // fit ellipse and "denormalize" + return leastSquares(ps) + .stretch(invStd[0], invStd[1]) + .translate(mean[0], mean[1]); +} + +double EllipseAtOrigin::area() const { + // https://math.stackexchange.com/q/2499695 + return 2 * std::numbers::pi * std::abs(F) / std::sqrt(4*A*C - B*B); +} + +EllipseAtOrigin EllipseAtOrigin::normalizeContours(double deltaArea) const { + // let g(x) = area(Q + x) and solve g'(1) = deltaArea for (scaling factor of) new coefficients + const double c = 2 * std::numbers::pi / (std::sqrt(4*A*C - B*B) * deltaArea); + return { c*A, c*B, c*C, c*F }; +} + +Ellipse::Parameters EllipseAtOrigin::parameters() const { + Parameters p; + p.angle = angle(); + p.x0 = p.y0 = 0; + + const double cos = std::cos(p.angle); + const double sin = std::sin(p.angle); + + // substitute x -> x cos(t) - y sin(t) and y -> x sin(t) + y cos(t) where t := angle + // this eliminates rotation and transforms ellipse into the form Ax² + Cy² + F = 0 + const double A2 = A*cos*cos + ( B*cos + C*sin) * sin; + const double C2 = C*cos*cos + (-B*cos + A*sin) * sin; + + p.a = std::sqrt(-F / A2); + p.b = std::sqrt(-F / C2); + + return p; +} + +double EllipseAtOrigin::radius(double slope) const { + // special case: vertical line intersection + if (std::isinf(slope)) return std::sqrt(-F / C); + + // substitute y -> mx i.e. the linear function with slope m through the origin + // and rewrite as quadratic equation in x, i.e., ax² + 0x + F, where: + const double a = A + (B + C*slope) * slope; + // then x = \pm\sqrt{-F/a} so: + const double xSq = -F / a; + // return distance from origin to (x, y) = (x, mx) + return std::sqrt(xSq * (1 + slope*slope)); +} + +EllipseAtOrigin EllipseAtOrigin::scaleTo(double area) const { + // note that area is linear in |F|, so areaNew / areaOld = |Fnew| / |Fold| = Fnew / Fold + // since the sign must remain the same + return { A, B, C, F * area / this->area() }; +} + +} // namespace cartocrow diff --git a/cartocrow/core/ellipse.h b/cartocrow/core/ellipse.h new file mode 100644 index 000000000..e11bf3444 --- /dev/null +++ b/cartocrow/core/ellipse.h @@ -0,0 +1,73 @@ +#ifndef CARTOCROW_CORE_ELLIPSE_H +#define CARTOCROW_CORE_ELLIPSE_H + +#include +#include +#include + +#include "core.h" + +namespace cartocrow { + +// TODO: convert to/from CGAL ellipse + +class EllipseAtOrigin; + +/// \author Gijs Pennings +class Ellipse { + protected: + double A, B, C, D, E, F; + + public: + struct Parameters { + double a, b, angle, x0, y0; + Eigen::Matrix3d matrix() const; + }; + + Ellipse() : A(1), B(), C(1), D(), E(), F(-1) {} + Ellipse(double a, double b, double c, double d, double e, double f); + + double angle() const; + Point center() const; + std::array coefficients() const { return { A, B, C, D, E, F }; } + Ellipse contour(double c) const { return { A, B, C, D, E, F - c }; } + double evaluate(double x, double y) const { return (A*x + B*y + D) * x + (C*y + E) * y + F; } + double evaluate(const Point &p) const { return evaluate(p.x(), p.y()); } + /// Returns a new ellipse where coefficients \c A and \c C are positive. + Ellipse normalizeSign() const; + virtual Parameters parameters() const; + Ellipse stretch(double cx, double cy) const; + Ellipse stretch(double c) const { return stretch(c, c); } + Ellipse translate(double dx, double dy) const; + Ellipse translate(const Vector &v) const { return translate(v.x(), v.y()); } + Ellipse translateTo(double x, double y) const; + Ellipse translateTo(const Point &p) const { return translateTo(p.x(), p.y()); } + EllipseAtOrigin translateToOrigin() const; + + friend std::ostream& operator<<(std::ostream &os, const Ellipse &e); + std::string toString(int precision = 3) const; + + template + static Ellipse fit(const Polygon &polygon); + static Ellipse fit(const Eigen::ArrayX2d &boundary); +}; + +/// \author Gijs Pennings +class EllipseAtOrigin : public Ellipse { + public: + EllipseAtOrigin() : Ellipse() {} + EllipseAtOrigin(double a, double b, double c, double f) : Ellipse(a, b, c, 0, 0, f) {} + + double area() const; + /// Scales the coefficients such that adding 1 to \c F increases the area by \c deltaArea. + EllipseAtOrigin normalizeContours(double deltaArea = 1) const; + Parameters parameters() const override; + /// Let ℓ be the line with slope \c slope through the origin. This function computes the length + /// of the part of ℓ that is contained in the ellipse. + double radius(double slope) const; + EllipseAtOrigin scaleTo(double area) const; +}; + +} // namespace cartocrow + +#endif // CARTOCROW_CORE_ELLIPSE_H diff --git a/cartocrow/core/region_map.cpp b/cartocrow/core/region_map.cpp index fbb1fb6b5..5c73a6d53 100644 --- a/cartocrow/core/region_map.cpp +++ b/cartocrow/core/region_map.cpp @@ -21,6 +21,7 @@ along with this program. If not, see . #include #include +#include #include #include @@ -92,6 +93,25 @@ RegionMap ipeToRegionMap(const std::filesystem::path& file) { return regions; } +std::vector> ipeToSalientPoints(const std::filesystem::path& file) { + std::shared_ptr document = IpeReader::loadIpeFile(file); + ipe::Page* page = document->page(0); + + std::vector> points; + for (int i = 0; i < page->count(); ++i) { + ipe::Object* object = page->object(i); + ipe::Object::Type type = object->type(); + if (type != ipe::Object::Type::EReference) { + continue; + } + ipe::Reference* symbol = object->asReference(); + ipe::Vector position = symbol->position(); + points.push_back(Point(position.x, position.y)); + } + + return points; +} + std::optional detail::findLabelInside(const PolygonSet& shape, const std::vector& labels) { std::optional labelId; diff --git a/cartocrow/core/region_map.h b/cartocrow/core/region_map.h index 49c75e943..b40dada8b 100644 --- a/cartocrow/core/region_map.h +++ b/cartocrow/core/region_map.h @@ -75,6 +75,10 @@ std::optional findLabelInside(const PolygonSet& shape, /// or if the file does not contain regions like specified above. RegionMap ipeToRegionMap(const std::filesystem::path& file); +/// (temp) Should be removed in favor of an algorithm that computes salient +/// points from a \ref RegionMap. +std::vector> ipeToSalientPoints(const std::filesystem::path& file); + } // namespace cartocrow #endif //CARTOCROW_CORE_REGION_MAP_H diff --git a/cartocrow/flow_map/CMakeLists.txt b/cartocrow/flow_map/CMakeLists.txt index f9b5fd538..5fb623270 100644 --- a/cartocrow/flow_map/CMakeLists.txt +++ b/cartocrow/flow_map/CMakeLists.txt @@ -44,6 +44,7 @@ set(HEADERS add_library(flow_map ${SOURCES}) target_link_libraries(flow_map + PUBLIC core PRIVATE glog::glog ) diff --git a/cartocrow/mosaic_cartogram/CMakeLists.txt b/cartocrow/mosaic_cartogram/CMakeLists.txt new file mode 100644 index 000000000..7e970306d --- /dev/null +++ b/cartocrow/mosaic_cartogram/CMakeLists.txt @@ -0,0 +1,33 @@ +set(SOURCES + graph.cpp + guiding_shape.cpp + mosaic_cartogram.cpp + orderly_spanning_tree.cpp + painting.cpp + tile_map.cpp + triangulation.cpp + visibility_drawing.cpp +) +set(HEADERS + edmonds_optimum_branching_impl.hpp + edmonds_optimum_branching.hpp + graph.h + guiding_shape.h + mosaic_cartogram.h + orderly_spanning_tree.h + painting.h + parameters.h + region.h + tile_map.h + triangulation.h + visibility_drawing.h +) + +add_library(mosaic_cartogram ${SOURCES}) +target_link_libraries(mosaic_cartogram + PUBLIC core + PRIVATE glog::glog +) + +cartocrow_install_module(mosaic_cartogram) +install(FILES ${HEADERS} DESTINATION ${CARTOCROW_INSTALL_DIR}/mosaic_cartogram) diff --git a/cartocrow/mosaic_cartogram/edmonds_optimum_branching.hpp b/cartocrow/mosaic_cartogram/edmonds_optimum_branching.hpp new file mode 100644 index 000000000..01d1d256d --- /dev/null +++ b/cartocrow/mosaic_cartogram/edmonds_optimum_branching.hpp @@ -0,0 +1,96 @@ +// https://github.com/atofigh/edmonds-alg +// Copyright (c) 2007 Ali Tofigh, Erik Sjölund +// MIT License + +#ifndef EDMONDS_OPTIMUM_BRANCHING_HPP +#define EDMONDS_OPTIMUM_BRANCHING_HPP + +// edmonds_optimum_branching() +// +// This template function implements Tarjan's implementation of +// Edmonds's algorithm for finding optimum branchings. The function +// uses concepts from the Boost graph library. The template parameters +// have the following definition: +// +// TOptimumIsMaximum: if true then the algorithm finds a branching of +// maximum weight. If false, the algorithm finds a branching with +// minimum weight. +// +// TAttemptToSpan: if true, the algorithm attempts to span the entire +// graph. If root vertices have been assigned by the caller (see +// description of roots_begin and roots_end) and at least one +// branching exists whose only roots are those specified, then the +// algorithm finds an optimum branching whose roots are exactly those +// specified. If no roots have been specified by the caller and at +// least one branching exists with exactly one root, then the +// algorithm finds an optimum branching with exactly one root. If the +// parameter is false, an optimum branching is returned that may not +// span the entire graph. For example, no edge that worsens the cost +// of the branching is included. +// +// TGraphIsDense: if true, the algorithm will have time complexity +// O(n^2) where n is the number of vertices of the graph. If false, +// the algorithm will have time complexity O(m log n) where n is the +// number of vertices and m is the number of edges of the +// graph. NOTE!!! currently, this parameter has no effect as the +// function is only implemented for dense graphs. +// +// TEdgeListGraph: the type of the graph that adheres to the +// EdgeListGraph concept of the Boost Graph Library. +// +// TVertexIndexMap: the type of the Boost property map that maps the +// vertices of the graph to non-negative integers. +// +// TWeightMap: the type of the Boost property map that associates +// weights with each edge of the graph. Note that the weights must be +// of a numeric type that supports the operations of +, -, <, >. +// +// TInputIterator: the type of iterator used for traversing +// vertices. The type must adhere to the Input Iterator concept of the STL. +// +// TOutputIterator: the type of iterator used for outputting the edges +// of the branching. The type must adhere to the Output Iterator +// concept of the STL. +// +// The input to the graph is as follows: +// +// g is the graph that adheres to the EdgeListGraph concept of the +// Boost Graph Library. +// +// index is a Boost property map that maps each vertex of g to a +// positive integer. If g contains n vertices, then index must map +// each vertex uniquely to an integer in the range 0..n-1. Constant +// time complexity is required. +// +// weight is a Boost property map associating a weight with each edge +// of g. Constant time complexity is required. +// +// roots_begin and roots_end are iterators over vertices of g. Any +// vertices in this range are guaranteed to be roots in the final +// branching. This range may of course be empty, in which case +// appropriate roots are found by the algorithm. +// +// out is an output iterator to which the edges of the optimum +// branching is written. +// +template +void +edmonds_optimum_branching(TEdgeListGraph &g, + TVertexIndexMap index, + TWeightMap weight, + TInputIterator roots_begin, + TInputIterator roots_end, + TOutputIterator out); + + +#include "edmonds_optimum_branching_impl.hpp" + + +#endif // not EDMONDS_OPTIMUM_BRANCHING_HPP diff --git a/cartocrow/mosaic_cartogram/edmonds_optimum_branching_impl.hpp b/cartocrow/mosaic_cartogram/edmonds_optimum_branching_impl.hpp new file mode 100644 index 000000000..ad44616df --- /dev/null +++ b/cartocrow/mosaic_cartogram/edmonds_optimum_branching_impl.hpp @@ -0,0 +1,555 @@ +// https://github.com/atofigh/edmonds-alg +// Copyright (c) 2007 Ali Tofigh, Erik Sjölund +// MIT License + +#ifndef EDMONDS_OPTIMUM_BRANCHING_IMPL_HPP +#define EDMONDS_OPTIMUM_BRANCHING_IMPL_HPP + +#include +#include +#include +#include +#include +#include +#include +#include +#include + + + +// namespace detail +// +// The namespace encapsulates classes and/or functions that are +// required for the implementation of edmonds's optimum branching +// algorithm which should not be visible to the user. This way the +// global namespace remains unpolluted. +namespace detail { + using namespace boost; + + + + // class OptimumBranching + // + // I encapsulate all the details of edmonds's algorithm inside a + // class. This makes the code easier to read (and easier to write) + // since the number of template declarations is reduced + // considerably. Besides, all the utility functions used to + // implement one algorithm conceptually do belong together. + // + // Note that any concept checks are performed in the function that + // uses this class, so there is no need to repeat them here. + template + class OptimumBranching { + public: + typedef TEdgeListGraph Graph; + typedef typename graph_traits::edge_descriptor Edge; + typedef typename graph_traits::vertex_descriptor Vertex; + typedef typename graph_traits::edge_iterator EdgeIter; + typedef typename property_traits::value_type weight_t; + typedef typename property_traits::value_type vertex_idx_t; + + + + // struct EdgeNode + // + // One unique EdgeNode object is created for each edge of the + // input graph. Any containers then store pointers to these + // objects. The edges of the graph F (which is described in + // the document describing the implementation) are stored in + // each EdgeNode object via the parent and children members. + // For efficiency reasons a boolean member 'removed_from_F' is + // also present in each EdgeNode object. If this member is + // set, then the edge (which is also a vertex in F) was + // removed during the expansion phase of the algorithm. + struct EdgeNode { + Edge edge; + vertex_idx_t source; + vertex_idx_t target; + weight_t weight; + EdgeNode *parent; + std::vector children; + bool removed_from_F; + + EdgeNode(const Edge &e, + const vertex_idx_t &s, + const vertex_idx_t &t, + const weight_t w) + : edge(e), source(s), target(t), weight(w), parent(0), + removed_from_F(false) + { + ; + } + + // operator< + // + // This is only used temporarily when sorting the + // EdgeNodes by their sources. Once a radix-sort algorithm + // has been implemented, this is no longer needed. + bool operator<(const EdgeNode &en) const + { + return source < en.source; + } + }; + + + + // The data members of the OptimumBranching class. These + // include both the input and the variables needed internally for the implementations. + const TEdgeListGraph &g; + const TVertexIndexMap &index; + const TWeightMap &weight; + TInputIterator roots_begin; + TInputIterator roots_end; + TOutputIterator out; + + // The constructor + OptimumBranching(const TEdgeListGraph &g, + const TVertexIndexMap &index, + const TWeightMap &weight, + TInputIterator roots_begin, + TInputIterator roots_end, + TOutputIterator out) + : g(g), index(index), weight(weight), + roots_begin(roots_begin), roots_end(roots_end), out(out) + { + ; + } + + + + // remove_from_F() + // + // It removes the EdgeNode en and all its ancestors from the + // graph F (by resetting the parent and children members and + // setting the flag removed_from_F). Any newly created roots + // of F are inserted into F_roots. Note that the root of F + // that is removed as a consequence is not actually removed + // from F_roots. It is simply marked as removed via the + // 'removed_from_F' flag. + void remove_from_F(EdgeNode *en, std::vector &F_roots) + { + // Note that en is inserted into F_roots as well. But + // since it is marked as removed_from_F it will not cause + // any trouble. This is more efficient than making sure + // that only the siblings of en are inserted into F_roots. + for ( ; en != 0; en = en->parent) + { + en->removed_from_F = true; + BOOST_FOREACH (EdgeNode *child, en->children) + { + F_roots.push_back(child); + child->parent = 0; + } + + // free the memory used in en->children. + std::vector().swap(en->children); + } + } + + + // sort_edges() + // + // sorts a vector of EdgeNode pointers with EdgeNode.source as + // key using the radix-sort algorithm. Also, if there are + // several EdgeNode pointers with the same source, the + // function only keeps the one with optimum weight. + void sort_edges(std::vector &edge_vec) + { + const int byte_len = 8; + const int num_buckets = 1u << byte_len; + const unsigned digits = (sizeof (vertex_idx_t)) * std::numeric_limits::digits; + const unsigned mask = (1u << byte_len) - 1; + + std::vector< std::list > buckets(num_buckets); + + for (unsigned i = 0; byte_len * i <= digits; ++i) + { + BOOST_FOREACH (EdgeNode *en, edge_vec) + { + buckets[(en->source >> byte_len * i) & mask].push_back(en); + } + + edge_vec.clear(); + BOOST_FOREACH (std::list &bucket, buckets) + { + BOOST_FOREACH (EdgeNode *en, bucket) + { + if (!edge_vec.empty() && edge_vec.back()->source == en->source) + { + bool en_is_better = TOptimumIsMaximum ? + en->weight > edge_vec.back()->weight : + en->weight < edge_vec.back()->weight; + if (en_is_better) + { + edge_vec.back() = en; + } + } + else + { + edge_vec.push_back(en); + } + } + } + + buckets.clear(); + buckets.resize(num_buckets); + } + } + + + // operator() + // + // This is the main function implementing Tarjan's + // implementation of Edmonds's algorithm. + void operator()() + { + std::vector all_edges; + vertex_idx_t max_vertex_idx; + + // Create EdgeNodes for all the edges and find the maximum vertex + // index. Note that we skip self-loops. + max_vertex_idx = 0; + BOOST_FOREACH (const Edge &e, edges(g)) + { + if (source(e, g) == target(e, g)) + continue; + + all_edges.push_back(EdgeNode (e, source(e, g), target(e, g), get(weight, e))); + max_vertex_idx = std::max(max_vertex_idx, index[target(e, g)]); + max_vertex_idx = std::max(max_vertex_idx, index[source(e, g)]); + } + + // insert into in_edges[v] all edges entering v. + + //!! TODO !! If sparse graphs, I have to change the + //representation of in_edges to a special kind of priority + //queue that are able to be merged in log n time. + + std::vector< std::vector > in_edges(max_vertex_idx + 1); + std::vector edge_weight_change(max_vertex_idx + 1); + BOOST_FOREACH (EdgeNode &en, all_edges) + { + in_edges[en.target].push_back(&en); + } + BOOST_FOREACH (std::vector &edges, in_edges) + { + sort_edges(edges); + } + + // Save the specified roots in a random access fashion. + std::vector is_specified_root(max_vertex_idx + 1); + std::vector final_roots; + for ( ; roots_begin != roots_end; ++roots_begin) + { + is_specified_root[index[*roots_begin]] = true; + final_roots.push_back(index[*roots_begin]); + } + + // Initialize S, W, roots, cycles, lambda, enter, F, and min + std::vector< std::vector > cycle(max_vertex_idx + 1); + std::vector lambda(max_vertex_idx + 1); + std::vector roots; + disjoint_sets_with_storage<> S(2*(max_vertex_idx +1)); + disjoint_sets_with_storage<> W(2*(max_vertex_idx +1)); + std::vector min(max_vertex_idx + 1); + std::vector enter(max_vertex_idx + 1); + std::vector F; + for (vertex_idx_t v = 0; v <= max_vertex_idx; ++v) + { + S.make_set(v); + W.make_set(v); + min[v] = v; + if (!is_specified_root[v]) + roots.push_back(v); + } + + // Keep adding critical edges and contracting cycles while + // doing a whole bunch of book-keeping. + while (!roots.empty()) + { + // Find an S-component with an entering edge + vertex_idx_t cur_root = roots.back(); roots.pop_back(); + if (in_edges[cur_root].empty()) + { + final_roots.push_back(min[cur_root]); + continue; + } + + // Find an optimum-weight edge entering cur_root + + //!! TODO !! We have to do this differently for sparse graphs. + EdgeNode *critical_edge = in_edges[cur_root].front(); + BOOST_FOREACH (EdgeNode *en, in_edges[cur_root]) + { + bool en_is_better = TOptimumIsMaximum ? + en->weight > critical_edge->weight : + en->weight < critical_edge->weight; + if (en_is_better) + { + critical_edge = en; + } + } + + // Do not add critical_edge if it worsens the total + // weight and we are not attempting to span. + if (!TAttemptToSpan) + { + bool improves = TOptimumIsMaximum ? + critical_edge->weight > weight_t(0) : + critical_edge->weight < weight_t(0); + if (!improves) + { + final_roots.push_back(min[cur_root]); + continue; + } + } + + // Insert critical_edge into "F" and let any edges in + // cycle[cur_root] be its children. + F.push_back(critical_edge); + BOOST_FOREACH (EdgeNode *en, cycle[cur_root]) + { + en->parent = critical_edge; + critical_edge->children.push_back(en); + } + + // If critical_edge is a leaf in "F", then add a + // pointer to it. + if (cycle[cur_root].empty()) + { + lambda[cur_root] = critical_edge; + } + + // If adding critical_edge didn't create a cycle + if (W.find_set(critical_edge->source) != + W.find_set(critical_edge->target)) + { + enter[cur_root] = critical_edge; + W.union_set(critical_edge->source, critical_edge->target); + } + else // If adding critical_edge did create a cycle + { + // Find the edges of the cycle, the + // representatives of the strong components in the + // cycle, and the least costly edge of the cycle. + std::vector cycle_edges; + std::vector cycle_repr; + EdgeNode *least_costly_edge = critical_edge; + enter[cur_root] = 0; + + cycle_edges.push_back(critical_edge); + cycle_repr.push_back(S.find_set(critical_edge->target)); + for (vertex_idx_t v = S.find_set(critical_edge->source); + enter[v] != 0; v = S.find_set(enter[v]->source)) + { + cycle_edges.push_back(enter[v]); + cycle_repr.push_back(v); + bool is_less_costly = TOptimumIsMaximum ? + enter[v]->weight < least_costly_edge->weight : + enter[v]->weight > least_costly_edge->weight; + if (is_less_costly) + { + least_costly_edge = enter[v]; + } + } + // change the weight of the edges entering + // vertices of the cycle. + //!! TODO !! Change this for sparse graphs + BOOST_FOREACH (EdgeNode *en, cycle_edges) + { + edge_weight_change[S.find_set(en->target)] = + least_costly_edge->weight - en->weight; + } + + // Save the vertex that would be root if the newly + // created strong component would be a root. + vertex_idx_t cycle_root = + min[S.find_set(least_costly_edge->target)]; + + // Union all components of the cycle into one component. + vertex_idx_t new_repr = cycle_repr.front(); + BOOST_FOREACH (vertex_idx_t v, cycle_repr) + { + S.link(v, new_repr); + new_repr = S.find_set(new_repr); + } + min[new_repr] = cycle_root; + roots.push_back(new_repr); + cycle[new_repr].swap(cycle_edges); + + //!! TODO !! Needs to be changed for sparse graphs. + BOOST_FOREACH (vertex_idx_t v, cycle_repr) + { + BOOST_FOREACH (EdgeNode *en, in_edges[v]) + { + en->weight += edge_weight_change[v]; + } + } + + // Merge all in_edges of the cycle into one list. + //!! TODO !! needs to be changed for sparse graphs. + std::vector new_in_edges; + for (unsigned i = 1; i < cycle_repr.size(); ++i) + { + typedef typename std::vector::iterator Iter; + Iter i1 = in_edges[cycle_repr[i]].begin(); + Iter e1 = in_edges[cycle_repr[i]].end(); + Iter i2 = in_edges[cycle_repr[i-1]].begin(); + Iter e2 = in_edges[cycle_repr[i-1]].end(); + + ///* + while (i1 != e1 || i2 != e2) + { + while (i1 != e1 && S.find_set((*i1)->source) == new_repr) + { + ++i1; + } + while (i2 != e2 && S.find_set((*i2)->source) == new_repr) + { + ++i2; + } + + if (i1 == e1 && i2 == e2) + break; + + if (i1 == e1) + { + new_in_edges.push_back(*i2); + ++i2; + } + else if (i2 == e2) + { + new_in_edges.push_back(*i1); + ++i1; + } + else if (((*i1)->source) < ((*i2)->source)) + { + new_in_edges.push_back(*i1); + ++i1; + } + else if ((*i1)->source > (*i2)->source) + { + new_in_edges.push_back(*i2); + ++i2; + } + else // if the sources are equal + { + bool i1_is_better = TOptimumIsMaximum ? + (*i1)->weight > (*i2)->weight : + (*i1)->weight < (*i2)->weight; + if (i1_is_better) + { + new_in_edges.push_back(*i1); + } + else + { + new_in_edges.push_back(*i2); + } + ++i1; + ++i2; + } + } + in_edges[cycle_repr[i]].swap(new_in_edges); + new_in_edges.clear(); + } + in_edges[new_repr].swap(in_edges[cycle_repr.back()]); + edge_weight_change[new_repr] = weight_t(0); + //*/ + } + } // while (!roots.empty()) + + // Extract the optimum branching + + // Find all roots of F. + std::vector F_roots; + BOOST_FOREACH (EdgeNode *en, F) + { + if (en->parent == 0) + { + F_roots.push_back(en); + } + } + + // Remove edges entering the root nodes. + BOOST_FOREACH (vertex_idx_t v, final_roots) + { + if (lambda[v] != 0) + { + remove_from_F(lambda[v], F_roots); + } + } + + while (!F_roots.empty()) + { + EdgeNode *en = F_roots.back(); F_roots.pop_back(); + if (en->removed_from_F) + continue; + + *out = en->edge; + ++out; + remove_from_F(lambda[en->target], F_roots); + } + } + + }; +} + +template +void +edmonds_optimum_branching(TEdgeListGraph &g, + TVertexIndexMap index, + TWeightMap weight, + TInputIterator roots_begin, + TInputIterator roots_end, + TOutputIterator out) +{ + using namespace boost; + + typedef typename graph_traits::edge_descriptor Edge; + typedef typename graph_traits::vertex_descriptor Vertex; + typedef typename graph_traits::edge_iterator EdgeIter; + typedef typename property_traits::value_type weight_t; + + function_requires< EdgeListGraphConcept >(); + function_requires< ReadablePropertyMapConcept >(); + function_requires< ReadablePropertyMapConcept >(); + function_requires< InputIteratorConcept >(); + function_requires< OutputIteratorConcept >(); + //!! Add the following requirements: + // + // property_traits::value_type is a built-in + // integral type, or perhaps require that it can be used to index + // into arrays. + // + // property_traits::value_type is a numeric type that + // handles the operations +, -, and <. + // + // TInputIterator's value type is Vertex + // TOutputIterator's value type is Edge + + + ::detail::OptimumBranching + optimum_branching(g, index, weight, roots_begin, roots_end, out); + optimum_branching(); +} + + + + +#endif // not EDMONDS_OPTIMUM_BRANCHING_IMPL_HPP diff --git a/cartocrow/mosaic_cartogram/graph.cpp b/cartocrow/mosaic_cartogram/graph.cpp new file mode 100644 index 000000000..858308301 --- /dev/null +++ b/cartocrow/mosaic_cartogram/graph.cpp @@ -0,0 +1,80 @@ +#include "graph.h" + +#include + +namespace cartocrow::mosaic_cartogram { + +std::optional Graph::getNextNeighbor(int v, int neighbor) const { + const auto &ns = m_adj[v]; + auto it = std::find(ns.begin(), ns.end(), neighbor); + if (it == ns.end()) return std::nullopt; + ++it; + return it == ns.end() ? ns.front() : *it; +} + +int Graph::getNumberOfCommonNeighbors(int u, int v) const { + // since the vectors are small, we use a simple quadratic-time approach with little overhead + int c = 0; + for (int x : m_adj[u]) { + for (int y : m_adj[v]) { + if (x == y) { + c++; + break; + } + } + } + return c; +} + +bool Graph::containsEdge(int u, int v) const { + auto &ns = m_adj[u]; + return std::find(ns.begin(), ns.end(), v) != ns.end(); +} + +std::vector> Graph::getEdges() const { + std::vector> edges; + for (int u = 0; u < m_adj.size(); u++) + for (int v : m_adj[u]) + edges.push_back({ u, v }); + return edges; +} + +bool Graph::addEdge(int u, int v) { + if (u == v || containsEdge(u, v)) return false; + addEdgeUnsafe(u, v); + return true; +} + +bool Graph::removeEdge(int u, int v) { + auto &ns = m_adj[u]; + auto it = std::find(ns.begin(), ns.end(), v); // note that there is at most one occurrence + if (it == ns.end()) return false; + ns.erase(it); + return true; +} + +void UndirectedGraph::addEdgeUnsafe(int u, int v) { + Graph::addEdgeUnsafe(u, v); + Graph::addEdgeUnsafe(v, u); +} + +bool UndirectedGraph::removeEdge(int u, int v) { + if (Graph::removeEdge(u, v)) { + // (u,v) existed and we removed it, so now we remove (v,u) as well + auto &ns = m_adj[v]; + ns.erase(std::find(ns.begin(), ns.end(), u)); + return true; + } else { + return false; + } +} + +void UndirectedGraph::isolate(int v) { + for (int u : m_adj[v]) { + auto &ns = m_adj[u]; + ns.erase(std::find(ns.begin(), ns.end(), v)); + } + m_adj[v].clear(); +} + +} // namespace cartocrow::mosaic_cartogram diff --git a/cartocrow/mosaic_cartogram/graph.h b/cartocrow/mosaic_cartogram/graph.h new file mode 100644 index 000000000..31edcc73a --- /dev/null +++ b/cartocrow/mosaic_cartogram/graph.h @@ -0,0 +1,98 @@ +#ifndef CARTOCROW_MOSAIC_CARTOGRAM_GRAPH_H +#define CARTOCROW_MOSAIC_CARTOGRAM_GRAPH_H + +#include +#include +#include + +namespace cartocrow::mosaic_cartogram { + +/// A simple, directed graph with a fixed number of vertices. +class Graph { + /// Invariants for all u,v: + /// - !m_adj[u].contains(u) + /// - m_adj[u].count(v) <= 1 + + protected: + std::vector> m_adj; + + public: + /// Creates an empty graph. + /// Runtime: O(1) + Graph() = default; + + /// Creates a graph consisting of \c n vertices and no edges. + /// Runtime: O(n) + explicit Graph(int n) : m_adj(n) {} + + /// Runtime: O(1) + int getNumberOfVertices() const { return m_adj.size(); } + + /// Runtime: O(1) + int getDegree(int v) const { return m_adj[v].size(); } + + /// Runtime: O(1) + const std::vector& getNeighbors(int v) const { return m_adj[v]; } + + /// Usually but not necessarily, "next" refers to the clockwise direction. + /// Runtime: O(deg(v)) + std::optional getNextNeighbor(int v, int neighbor) const; + + /// Runtime: O(deg(u) deg(v)) + int getNumberOfCommonNeighbors(int u, int v) const; + + /// Runtime: O(deg(u)) + bool containsEdge(int u, int v) const; + + /// Runtime: O(|E|) + std::vector> getEdges() const; + + /// Adds an edge from \c u to \c v, even if it violates the class invariants. + /// Runtime: O(1) + virtual void addEdgeUnsafe(int u, int v) { m_adj[u].push_back(v); } + + /// Adds an edge from \c u to \c v, unless it already exists or it's a self-loop. + /// Runtime: O(deg(u)) + /// \return whether an edge was added + bool addEdge(int u, int v); + + /// Removes the edge from \c u to \c v (if it exists, otherwise there's no effect). + /// Runtime: O(deg(u)) + /// \return whether an edge was removed + virtual bool removeEdge(int u, int v); + + /// Runtime: O(deg(v) + len(a)) + void setAdjacenciesUnsafe(int v, std::vector a) { m_adj[v] = a; } +}; + +/// A simple, undirected graph with a fixed number of vertices. +class UndirectedGraph : public Graph { + /// Additional invariants for all u,v: + /// - m_adj[u].contains(v) iff m_adj[v].contains(u) + + public: + /// Creates an empty graph. + /// Runtime: O(1) + UndirectedGraph() = default; + + /// Creates a graph consisting of \c n vertices and no edges. + /// Runtime: O(n) + explicit UndirectedGraph(int n) : Graph(n) {} + + /// Adds an edge between \c u and \c v, even if it violates the class invariants. + /// Runtime: O(1) + void addEdgeUnsafe(int u, int v) override; + + /// Removes the edge between \c u and \c v (if it exists, otherwise there's no effect). + /// Runtime: O(deg(u) + deg(v)) + /// \return whether an edge was removed + bool removeEdge(int u, int v) override; + + /// Removes all edges incident to \c v. + /// Runtime: O(\sum_u deg(u)) where u is a neighbor of v + void isolate(int v); +}; + +} // namespace cartocrow::mosaic_cartogram + +#endif // CARTOCROW_MOSAIC_CARTOGRAM_GRAPH_H diff --git a/cartocrow/mosaic_cartogram/guiding_shape.cpp b/cartocrow/mosaic_cartogram/guiding_shape.cpp new file mode 100644 index 000000000..916707d04 --- /dev/null +++ b/cartocrow/mosaic_cartogram/guiding_shape.cpp @@ -0,0 +1,59 @@ +#include "guiding_shape.h" + +#include +#include + +#include "../core/centroid.h" + +namespace cartocrow::mosaic_cartogram { + +GuidingPair::GuidingPair(const LandRegion ®ion1, const LandRegion ®ion2) { + // internally, tiles have unit area + // here, we approximate tiles by circles, and those have radius sqrt(1/pi) + static constexpr double tileRadius = std::numbers::inv_sqrtpi_v; + + const Point centroid1 = centroid(region1.shape); + const Point centroid2 = centroid(region2.shape); + + const EllipseAtOrigin &guide1 = region1.guidingShape; + const EllipseAtOrigin &guide2 = region2.guidingShape; + + const double area1 = guide1.area(); + const double area2 = guide2.area(); + + + // slope of line through the centroids (TODO: what if x1 = x2?) + const double m = CGAL::to_double((centroid1.y() - centroid2.y()) / (centroid1.x() - centroid2.x())); + + // Δx per unit of distance between the centroids + const double dx = 1 / std::sqrt(1 + m*m); + + // -1 if `region1` lies left of `region2`, else +1 (w.r.t. their centroids) + const int direction = centroid1.x() < centroid2.x() ? -1 : +1; + + const double dx1 = dx * (guide1.radius(m) - tileRadius) * direction; + const double dx2 = dx * (guide2.radius(m) - tileRadius) * -direction; + + // new (relative) centers for guiding shapes, equivalent to: + // moving them along y = m x such that they overlap the diameter of one tile w.r.t. this line + // TODO: yields undesirable results if guiding shapes are small compared to a tile + const Vector center1 = { dx1, m * dx1 }; + const Vector center2 = { dx2, m * dx2 }; + + // together, the guiding shapes should be centered around 0 + // so we add the opposite of their "joint" center (note: overlap counted twice) + const Vector correction = -(area1 * center1 + area2 * center2) / (area1 + area2); + + // apply translation + ellipse1 = guide1.translate(center1 + correction); + ellipse2 = guide2.translate(center2 + correction); +} + +std::pair GuidingPair::translate(const Vector &v) const { + return { + ellipse1.translate(v).normalizeSign(), + ellipse2.translate(v).normalizeSign() + }; +} + +} // namespace cartocrow::mosaic_cartogram diff --git a/cartocrow/mosaic_cartogram/guiding_shape.h b/cartocrow/mosaic_cartogram/guiding_shape.h new file mode 100644 index 000000000..f9dfcac3b --- /dev/null +++ b/cartocrow/mosaic_cartogram/guiding_shape.h @@ -0,0 +1,28 @@ +#ifndef CARTOCROW_MOSAIC_CARTOGRAM_GUIDING_SHAPE_H +#define CARTOCROW_MOSAIC_CARTOGRAM_GUIDING_SHAPE_H + +#include "../core/core.h" +#include "../core/ellipse.h" +#include "region.h" + +namespace cartocrow::mosaic_cartogram { + +/// A pair of guiding shapes for two adjacent land regions. +/// +/// To determine which tile should be transferred between two regions we use a cost function based +/// on guiding shapes. In particular, for two land regions, we use guiding pairs. These +/// are special, precomputed pairs of guiding shapes that have the correct relative position to each +/// other, based on the input map. Furthermore, their joint centroid is at zero, so they can be +/// easily translated to the joint centroid of the configurations in the tile map. +class GuidingPair { + public: + Ellipse ellipse1, ellipse2; + + GuidingPair(const LandRegion ®ion1, const LandRegion ®ion2); + + std::pair translate(const Vector &v) const; +}; + +} // namespace cartocrow::mosaic_cartogram + +#endif // CARTOCROW_MOSAIC_CARTOGRAM_GUIDING_SHAPE_H diff --git a/cartocrow/mosaic_cartogram/mosaic_cartogram.cpp b/cartocrow/mosaic_cartogram/mosaic_cartogram.cpp new file mode 100644 index 000000000..b3343dd8e --- /dev/null +++ b/cartocrow/mosaic_cartogram/mosaic_cartogram.cpp @@ -0,0 +1,332 @@ +#include "mosaic_cartogram.h" + +#include +#include +#include +#include +#include +#include +#include +#include +#include + +#include "../core/centroid.h" +#include "triangulation.h" + +namespace cartocrow::mosaic_cartogram { + +void MosaicCartogram::compute() { + validate(); + computeLandRegions(); + computeArrangement(); + computeDual(); + computeTileMap(); +} + +void MosaicCartogram::absorbMoldova() { + std::vector remove; + for (auto e : m_arrangement.edge_handles()) + if (e->face()->data() == "MDA" && e->twin()->face()->data() == "UKR" || e->face()->data() == "UKR" && e->twin()->face()->data() == "MDA") + remove.push_back(e); + for (auto e : remove) { + auto f = m_arrangement.remove_edge(e); + f->set_data("UKR"); // this is actually only necessary once + } + std::cerr << "[info] removed " << remove.size() << " edges to absorb MDA into UKR" << std::endl; + + // remove the corresponding land region as well (and then reassign indices) + m_landRegions.erase(m_landRegions.begin() + m_regionIndices.at("MDA")); + m_regionIndices.erase("MDA"); + int i = 0; + for (auto &r : m_landRegions) { + r.id = i++; + m_regionIndices[r._name] = r.id; + } + for (const auto &r : m_seaRegions) m_regionIndices[r.name()]--; +} + +PolygonWithHoles getShape(const RegionArrangement::Face_const_handle face) { + Polygon polygon; + const auto circ = face->outer_ccb(); + auto curr = circ; + int n = 0; + do { + const auto p = curr->source()->point(); + n++; + polygon.push_back(p); + } while (++curr != circ); + std::cout << n << std::endl; + return PolygonWithHoles(polygon); +} + +void MosaicCartogram::computeArrangement() { + // if sea regions were manually specified, read them now + if (m_parameters.manualSeas) { + for (const auto &[name, region] : *m_inputMap) { + if (name.starts_with("_sea")) { + std::vector> ps; + region.shape.polygons_with_holes(std::back_inserter(ps)); + + SeaRegion r; + r.id = parseIntAtEnd(name); + r.shape = ps[0]; + r.guidingShape = computeGuidingShape(r.shape); + m_seaRegions.push_back(r); + + assert(r.name() == name); + m_regionIndices.insert({ name, r.id + m_landRegions.size() }); + } + } + + } + + // construct arrangement from processed regions + RegionMap map; + for (const auto &r : m_landRegions) map.insert({ r._name, r.basic() }); + for (const auto &p : *m_inputMap) + if (p.first.starts_with('_')) + map.insert(p); + m_arrangement = regionMapToArrangement(map); + + // if sea regions were not manually specified, generate them now + if (!m_parameters.manualSeas) { + // ensure that all salient points exactly equal one vertex point + // this is necessary since the input map may contain "rounding errors" + for (auto pit = m_salientPoints.begin(); pit != m_salientPoints.end(); ++pit) { + const Point *nearest = nullptr; + Number nearestDistance; + + for (const auto vit : m_arrangement.vertex_handles()) { + const Point &q = vit->point(); + const Number d = CGAL::squared_distance(*pit, q); + if (!nearest || d < nearestDistance) nearest = &q, nearestDistance = d; + } + + *pit = *nearest; + } + + // add sea regions such that dual is triangular + triangulate(m_arrangement, m_salientPoints); + + // extract sea regions from new faces + for (const RegionArrangement::Face_const_handle fit : m_arrangement.face_handles()) { + const std::string &name = fit->data(); + if (name.starts_with("_sea")) { + SeaRegion r; + r.id = parseIntAtEnd(name); + r.shape = getShape(fit); + r.guidingShape = computeGuidingShape(r.shape); + m_seaRegions.push_back(r); + m_regionIndices.insert({ name, r.id + m_landRegions.size() }); + } + } + } + + // (temp) solve Europe-specific problem + absorbMoldova(); + + // add indices for three outer sea regions + const int i = m_landRegions.size() + m_seaRegions.size(); + m_regionIndices.insert({ "_outer0", i }); + m_regionIndices.insert({ "_outer1", i+1 }); + m_regionIndices.insert({ "_outer2", i+2 }); +} + +void MosaicCartogram::computeDual() { + m_dual = UndirectedGraph(getNumberOfRegions()); + for (const auto fit : m_arrangement.face_handles()) { + if (fit->is_unbounded()) continue; // all other faces (should) have a label + + // get region index corresponding to face + const std::string &vName = fit->data(); + const int v = m_regionIndices[vName]; + + auto circ = fit->outer_ccb(); + + // for the three outer sea regions, start at the unbounded face + if (vName.starts_with("_outer")) + while (!circ->twin()->face()->is_unbounded()) + ++circ; + + // walk along boundary to find adjacent regions + auto curr = circ; + std::vector adj; + do { + const std::string &uName = curr->twin()->face()->data(); + if (uName.empty()) continue; + const int u = m_regionIndices[uName]; + if (std::find(adj.begin(), adj.end(), u) == adj.end()) adj.push_back(u); + } while (--curr != circ); // in reverse order (so clockwise) + + // add adjacencies to dual + m_dual.setAdjacenciesUnsafe(v, adj); + } +} + +void MosaicCartogram::computeLandRegions() { + // POD for internal use + struct Part { + const PolygonWithHoles *shape; // pointer to avoid copies (has no ownership!) + Number area; + Number value; + int tiles; + }; + + for (const auto &[name, region] : *m_inputMap) { + if (name[0] == '_') continue; // skip sea regions (if they were defined manually) + + const Number value = m_dataValues.at(name); // already validated + int tiles = getTileCount(value); + if (!tiles) { + // TODO: how to handle? + std::cerr << "[warning] " << name << " is too small\n"; + } + + std::vector> polygons; + region.shape.polygons_with_holes(std::back_inserter(polygons)); + + // simple case: the region is contiguous + if (polygons.size() == 1) { + const auto &p = polygons[0]; + LandRegion r; + r._name = name; + r._color = region.color; + r.dataValue = value; + r.targetTileCount = tiles; + r.shape = p; + r.guidingShape = computeGuidingShape(p, tiles); + m_landRegions.push_back(std::move(r)); + continue; + } + + // compute area of each part + std::vector parts; + Number totalArea = 0; + for (const auto &p : polygons) { + const auto a = area(p); + parts.push_back({ &p, a }); + totalArea += a; + } + + // sort parts from largest to smallest area + std::sort(parts.begin(), parts.end(), [](const auto &p1, const auto &p2) { + return p1.area > p2.area; + }); + + // allocate tiles + // TODO: improve, like e.g. seats are assigned in parliament + for (auto &p : parts) { + p.value = CGAL::to_double(p.area / totalArea * value); + const int n = std::min(getTileCount(p.value), tiles); + p.tiles = n; + tiles -= n; + } + parts[0].tiles += tiles; // assign any remaining tiles to the largest part + + int i = 0; + for (const auto &p : parts) { + if (!p.tiles) { + // TODO: redistribute remaining value? + // TODO: how to handle holes? (if they're not adjacent to sea) + std::cerr << "[warning] " << parts.size() - i << " subregion(s) of " << name + << " are too small and have been removed\n"; + break; + } + LandRegion r; + r._name = name + '_' + std::to_string(i++); + r.superName = name; + r._color = region.color; + r.dataValue = p.value; + r.targetTileCount = p.tiles; + r.shape = *p.shape; + r.guidingShape = computeGuidingShape(*p.shape, p.tiles); + m_landRegions.push_back(std::move(r)); + } + } + std::cerr << std::flush; + + // sort land regions by name and assign indices in that order + std::sort(m_landRegions.begin(), m_landRegions.end(), [](const auto &r1, const auto &r2) { + return r1._name < r2._name; + }); + int i = 0; + for (auto &r : m_landRegions) { + r.id = i++; + m_regionIndices.insert({ r._name, r.id }); + } +} + +void MosaicCartogram::computeTileMap() { + std::vector> centroids(getNumberOfRegions()); + for (const auto f : m_arrangement.face_handles()) { + const std::string label = f->data(); + if (!label.empty()) centroids[m_regionIndices[label]] = centroid(f); + } + + VisibilityDrawing vd( + m_dual, + m_regionIndices["_outer0"], + m_regionIndices["_outer1"], + m_regionIndices["_outer2"], + centroids + ); + + m_tileMap = HexagonalMap(vd, m_landRegions, m_seaRegions); +} + +void MosaicCartogram::validate() const { + if (m_parameters.manualSeas != m_salientPoints.empty()) { + throw std::logic_error("There must be no salient points if and only if manual seas are specified"); + } + + // validate region names and data values + for (const auto &[name, region] : *m_inputMap) { + if (name.empty()) { + throw std::logic_error("Region names cannot be empty"); + } + if (name.find('_', m_parameters.manualSeas ? 1 : 0) != std::string::npos) { + throw std::logic_error("The region name '" + name + "' contains illegal underscores"); + } + if (name[0] == '_') { + if (!name.starts_with("_sea") && !name.starts_with("_outer")) { // TODO: also validate numbering (format and missing values) + throw std::logic_error("The region name '" + name + "' is illegal; the only legal special names are '_sea' and '_outer'"); + } + if (m_dataValues.contains(name)) { + throw std::logic_error("A data value is specified for region '" + name + "', but sea regions may not have a value"); + } + std::vector> ps; + region.shape.polygons_with_holes(std::back_inserter(ps)); + if (ps.size() != 1 || ps[0].has_holes()) { + throw std::logic_error("Region '" + name + "' must consist of one polygon without holes"); + } + } else { + if (!m_dataValues.contains(name)) { + throw std::logic_error("No data value is specified for region '" + name + "'"); + } + const double v = m_dataValues.at(name); + if (!std::isfinite(v) || v < 0) { + throw std::logic_error("Region '" + name + "' has an illegal data value; it must be non-negative"); + } + } + } + + // report on any ignored data + std::vector ignored; + for (const auto &[name, region] : m_dataValues) + if (!m_inputMap->contains(name)) + ignored.push_back(name); + if (!ignored.empty()) { + std::sort(ignored.begin(), ignored.end()); + std::cerr << "[warning] For the following regions, data was provided, but they are not on the map:"; + for (const auto &s : ignored) std::cerr << ' ' << s << ','; + std::cerr << "\b " << std::endl; + } +} + +int MosaicCartogram::parseIntAtEnd(const std::string &s) { + int n = 0, i = 1; + for (auto c = s.rbegin(); std::isdigit(*c); ++c) n += i * (*c - '0'), i *= 10; + return n; +} + +} // namespace cartocrow::mosaic_cartogram diff --git a/cartocrow/mosaic_cartogram/mosaic_cartogram.h b/cartocrow/mosaic_cartogram/mosaic_cartogram.h new file mode 100644 index 000000000..cdb8a999c --- /dev/null +++ b/cartocrow/mosaic_cartogram/mosaic_cartogram.h @@ -0,0 +1,112 @@ +#ifndef CARTOCROW_MOSAIC_CARTOGRAM_MOSAIC_CARTOGRAM_H +#define CARTOCROW_MOSAIC_CARTOGRAM_MOSAIC_CARTOGRAM_H + +#include +#include +#include +#include +#include + +#include "../core/core.h" +#include "../core/ellipse.h" +#include "../core/region_arrangement.h" +#include "../core/region_map.h" +#include "graph.h" +#include "parameters.h" +#include "region.h" +#include "tile_map.h" + +namespace cartocrow::mosaic_cartogram { + +/// The entrypoint for computing mosaic cartograms. +/// First, we transform the input map into a set of contiguous land regions, each with a desired +/// number of tiles (\ref computeLandRegions). +/// Next, we add sea regions, either manually from the input map, or computed using a straight +/// skeleton (\ref computeArrangement). +/// Then, we compute the dual of the processed regions, where nodes corresponds to regions and edges +/// to adjacencies (\ref computeDual). +/// Finally, we compute a \ref VisibilityDrawing that will serve as an initial tile map +/// (\ref computeTileMap). Computation then carries on in \ref HexagonalMap. +class MosaicCartogram { + friend class Painting; + + public: + /// Constructs a mosaic cartogram with the given regions. + /// + /// This does not compute the mosaic cartogram: use \ref compute() to run + /// the computation. Modifying the RegionMap passed here after the mosaic + /// cartogram has been constructed results in undefined behavior. + MosaicCartogram( + std::shared_ptr map, + std::unordered_map> &&dataValues, + std::vector> &&salientPoints // (temp) should be computed automatically from the input map + ) : m_inputMap(map), + m_dataValues(std::move(dataValues)), + m_salientPoints(std::move(salientPoints)) {} + + void compute(); + Parameters& parameters() { return m_parameters; } + + private: + Parameters m_parameters; + const std::shared_ptr m_inputMap; + /// A mapping from region names (in the input map) to the corresponding user-supplied values. + /// After \ref computeLandRegions(), these raw values should not be used anymore. + const std::unordered_map> m_dataValues; + /// The points (vertices of land regions) that control the creation of sea regions. + std::vector> m_salientPoints; + + std::vector m_landRegions; + std::vector m_seaRegions; // excluding the three outer regions + /// Maps region names to the corresponding indices. + std::unordered_map m_regionIndices; + + RegionArrangement m_arrangement; + UndirectedGraph m_dual; + HexagonalMap m_tileMap; + + int getTileCount(double value) const { + return std::round(value / m_parameters.unitValue); + } + /// Fits ellipse to (the boundary of) the given \c polygon, translates it to the origin, scales + /// it to size \c tileCount, and normalizes the contours. + template + EllipseAtOrigin computeGuidingShape(const PolygonWithHoles &polygon, int tileCount = 1) const { + // internally, we define tiles to have unit area + return Ellipse::fit(polygon.outer_boundary()) + .translateToOrigin() + .scaleTo(tileCount) + .normalizeContours(); + } + + int getNumberOfRegions() const { + return m_regionIndices.size(); // == m_landRegions.size() + m_seaRegions.size() + 3 + } + + /// Step 0. Check parameters, region names, and region data. + void validate() const; + /// Step 1. Transforms \c m_inputMap to \c m_landRegions such that each region is contiguous, + /// i.e., consists of one polygon (possibly with holes). All properties of each land region are + /// set, except \c neighbors, which is computed during step 3. + void computeLandRegions(); + /// Step 2. Construct arrangement from the contiguous regions, and create sea regions such that + /// the dual is triangular. + void computeArrangement(); + /// Step 3. Create a vertex for each face in the arrangement and connect two vertices if the + /// corresponding faces are adjacent. + void computeDual(); + /// Step 4. Compute an initial tile map using a visibility diagram and continue computation in + /// \ref HexagonalMap using a flow-based algorithm. + void computeTileMap(); + + /// (temp) Fixes the only internal problem in Europe, i.e., Moldova having degree 2. This is + /// achieved by absorbing Moldova into Ukraine at the end of step 2. It should be replaced by a + /// generalized solution. + void absorbMoldova(); + + static int parseIntAtEnd(const std::string &s); +}; + +} // namespace cartocrow::mosaic_cartogram + +#endif //CARTOCROW_MOSAIC_CARTOGRAM_MOSAIC_CARTOGRAM_H diff --git a/cartocrow/mosaic_cartogram/orderly_spanning_tree.cpp b/cartocrow/mosaic_cartogram/orderly_spanning_tree.cpp new file mode 100644 index 000000000..ef591a3fb --- /dev/null +++ b/cartocrow/mosaic_cartogram/orderly_spanning_tree.cpp @@ -0,0 +1,97 @@ +#include "orderly_spanning_tree.h" + +#include +#include + +namespace cartocrow::mosaic_cartogram { + +OrderlySpanningTree::OrderlySpanningTree(const UndirectedGraph &g, int r1, int r2, int r3, const std::vector> &positions) + : m_graph(g), m_root1(r1), m_root2(r2), m_root3(r3), m_positions(positions), m_gc(g), + m_parent(g.getNumberOfVertices(), r1), m_tree(g.getNumberOfVertices()), + m_treePreordering(g.getNumberOfVertices()) { + // TODO: assert that `g` is not too small, connected, triangular, etc. + contract(g.getNumberOfVertices()); + buildTree(r1); +} + +std::vector OrderlySpanningTree::getVerticesInOrder() const { + std::vector vs(m_graph.getNumberOfVertices()); + std::iota(vs.begin(), vs.end(), 0); // fill `vs` with 0, .., n-1 + std::sort(vs.begin(), vs.end(), [&](int u, int v) { + return m_treePreordering[u] < m_treePreordering[v]; + }); + return vs; +} + +void OrderlySpanningTree::contract(const int n) { + if (n <= 3) return; // only the roots remain, so there's no contractible edge => done + + // 1. Find (the best) contractible edge (from `m_root1` to `target`) + // TODO: is it more efficient to precompute an expansion sequence using a *canonical ordering*? (see Schnyder 1990, section 8) + int target = -1; + for (int v : m_gc.getNeighbors(m_root1)) { + // we consider all non-root neighbors of `m_root1` that share exactly two neighbors with it + if (v != m_root2 && v != m_root3 && m_gc.getNumberOfCommonNeighbors(m_root1, v) == 2) { + // among all candidates, choose the topmost ("the contraction heuristic") + if (target == -1 || m_positions[v].y() > m_positions[target].y()) { + target = v; + } + } + } + + // 2. Contract the edge by: + // • removing all edges incident to `target` (which effectively removes `target` from the graph) + // • for each removed edge `(target, v)`, adding a new edge `(m_root1, v)` if it did not exist before + std::vector newNeighbors; // of `m_root1` + for (int v : m_gc.getNeighbors(target)) + if (m_gc.addEdge(m_root1, v)) + newNeighbors.push_back(v); + m_gc.isolate(target); // after the loop to prevent concurrent modification + + // 3. Contract the remaining edges + contract(n - 1); + + // 4. Assign parents to construct the "next" part of the red spanning tree + // Note that this occurs post-order, i.e., we process the "expansions" + for (int v : newNeighbors) m_parent[v] = target; +} + +int OrderlySpanningTree::buildTree(const int v, int label) { + m_treePreordering[v] = label++; + + const auto &neighbors = m_graph.getNeighbors(v); // not empty + const int parent = m_parent[v]; + + const int n = neighbors.size(); + int iEnd = n - 1; + + if (parent != v) { + // below, we want to start after the parent + // such that the child at index 0 will be the first child after the parent + while (neighbors[iEnd] != parent) iEnd--; + } else { + // if `v` is the root, we mustn't skip the first neighbor + buildTreeRecur(v, neighbors[iEnd], label); + } + + // recur for each child + // `neighbors` is (assumed to be) in clockwise order, but we want to label vertices left to right, so we iterate in reverse order + int i = iEnd; + while (true) { + i = (i-1 + n) % n; + if (i == iEnd) break; + buildTreeRecur(v, neighbors[i], label); + } + + return label; +} + +void OrderlySpanningTree::buildTreeRecur(const int v, const int neighbor, int &label) { + // if `neighbor` is child of `v`, then add edge to `m_tree` and recur (to find children of `neighbor`) + if (v == m_parent[neighbor]) { + m_tree.addEdgeUnsafe(v, neighbor); + label = buildTree(neighbor, label); + } +} + +} // namespace cartocrow::mosaic_cartogram diff --git a/cartocrow/mosaic_cartogram/orderly_spanning_tree.h b/cartocrow/mosaic_cartogram/orderly_spanning_tree.h new file mode 100644 index 000000000..48a2987a2 --- /dev/null +++ b/cartocrow/mosaic_cartogram/orderly_spanning_tree.h @@ -0,0 +1,66 @@ +#ifndef CARTOCROW_MOSAIC_CARTOGRAM_OST_H +#define CARTOCROW_MOSAIC_CARTOGRAM_OST_H + +#include + +#include "../core/core.h" +#include "graph.h" + +namespace cartocrow::mosaic_cartogram { + +/// A class that computes and represents an orderly spanning tree. It uses the algorithm described +/// by Schnyder (1990) in sections 4 and 8. +class OrderlySpanningTree { + public: + /// Creates an OST for the given graph, which must be connected and triangular (i.e., maximal + /// planar). The three vertices on the outer boundary must also be specified, as well as the + /// geometric position of each vertex (which is only used for the contraction heuristic). + OrderlySpanningTree(const UndirectedGraph &g, int r1, int r2, int r3, const std::vector> &positions); + + int getNumberOfVertices() const { return m_graph.getNumberOfVertices(); } + + int getRoot() const { return m_root1; } + + /// Returns the parent of the given vertex w.r.t. the OST. A vertex is its own parent if and + /// only if it's the root. + int getParent(int v) const { return m_parent[v]; } + + /// Returns the children of the given vertex w.r.t. the OST. They have the same order as in the + /// original graph. + const std::vector& getChildren(int v) const { return m_tree.getNeighbors(v); } + + /// Returns the index of the given vertex w.r.t. the counterclockwise preordering of the OST. + int getLabel(int v) const { return m_treePreordering[v]; } + + /// Returns the list of vertices sorted by their label. + std::vector getVerticesInOrder() const; + + private: + const UndirectedGraph m_graph; + const int m_root1, m_root2, m_root3; // .. of the red, blue, and green trees + const std::vector> &m_positions; + + /// The contracted graph, only used for computation. + UndirectedGraph m_gc; + + /// This array defines the red tree: it specifies for each vertex its parent. Note that we are + /// not interested in the blue or green tree. + /// At initialization, it's filled with \c m_root1. In \c contract, we only update the array for + /// vertices that have a different parent. + std::vector m_parent; + + /// This graph is a more convenient specification of the red tree, computed after \c m_parent. + Graph m_tree; + + /// Counterclockwise preordering of \c m_tree. + std::vector m_treePreordering; + + void contract(const int n); + + int buildTree(const int v, int label = 0); + void buildTreeRecur(const int v, const int neighbor, int &label); +}; + +} // namespace cartocrow::mosaic_cartogram + +#endif //CARTOCROW_MOSAIC_CARTOGRAM_OST_H diff --git a/cartocrow/mosaic_cartogram/painting.cpp b/cartocrow/mosaic_cartogram/painting.cpp new file mode 100644 index 000000000..13c5aa165 --- /dev/null +++ b/cartocrow/mosaic_cartogram/painting.cpp @@ -0,0 +1,183 @@ +#include "painting.h" + +#include +#include +#include +#include +#include +#include +#include + +namespace cartocrow::mosaic_cartogram { + +void Painting::Options::validate() const { + if (tileArea <= 0) { + throw std::invalid_argument("`tileArea` must be positive"); + } +} + +Painting::Painting(std::shared_ptr mosaicCartogram, Options &&options) + : m_mosaicCartogram(mosaicCartogram), m_options(options), + tileScale(std::sqrt(m_options.tileArea)) { + for (int i = -1; i < 5; i++) { // such that right edge is first + const auto a = (1 + 2*i) * std::numbers::pi / 6; + tileShape.push_back({ + tileScale * HexagonalMap::tileExradius * std::cos(a), + tileScale * HexagonalMap::tileExradius * std::sin(a) + }); + } +} + +void Painting::paint(Renderer &renderer) const { + renderer.pushStyle(); + + paintMap(renderer, std::bind(&Painting::getColorDefault, this, std::placeholders::_1)); + + /* + for (const auto &config : map().configurations) + for (const auto c : config.boundary) + paintMark(renderer, c); + */ + + renderer.popStyle(); // restore style +} + +Point Painting::getCentroid(Coordinate c) const { + return CGAL::ORIGIN + tileScale * (HexagonalMap::getCentroid(c) - CGAL::ORIGIN); +} + +Polygon Painting::getTile(const Coordinate c) const { + // https://stackoverflow.com/a/45452642 + CGAL::Aff_transformation_2 t(CGAL::TRANSLATION, getCentroid(c) - CGAL::ORIGIN); + return CGAL::transform(t, tileShape); +} + +Color Painting::getColorDefault(Coordinate c) const { + const auto config = map().getConfiguration(c); + return config ? config->region->color() : Color{255, 255, 255}; +} + +Color Painting::getColorUniform(Coordinate c) const { + const auto config = map().getConfiguration(c); + return !config || config->isSea() ? m_options.colorSea : m_options.colorLand; +} + +void Painting::paintMark(Renderer &renderer, Coordinate c) const { + const Point p = getCentroid(c); + const Number x = p.x(), y = p.y(); + const Number w = tileScale / 5; + + renderer.setMode(Renderer::stroke); + renderer.setStroke(m_options.colorBorder, w); + + renderer.draw(Segment(Point(x-w, y-w), Point(x+w, y+w))); + renderer.draw(Segment(Point(x-w, y+w), Point(x+w, y-w))); +} + +void Painting::paintBorders(Renderer &renderer, const Configuration &config) const { + for (const Coordinate c0 : config) { + const auto tile = getTile(c0); + auto edge = tile.edges_begin(); + for (const Coordinate c1 : c0.neighbors()) { // edges are in same order as neighbors! + if (!config.contains(c1)) renderer.draw(*edge); + ++edge; + } + } +} + +void Painting::paintMap(Renderer &renderer, ColorFunction tileColor) const { + // draw tiles + renderer.setMode(Renderer::fill | Renderer::stroke); + renderer.setStroke(m_options.colorBorder, tileScale / 10); + for (const auto &config : map().configurations) { + for (const Coordinate c : config) { + renderer.setFill(tileColor(c)); + renderer.draw(getTile(c)); + } + } + + // optionally, draw borders between regions + if (m_options.drawBorders) { + renderer.setStroke(m_options.colorBorder, tileScale / 4); + for (const auto &config : map().configurations) paintBorders(renderer, config); + } +} + +void Painting::paintGuidingPair(Renderer &renderer, const std::string &sourceName, const std::string &targetName) const { + const auto &source = map().configurations[m_mosaicCartogram->m_regionIndices.at(sourceName)]; + const auto &target = map().configurations[m_mosaicCartogram->m_regionIndices.at(targetName)]; + + auto [guideSource, guideTarget] = map().getGuidingShapes(source, target); + guideSource = guideSource.stretch(1 / tileScale); + guideTarget = guideTarget.stretch(1 / tileScale); + + auto transfers = map().computeAllTransfers(source, target); + std::sort(transfers.begin(), transfers.end()); // best is first + + // normalize all costs to [0.5, 1.5] + HexagonalMap::CoordinateMap costs; + double minCost = 1e10, + maxCost = -1e10; + for (const auto &t : transfers) { + minCost = std::min(minCost, t.cost); + maxCost = std::max(maxCost, t.cost); + } + for (const auto &t : transfers) { + costs.insert({ t.tile, 1.5 - (t.cost - minCost) / (maxCost - minCost) }); + } + + paintMap(renderer, [&](const Coordinate c) { + if (costs.contains(c)) + return Color{255, 140, 0}.shaded(costs[c]); // dark orange + else if (source.contains(c)) + return m_options.colorLand.shaded(.6); + else if (target.contains(c)) + return Color{50, 205, 50}; // lime green + else + return getColorUniform(c); + }); + + // draw mark to indicate best transfer + paintMark(renderer, transfers[0].tile); + + // draw guiding shapes + renderer.setMode(renderer::GeometryRenderer::stroke); + renderer.setStroke({139, 69, 19}, tileScale / 5); // saddle brown + renderer.draw(guideSource); + renderer.draw(guideTarget); +} + +void Painting::paintTransfers(Renderer &renderer) const { + renderer.setMode(renderer::GeometryRenderer::stroke); + renderer.setStroke({139, 69, 19}, tileScale / 5); // saddle brown + for (const auto [i, j] : map().configGraph.getEdges()) { + const auto &source = map().configurations[i]; + const auto &target = map().configurations[j]; + + const auto t = map().computeBestTransfer(source, target); + if (t) { + renderer.setStroke( + t->cost < 0 ? Color{0, 255, 0} : Color{255, 0, 0}, + std::sqrt(std::abs(t->cost)) / 10 + ); + + auto sourceCentroid = map().getCentroid(source) - CGAL::ORIGIN; + auto targetCentroid = map().getCentroid(target) - CGAL::ORIGIN; + + sourceCentroid *= tileScale; + targetCentroid *= tileScale; + + auto normal = targetCentroid - sourceCentroid; + normal = Vector(normal.y(), -normal.x()); + normal /= std::sqrt(normal.squared_length()); + normal *= 2; + + renderer.draw(Segment( + CGAL::ORIGIN + sourceCentroid + normal, + CGAL::ORIGIN + targetCentroid + normal + )); + } + } +} + +} // namespace cartocrow::mosaic_cartogram diff --git a/cartocrow/mosaic_cartogram/painting.h b/cartocrow/mosaic_cartogram/painting.h new file mode 100644 index 000000000..fe444b8aa --- /dev/null +++ b/cartocrow/mosaic_cartogram/painting.h @@ -0,0 +1,88 @@ +#ifndef CARTOCROW_MOSAIC_CARTOGRAM_PAINTING +#define CARTOCROW_MOSAIC_CARTOGRAM_PAINTING + +#include +#include + +#include "../core/core.h" +#include "../renderer/geometry_painting.h" +#include "../renderer/geometry_renderer.h" +#include "mosaic_cartogram.h" +#include "tile_map.h" + +namespace cartocrow::mosaic_cartogram { + +/// The \ref renderer::GeometryPainting "GeometryPainting" for a \ref MosaicCartogram. +class Painting : public renderer::GeometryPainting { + + // TODO: generalize to also support square tiles + + using Configuration = HexagonalMap::Configuration; + using Coordinate = HexagonalMap::Coordinate; + using Renderer = renderer::GeometryRenderer; + + public: + /// Options that determine what to draw in the painting and how. + struct Options { + + Color colorBorder = { 32, 32, 32 }; + Color colorLand = { 34, 139, 34 }; // forest green + Color colorSea = { 175, 238, 238 }; // pale turquoise + + /// Whether to draw borders between regions with thicker lines. This parameter is optional + /// and \c false by default. + bool drawBorders; + + /// The area of one tile. This essentially controls the scale of the painting (compared to + /// the internal representation, which uses unit areas). + Number tileArea; + + /// Checks whether the parameters are valid. If not, an exception is thrown. + void validate() const; + + }; + + private: + /// A function that maps a tile coordinate to a color. Used as a parameter for painting, so + /// different "views" can be drawn with the same function. + using ColorFunction = std::function; + + std::shared_ptr m_mosaicCartogram; + Options m_options; + + /// The factor with which to scale (the inradius and exradius of) the unit hexagon to attain the + /// user-supplied area. + Number tileScale; + /// The hexagon used for painting. Its centroid is at the origin. + Polygon tileShape; + + public: + Painting(std::shared_ptr mosaicCartogram, Options &&options); + + void paint(Renderer &renderer) const override; + + private: + const HexagonalMap& map() const { return m_mosaicCartogram->m_tileMap; } + + Point getCentroid(Coordinate c) const; + Polygon getTile(Coordinate c) const; + + // implementations of `ColorFunction` + Color getColorDefault(Coordinate c) const; + Color getColorUniform(Coordinate c) const; + + void paintMark(Renderer &renderer, Coordinate c) const; + void paintBorders(Renderer &renderer, const Configuration &config) const; + + void paintMap(Renderer &renderer, ColorFunction tileColor) const; + + /// Debug function to visualize the cost computation between two regions. + void paintGuidingPair(Renderer &renderer, const std::string &sourceName, const std::string &targetName) const; + + void paintTransfers(Renderer &renderer) const; + +}; + +} // namespace cartocrow::mosaic_cartogram + +#endif //CARTOCROW_MOSAIC_CARTOGRAM_PAINTING diff --git a/cartocrow/mosaic_cartogram/parameters.h b/cartocrow/mosaic_cartogram/parameters.h new file mode 100644 index 000000000..40bf2592c --- /dev/null +++ b/cartocrow/mosaic_cartogram/parameters.h @@ -0,0 +1,31 @@ +#ifndef CARTOCROW_MOSAIC_CARTOGRAM_PARAMETERS_H +#define CARTOCROW_MOSAIC_CARTOGRAM_PARAMETERS_H + +#include + +#include "../core/core.h" + +namespace cartocrow::mosaic_cartogram { + +/// The parameters used for computing the mosaic cartogram. +struct Parameters { + + /// Whether the sea and outer regions have already been added to the input map. This parameter + /// is optional and \c false by default. + bool manualSeas; + + /// The value represented by one tile. This parameter is required. + Number unitValue; + + /// Checks whether the parameters are valid. If not, an exception is thrown. + void validate() const { + if (unitValue <= 0) { + throw std::invalid_argument("`unitValue` must be positive (Did you forget to specify it?)"); + } + } + +}; + +} // namespace cartocrow::mosaic_cartogram + +#endif //CARTOCROW_MOSAIC_CARTOGRAM_PARAMETERS_H diff --git a/cartocrow/mosaic_cartogram/region.h b/cartocrow/mosaic_cartogram/region.h new file mode 100644 index 000000000..d58c72275 --- /dev/null +++ b/cartocrow/mosaic_cartogram/region.h @@ -0,0 +1,77 @@ +#ifndef CARTOCROW_MOSAIC_CARTOGRAM_REGION_H +#define CARTOCROW_MOSAIC_CARTOGRAM_REGION_H + +#include +#include + +#include "../core/core.h" +#include "../core/ellipse.h" +#include "../core/region_map.h" + +namespace cartocrow::mosaic_cartogram { + +enum class RegionType : bool { + /// Regions with a data value (and hence a target tile count). + Land, + /// Regions without a data value (which, hence, are flexible in size). + Sea +}; + +/// A contiguous region in a mosaic cartogram. +struct MosaicRegion { + /// The non-negative integer identifying this region. Identifiers are unique among regions of + /// the same type, and there are no gaps. + int id; + /// The shape of this region as specified by the input map. + PolygonWithHoles shape; + /// An approximation of the desired final shape of this region. It is centered at the origin, + /// scaled according to the desired number of tiles, and its contour lines are normalized such + /// that the additional area is equal to one tile. + EllipseAtOrigin guidingShape; + + /// The color of this region as specified by the input map, or white for sea regions. This is + /// only used for visualization. Note that all subregions have the same color. + virtual Color color() const = 0; + virtual std::string name() const = 0; + virtual RegionType type() const = 0; + + /// Returns the corresponding \c Region. + Region basic() const { + return { name(), color(), PolygonSet(shape) }; + } +}; + +/// A contiguous land region in a mosaic cartogram. +/// Note that the input map may contain non-contiguous regions. These "superregions" are partitioned +/// into "subregions", which are henceforth processed separately. The data value of the superregion +/// is split among the subregions by area. +struct LandRegion : public MosaicRegion { + std::string _name; + /// The superregion's name, if this region has one. In that case, the region's name has the + /// following format: "_". + std::optional superName; + Color _color; + /// The data value of this region. + Number dataValue; + /// The desired number of tiles to represent this region. This is computed from the data value + /// and unit value. + int targetTileCount; + + Color color() const override { return _color; } + std::string name() const override { return _name; } + RegionType type() const override { return RegionType::Land; } +}; + +/// A contiguous sea region in a mosaic cartogram. +struct SeaRegion : public MosaicRegion { + // TODO: add "original tile count" field? based on area of `shape` and avg. tile density of land regions + // could be used to finetune tile maps + + Color color() const override { return { 255, 255, 255 }; } + std::string name() const override { return "_sea" + std::to_string(id); } + RegionType type() const override { return RegionType::Sea; } +}; + +} // namespace cartocrow::mosaic_cartogram + +#endif //CARTOCROW_MOSAIC_CARTOGRAM_REGION_H diff --git a/cartocrow/mosaic_cartogram/tile_map.cpp b/cartocrow/mosaic_cartogram/tile_map.cpp new file mode 100644 index 000000000..7d05eb316 --- /dev/null +++ b/cartocrow/mosaic_cartogram/tile_map.cpp @@ -0,0 +1,527 @@ +#include "tile_map.h" + +#include +#include +#include +#include +#include +#include +#include +#include +#include + +#include "edmonds_optimum_branching.hpp" + +namespace cartocrow::mosaic_cartogram { + +std::array HexagonalMap::Coordinate::neighbors() const { + // we must use double outer braces to indicate that the inner braces initialize a Coordinate + return {{ + { m_x + 1, m_y + 0 }, + { m_x + 1, m_y + 1 }, + { m_x + 0, m_y + 1 }, + { m_x - 1, m_y + 0 }, + { m_x - 1, m_y - 1 }, + { m_x + 0, m_y - 1 } + }}; +} + +std::ostream& operator<<(std::ostream &os, HexagonalMap::Coordinate c) { + return os << '(' << c.m_x << ", " << c.m_y << ')'; +} + +bool HexagonalMap::Configuration::containsInInterior(const Coordinate c) const { + if (!contains(c)) return false; + for (const Coordinate d : c.neighbors()) + if (!contains(d)) + return false; + return true; +} + +bool HexagonalMap::Configuration::isAdjacent(const Coordinate c) const { + if (contains(c)) return false; + for (const Coordinate d : c.neighbors()) + if (boundary.contains(d)) + return true; + return false; +} + +bool HexagonalMap::Configuration::remainsContiguousWithout(const Coordinate c) const { + if (!contains(c)) return true; // no effect + if (!boundary.contains(c)) return false; // this would create a hole + + const auto neighbors = c.neighbors(); + + bool open = !contains(neighbors.back()); // check if already open (we count this opening later) + int openings = 0; + for (const Coordinate d : neighbors) { + if (contains(d)) { + open = false; + } else if (!open) { + open = true; + openings++; + } + } + + return openings <= 1; // otherwise the config would be split in twain (at least) + // if all neighbors are outside, we incorrectly find `openings == 0`, but this still yields the correct conclusion +} + +HexagonalMap::HexagonalMap(const VisibilityDrawing &initial, + const std::vector &landRegions, + const std::vector &seaRegions) + : guidingPairs(landRegions.size() - 1), + configurations(landRegions.size() + seaRegions.size()), + configGraph(configurations.size()) { + + // associate each configuration with corresponding region + for (const LandRegion &r : landRegions) configurations[r.id].region = &r; + for (const SeaRegion &r : seaRegions) configurations[r.id + landRegions.size()].region = &r; + + // initialize tiles of each configuration + const int w = initial.grid.size() - 2; // the left and right columns contain only outer sea regions, which are ignored + const int h = initial.grid[0].size() - 2; // the bottom and top rows ... + for (int x = 0; x < w; x++) { + for (int y = 0; y < h; y++) { + int i = initial.grid[x+1][h-y]; // vertical flip + if (i < configurations.size()) // don't add tiles for outer sea regions + configurations[i].tiles.insert({ x+y, y }); // convert grid coordinate to barycentric coordinate + } + } + + // initialize tile -> configuration mapping + for (int i = 0; i < configurations.size(); i++) { + configurations[i].index = i; + for (const Coordinate c : configurations[i]) tiles[c] = i; + } + + // compute boundary and neighbors of each configuration + for (Configuration &config : configurations) { + for (const Coordinate c0 : config) { + for (const Coordinate c1 : c0.neighbors()) { + const auto it = tiles.find(c1); + if (it == tiles.end()) { + // `c0` has an unassigned neighboring tile + config.boundary.insert(c0); + } else if (it->second != config.index) { + // `c0` has a neighboring tile in another config + config.boundary.insert(c0); + configGraph.addEdge(config.index, it->second); + } + } + } + } + + // determine which configurations are at the horizon + for (Configuration &config : configurations) { + config.atHorizon = false; + for (const Coordinate c0 : config.boundary) + for (const Coordinate c1 : c0.neighbors()) + if (!tiles.contains(c1)) { + config.atHorizon = true; + assert(config.isSea()); + goto next; + } + next: + ; + } + + // precompute all guiding pairs + for (const LandRegion &r1 : landRegions) { + for (const int i2 : configGraph.getNeighbors(r1.id)) { + if (r1.id > i2) continue; + const auto &c2 = configurations[i2]; + if (c2.isSea()) continue; + guidingPairs[r1.id].insert({ i2, GuidingPair(r1, c2.landRegion()) }); + } + } + + grow(10); + run(1000); +} + +Point HexagonalMap::getCentroid(const Coordinate c) { + return { + tileInradius * (2*c.x() - c.y()), + tileExradius * 3/2 * c.y() + }; +} + +Point HexagonalMap::getCentroid(const Configuration &config) { + Vector v(0, 0); + for (const Coordinate c : config) v += getCentroid(c) - CGAL::ORIGIN; + return CGAL::ORIGIN + v / config.size(); +} + +const HexagonalMap::Configuration* HexagonalMap::getConfiguration(const Coordinate c) const { + const auto it = tiles.find(c); + return it == tiles.end() ? nullptr : &configurations[it->second]; +} + +HexagonalMap::Configuration* HexagonalMap::getConfiguration(const Coordinate c) { + // since `this` is non-const, the following casts are safe + // https://stackoverflow.com/a/47369227 + return const_cast(std::as_const(*this).getConfiguration(c)); +} + +Ellipse HexagonalMap::getGuidingShape(const Configuration &config) const { + auto gs = config.region->guidingShape; + if (config.isSea()) gs = gs.scaleTo(config.size()); + return gs.translate(getCentroid(config) - CGAL::ORIGIN).normalizeSign(); +} + +std::pair HexagonalMap::getGuidingPair(const Configuration &c1, const Configuration &c2) const { + // compute centroid of union of configurations + const int size1 = c1.size(); + const int size2 = c2.size(); + const auto centroid = (size1 * (getCentroid(c1) - CGAL::ORIGIN) + + size2 * (getCentroid(c2) - CGAL::ORIGIN)) / (size1 + size2); + + int id1 = c1.index; + int id2 = c2.index; + if (id1 > id2) std::swap(id1, id2); + + // get precomputed guiding pair and translate to `centroid` + const auto p = guidingPairs[id1].at(id2).translate(centroid); + return id1 == c1.index ? p : std::make_pair(p.second, p.first); +} + +std::pair HexagonalMap::getGuidingShapes(const Configuration &c1, const Configuration &c2) const { + if (!configGraph.containsEdge(c1.index, c2.index)) + throw std::invalid_argument("A guiding pair only exists for two distinct, adjacent regions"); + + if (c1.isLand() && c2.isLand()) + return getGuidingPair(c1, c2); + else + return { getGuidingShape(c1), getGuidingShape(c2) }; +} + +/// Checks whether \c config1 is adjacent to \c config2 via tiles other than \c ignore (which is part of \c config1). +bool adjacent(const HexagonalMap::Configuration &config1, const HexagonalMap::Configuration &config2, const HexagonalMap::Coordinate ignore) { + for (const HexagonalMap::Coordinate c : config1.boundary) + if (c != ignore && config2.isAdjacent(c)) + return true; + return false; +} + +std::vector HexagonalMap::computeTransferCandidates(const Configuration &source, const Configuration &target) const { + if (source.index == target.index) + throw std::invalid_argument("Tiles cannot be transferred from a configuration to itself"); + + // the candidates must: + // 1. be part of `source` + // 2. be adjacent to `target` + // 3. not remove neighbors of `source` + // 4. not add neighbors to `target` + // 5. not break the contiguity of `source` + std::vector candidates; + + // ensure (1), (2), and (5) + for (const Coordinate &c : source.boundary) + if (target.isAdjacent(c) && source.remainsContiguousWithout(c)) + candidates.push_back(c); + + // ensure (4) + std::vector keep; + for (const Coordinate c0 : candidates) { + for (const Coordinate c1 : c0.neighbors()) { + const auto it = tiles.find(c1); + if (it == tiles.end()) continue; + const int neighborIndex = it->second; + if (neighborIndex == target.index) continue; + if (!configGraph.containsEdge(target.index, neighborIndex)) { + // if `c0` is transferred to `target`, there would be an illegal adjacency between `target` and `neighbor` + goto next4; + } + } + keep.push_back(c0); + next4: + ; + } + + // ensure (3) + candidates.clear(); + for (const Coordinate c : keep) { + for (const int neighborIndex : configGraph.getNeighbors(source.index)) + if (neighborIndex != target.index && !adjacent(source, configurations[neighborIndex], c)) + goto next3; // if `c` is removed from `source`, the adjacency between `source` and `neighbor` would break + candidates.push_back(c); + next3: + ; + } + + return candidates; +} + +std::vector HexagonalMap::computeAllTransfers(const Configuration &source, const Configuration &target) const { + const auto candidates = computeTransferCandidates(source, target); + if (candidates.empty()) return {}; + + std::vector transfers; + transfers.reserve(candidates.size()); + + // compute cost for each candidate + const auto [guideSource, guideTarget] = getGuidingShapes(source, target); + for (const Coordinate c : candidates) { + const Point p = getCentroid(c); + const double cost = guideTarget.evaluate(p) * (target.isSea() ? seaCostMultiplier : 1) + - guideSource.evaluate(p) / (source.isSea() ? seaCostMultiplier : 1); + transfers.emplace_back(c, target.index, cost); + } + + return transfers; +} + +std::optional HexagonalMap::computeBestTransfer(const Configuration &source, const Configuration &target) const { + const auto transfers = computeAllTransfers(source, target); + if (transfers.empty()) return std::nullopt; + + const Transfer *best = nullptr; + for (const Transfer &t : transfers) + if (!best || t.cost < best->cost) // minimize + best = &t; + + return *best; +} + +// https://github.com/atofigh/edmonds-alg/blob/master/doc/examples/sparse-example.cpp +std::vector HexagonalMap::computeBestTransferPath() const { + using BoostGraph = boost::adjacency_list>; + using Vertex = boost::graph_traits::vertex_descriptor; + using Edge = boost::graph_traits::edge_descriptor; + + const int n = configGraph.getNumberOfVertices(); + + // create (cost graph with) vertices + BoostGraph graph(n); + boost::property_map::type vertexIndices = get(boost::vertex_index, graph); + boost::property_map::type weights = get(boost::edge_weight, graph); + + // copy vertices to vector + std::vector vs; + copy(boost::make_iterator_range(vertices(graph)), std::back_inserter(vs)); + + // create edges (which are a subset of the configuration graph, and weighted by cost) + std::vector transfers(n, std::vector>(n)); + for (const auto [i, j] : configGraph.getEdges()) { + const auto t = computeBestTransfer(configurations[i], configurations[j]); + if (t) { + transfers[i][j] = t; + add_edge(vs[i], vs[j], t->cost, graph); + } + } + + // internal structure for paths of transfers + struct Path { + std::vector configs; + double cost; + + Path(const int source) : configs({ source }), cost(-1e10) {} // creates singleton + + int length() const { + return configs.size(); + } + bool operator<(const Path &p) const { + return length() <= p.length() && cost < p.cost; // whether `this` is "strictly better" than `p` + } + }; + + std::optional best; + for (int source = 0; source < n; source++) { + const auto &sourceConfig = configurations[source]; + + // if the configuration wants to grow, it cannot be a source + if (sourceConfig.isLand() && sourceConfig.desire() >= 0) continue; + + // using Edmonds' algorithm, compute minimum branching (a.k.a. spanning arborescence) with `source` as root + std::vector branching; + edmonds_optimum_branching( + graph, vertexIndices, weights, + vs.begin() + source, vs.begin() + source + 1, + std::back_inserter(branching) + ); + + // convert edge list to adjacency list + std::vector>> adj(n); + for (const auto &e : branching) { + adj[boost::source(e, graph)].push_back({ boost::target(e, graph), get(weights, e) }); + } + + // DFS to find the "minimum" path + std::vector queue { Path(source) }; + while (!queue.empty()) { + const Path p = queue.back(); + queue.pop_back(); + + // prune + if (best && p.length() >= best->length()) continue; + + for (const auto [target, cost] : adj[p.configs.back()]) { + Path q = p; + q.configs.push_back(target); + q.cost = std::max(q.cost, cost); + + const auto &targetConfig = configurations[target]; + if (targetConfig.isSea() || targetConfig.desire() > 0) + if (sourceConfig.isLand() || targetConfig.isLand()) // TODO: bad band-aid fix + if (!best || q < *best) + best = q; + + queue.push_back(q); + } + } + } + + // convert path into list of transfers, and return it + std::vector result; + if (best) { + for (int i = 1; i < best->configs.size(); i++) { + const int a = best->configs[i-1]; + const int b = best->configs[i]; + result.push_back(*transfers[a][b]); + } + } + return result; +} + +HexagonalMap::Configuration& HexagonalMap::getNearestAdjacent( + const Coordinate c0, + const std::unordered_map> ¢roids +) { + int nearest = -1; + double nearestDistance = 1e10; + + const auto p = getCentroid(c0); + for (const Coordinate c1 : c0.neighbors()) { + const auto it = tiles.find(c1); + if (it == tiles.end() || it->second == nearest) continue; + const auto d = (p - centroids.at(it->second)).squared_length(); + if (d < nearestDistance) nearest = it->second, nearestDistance = d; + } + + return configurations.at(nearest); +} + +void HexagonalMap::resetBoundary(Configuration &config) const { + config.boundary.clear(); + for (const Coordinate c0 : config.tiles) { + for (const Coordinate c1 : c0.neighbors()) { + const auto it = tiles.find(c1); + if (it == tiles.end() || it->second != config.index) { + config.boundary.insert(c0); + break; + } + } + } +} + +void HexagonalMap::grow(const int layers) { + std::unordered_map> centroids; + CoordinateMap distance; + std::queue queue; + + for (const Configuration &config : configurations) { + if (!config.atHorizon) continue; + centroids.insert({ config.index, getCentroid(config) }); + for (const Coordinate c0 : config.boundary) { + for (const Coordinate c1 : c0.neighbors()) { + if (distance.contains(c1)) continue; + const auto p = tiles.find(c1); + if (p == tiles.end() || p->second == config.index) continue; + distance[c1] = 0; + queue.push(c1); + } + } + } + + int added = 0; + while (!queue.empty()) { + const Coordinate c0 = queue.front(); queue.pop(); + const int d = distance[c0]; + for (const Coordinate c1 : c0.neighbors()) { + if (distance.contains(c1)) continue; // already visited + const auto p = tiles.find(c1); + if (p == tiles.end()) { + Configuration &config = getNearestAdjacent(c1, centroids); + config.tiles.insert(c1); + tiles[c1] = config.index; + added++; + } + if (p == tiles.end() || configurations[p->second].atHorizon) { + distance[c1] = d+1; + if (d+1 < layers) queue.push(c1); + } + } + } + + for (Configuration &config : configurations) + if (config.atHorizon) + resetBoundary(config); + + std::cerr << "[info] grew by " << added << " tiles" << std::endl; +} + +void HexagonalMap::perform(const Transfer &transfer) { + Configuration &source = configurations[tiles[transfer.tile]]; + Configuration &target = configurations[transfer.targetIndex]; + + tiles[transfer.tile] = target.index; + + source.tiles.erase(transfer.tile); + source.boundary.erase(transfer.tile); + + target.tiles.insert(transfer.tile); + target.boundary.insert(transfer.tile); + + // maintain boundary of source and target + for (const Coordinate c : transfer.tile.neighbors()) { + const auto it = tiles.find(c); + if (it == tiles.end()) continue; + if (it->second == source.index) { + source.boundary.insert(c); + } else if (it->second == target.index && target.containsInInterior(c)) { + target.boundary.erase(c); + } + } +} + +void HexagonalMap::perform(const std::vector &path) { + std::cout << "path of length " << path.size() + 1 << " : " + << configurations[tiles[path[0].tile]].label(); + for (const Transfer &transfer : path) { + perform(transfer); + std::cout << " -> " << configurations[transfer.targetIndex].label(); + } + std::cout << '\n'; +} + +void HexagonalMap::run(int iterations) { + // find and perform transfers + for (int i = 0; i < iterations; i++) { + const auto path = computeBestTransferPath(); + if (path.empty()) { + std::cout << "no more valid transfers!\n"; + break; + } + perform(path); + } + + // print list of regions with wrong size + std::vector> desires; + for (const Configuration &config : configurations) + if (config.isLand() && config.desire()) + desires.push_back({ config.desire(), config.label() }); + std::sort(desires.begin(), desires.end()); + std::cout << '\n'; + for (const auto &[desire, label] : desires) { + std::cout << std::setfill(' ') << std::setw(5) << std::left << label << " : " + << std::setw(4) << std::right << desire << '\n'; + } + std::cout << std::flush; +} + +} // namespace cartocrow::mosaic_cartogram diff --git a/cartocrow/mosaic_cartogram/tile_map.h b/cartocrow/mosaic_cartogram/tile_map.h new file mode 100644 index 000000000..477010551 --- /dev/null +++ b/cartocrow/mosaic_cartogram/tile_map.h @@ -0,0 +1,258 @@ +#ifndef CARTOCROW_MOSAIC_CARTOGRAM_MAP_H +#define CARTOCROW_MOSAIC_CARTOGRAM_MAP_H + +#include +#include +#include +#include +#include +#include +#include +#include +#include + +#include "../core/core.h" +#include "../core/ellipse.h" +#include "graph.h" +#include "guiding_shape.h" +#include "region.h" +#include "visibility_drawing.h" + +namespace cartocrow::mosaic_cartogram { + +// TODO: make base class and separate subclass SquareMap +// TODO: fix member visibilities and befriend Painting +// TODO: if there are not valid transfer paths, find a cycle instead + +/// A class that represents a tile map (in particular with hexagonal tiles; square tiles are TODO). +/// The main function \ref run() iteratively improves the map through augmenting paths. The +/// image below is the output when run on europe-population-mosaic-manual-sea.json. +/// +/// \section Problems +/// The implementation of the flow algorithm is a work-in-progress, and has several issues or +/// missing features. The main cause for issues is that, on the one hand, sea regions should have +/// few constraints to give land regions more flexibility and since they do not represent data, but +/// on the other hand, sea regions needs constraints to ensure the algorithm works properly. +/// - Since sea regions do not have a desired number of tiles, they tend to become "snakes" (e.g., +/// consider the English Channel below). Then, however, they do not allow transfers anymore, since +/// they would make the region discontiguous. Therefore, sea regions need to stay "fat". +/// - Two adjacent land regions use guiding pairs for their cost calculation, but sea regions simply +/// use guiding shapes centered at the region's centroid. As a result, the placement of islands +/// is not enforced in any way (e.g., consider Sicily below). +/// - If the cost graph (see \ref computeBestTransferPath) is disconnected, it seems the current +/// implementation of Edmonds' algorithm does not produce the transfers you'd expect (e.g., +/// consider Russia below). The exact reason for this is unknown and needs to be investigated. +/// Note in general that Edmonds' algorithm was not the preferred choice of approach, but a] +/// compromise, since finding minimum-length simple paths is NP-hard. +/// - Currently, if you allow transfer paths where both the source and target are sea regions, the +/// algorithm does not converge. +/// - In the end, when all regions have their desired number of tiles, resolving paths would worsen +/// the solution. However, cost-wise, you may still be able to improve the map. Therefore, you +/// should compute transfer cycles that maintain all tile counts, but improve shape, +/// position, etc. This has not been implemented. +/// +/// \image html mosaic-cartogram-europe.svg +class HexagonalMap { + public: + struct CoordinateHash; // forward declaration + + /// Sea regions, like land regions, also have guiding shapes, to prevent snaking. However, the + /// shape of land regions is much more important, so costs for sea regions are multiplied by + /// this constant. + static constexpr double seaCostMultiplier = 5; + + /// The radius of the inscribed circle of the unit hexagon (i.e., the largest circle that fits). + /// Also known as the apothem. + static constexpr Number tileInradius = 0.537284965911770959776669078352965289L; + /// The radius of the circumcircle of the unit hexagon (i.e., the circle that passes through all + /// six vertices). Also known as the circumradius, and equal to the side length. + static constexpr Number tileExradius = 0.620403239401399732627479164655489392L; + + /// To represent a position in the hexagonal tiling, we use barycentric coordinates. These are + /// of the form (x,y,z). A step towards the right increases x, towards the top-left increases y, + /// and towards the bottom-left increases z. Compared to ordinary coordinates, the advantage of + /// barycentric coordinates is that we can easily move into any direction. + /// + /// If we move to the right, top-left, and then to the bottom-left, we return to the original + /// position. Hence, (0,0,0) represents the same position as (1,1,1). In general, (x,y,z) and + /// (x+a, y+a, z+a) represent the same position. Therefore, we can normalize (x,y,z) to + /// (x-z, y-z, 0). This class only stores normalized coordinates. + /// + /// This class is immutable. + struct Coordinate { + friend CoordinateHash; + + private: + int m_x, m_y; + + public: + int x() const { return m_x; } + int y() const { return m_y; } + int z() const { return 0; } + + Coordinate() {} + Coordinate(int x, int y) : m_x(x), m_y(y) {} + Coordinate(int x, int y, int z) : Coordinate(x-z, y-z) {} + + bool operator==(Coordinate c) const { + return m_x == c.m_x && m_y == c.m_y; + } + + std::array neighbors() const; + + friend std::ostream& operator<<(std::ostream &os, Coordinate c); + }; + + struct CoordinateHash { + size_t operator()(Coordinate c) const noexcept { + constexpr int width = SIZE_WIDTH >> 1; + constexpr int offset = 1 << (width >> 1); + + // size_t is likely (at least) 64 bits + // and abs(x), abs(y) should fit in 16 bits + // so it's reasonable to assume that x, y can be packed into a single size_t + // and otherwise the consequences are not disastrous + size_t x = c.m_x + offset; + size_t y = c.m_y + offset; + return x + (y << width); + } + }; + + template + using CoordinateMap = std::unordered_map; + using CoordinateSet = std::unordered_set; + + /// Invariant: all tiles are connected and there are no holes. We say the configuration is \a contiguous. + struct Configuration { + int index; + const MosaicRegion *region; + CoordinateSet tiles, boundary; + /// Whether this configuration is adjacent to the edge of the map. + bool atHorizon; + + // implement iterators so we can use foreach loops + CoordinateSet::const_iterator begin() const noexcept { return tiles.begin(); } + CoordinateSet::const_iterator end() const noexcept { return tiles.end(); } + + bool contains(Coordinate c) const { + return tiles.contains(c); + } + int desire() const { + return isLand() ? landRegion().targetTileCount - size() : 0; + } + bool isLand() const { + return region->type() == RegionType::Land; + } + bool isSea() const { + return region->type() == RegionType::Sea; + } + std::string label() const { + return region->name(); + } + const LandRegion& landRegion() const { + assert(isLand()); + return *dynamic_cast(region); + } + int size() const { + return tiles.size(); + } + + bool operator==(const Configuration &config) const { return index == config.index; } + + /// Checks whether \c c and all its neighbors are contained in this configuration. This + /// function only queries \c tiles, not \c boundary. + bool containsInInterior(Coordinate c) const; + + bool isAdjacent(Coordinate c) const; + + bool remainsContiguousWithout(Coordinate c) const; + }; + + /// Represents a tile that can be moved from its current configuration to the one indexed by + /// \c targetIndex at a particular \c cost. + struct Transfer { + Coordinate tile; + int targetIndex; + double cost; // lower is better + + bool operator<(const Transfer &t) const { + return cost < t.cost; + } + }; + + std::vector> guidingPairs; + + std::vector configurations; + + /// The mapping from tiles (coordinates) to the configurations they belong to. + CoordinateMap tiles; + + /// A graph that stores the adjacencies between configurations: there is an edge (u,v) iff the + /// u-th configuration is adjacent to the v-th configuration. + UndirectedGraph configGraph; + + HexagonalMap() {} + HexagonalMap(const VisibilityDrawing &initial, + const std::vector &landRegions, + const std::vector &seaRegions); + + static Point getCentroid(Coordinate c); + static Point getCentroid(const Configuration &config); + + int getNumberOfLandRegions() const { return guidingPairs.size() + 1; } + int getNumberOfSeaRegions() const { return configurations.size() - getNumberOfLandRegions(); } + + // TODO: `std::optional>` instead of pointer? + const Configuration* getConfiguration(Coordinate c) const; + Configuration* getConfiguration(Coordinate c); + + /// Get the guiding shape for a land region (scaled to its desired size) or sea region (scaled + /// to its current size). For the input europe-population-mosaic.json, the guiding + /// shapes of all regions are visualized below. + /// \image html mosaic-cartogram-guiding-shapes.svg + Ellipse getGuidingShape(const Configuration &config) const; + /// Get the pair of guiding shapes for two adjacent land regions. This is not equivalent to + /// getting two separate guiding shapes! This pair has the correct relative positions (of the + /// original regions) and is centered on the joint centroid. + std::pair getGuidingPair(const Configuration &config1, const Configuration &config2) const; + /// Get the pair of guiding shapes for any two regions. + std::pair getGuidingShapes(const Configuration &config1, const Configuration &config2) const; + + /// Computes the set of tiles that can be transferred from \c source to \c target without + /// adding/removing adjacencies, creating holes, etc. + std::vector computeTransferCandidates(const Configuration &source, const Configuration &target) const; + /// Computes the set of transfers from \c source to \c target, i.e., the set of tiles that can + /// be transferred, together with the cost of transferal based on guiding shapes. Lower cost is + /// better. + std::vector computeAllTransfers(const Configuration &source, const Configuration &target) const; + /// Computes the best transfer from \c source to \c target among all valid options. For example, + /// all candidate transfers from France to Germany are visualized below, with a lighter shade + /// indicating a lower cost, and the best transfer marked by an X. + /// \image html mosaic-cartogram-best-transfer.svg + std::optional computeBestTransfer(const Configuration &source, const Configuration &target) const; + /// A complex function that aims to compute the best of transfers. First, it computes a cost + /// graph using \ref computeBestTransfer for each edge in \ref configGraph. Next, for every + /// source, it computes a minimum branching using Edmonds' algorithm. Then, for each branching, + /// using a DFS, it finds the shortest path that minimizes the maximum cost among its path. + std::vector computeBestTransferPath() const; + + Configuration& getNearestAdjacent(Coordinate c, const std::unordered_map> ¢roids); + /// Clears and recomputes the boundary of \c config. + void resetBoundary(Configuration &config) const; + /// Add new tiles to configurations at the horizon until the inner configurations are enclosed + /// by \c layers of tiles. + void grow(int layers = 5); + + /// Performs a single transfer between two regions, maintaining their boundary. + void perform(const Transfer &transfer); + void perform(const std::vector &path); + + /// Repeatedly runs \ref computeBestTransferPath and \ref perform until there are no valid + /// transfer paths, or until we reach the iteration limit. + void run(int iterations); + +}; + +} // namespace cartocrow::mosaic_cartogram + +#endif // CARTOCROW_MOSAIC_CARTOGRAM_MAP_H diff --git a/cartocrow/mosaic_cartogram/triangulation.cpp b/cartocrow/mosaic_cartogram/triangulation.cpp new file mode 100644 index 000000000..daab086e3 --- /dev/null +++ b/cartocrow/mosaic_cartogram/triangulation.cpp @@ -0,0 +1,170 @@ +#include "triangulation.h" + +#include +#include +#include +#include +#include + +#include "../core/core.h" +#include "graph.h" + +namespace cartocrow::mosaic_cartogram { + +using StraightSkeleton = CGAL::Straight_skeleton_2; + +std::vector> addOuterTriangle(RegionArrangement &arr) { + Number xMin = std::numeric_limits::max(); + Number xMax = std::numeric_limits::min(); + Number yMin = std::numeric_limits::max(); + Number yMax = std::numeric_limits::min(); + for (auto v : arr.vertex_handles()) { + auto &p = v->point(); + xMin = std::min(xMin, p.x()); + xMax = std::max(xMax, p.x()); + yMin = std::min(yMin, p.y()); + yMax = std::max(yMax, p.y()); + } + + const auto w = xMax - xMin; + const auto h = yMax - yMin; + + // defined such that there is one large sea region "on top", which will become the root of the OST + const Point p0(xMin - w, yMax + h / 2 ); // top left + const Point p1((xMin + xMax) / 2, yMin - h * 3/2); // bottom + const Point p2(xMax + w, yMax + h / 2 ); // top right + + const auto v0 = arr.insert_in_face_interior(p0, arr.unbounded_face()); + const auto v1 = arr.insert_in_face_interior(p1, arr.unbounded_face()); + const auto v2 = arr.insert_in_face_interior(p2, arr.unbounded_face()); + + arr.insert_at_vertices(Segment(p0, p1), v0, v1); + arr.insert_at_vertices(Segment(p1, p2), v1, v2); + arr.insert_at_vertices(Segment(p2, p0), v2, v0); + + return { p0, p1, p2 }; +} + +Polygon ccbToPolygon(const RegionArrangement::Ccb_halfedge_const_circulator &circ) { + Polygon polygon; + auto curr = circ; + do { + polygon.push_back(curr->target()->point()); + } while (++curr != circ); + return polygon; +} + +PolygonWithHoles arrangementToPolygon(const RegionArrangement &arr) { + // create polygon from outer boundary of arrangement + const auto outerFace = arr.unbounded_face()->holes_begin()->ptr()->twin()->face(); + const auto boundary = ccbToPolygon(outerFace->outer_ccb()); // counterclockwise! + PolygonWithHoles polygon(boundary); + + // add all holes to polygon + for (auto hit = outerFace->holes_begin(); hit != outerFace->holes_end(); ++hit) + polygon.add_hole(ccbToPolygon(*hit)); // clockwise! + + return polygon; +} + +int labelSeaRegions(RegionArrangement &arr) { + auto circ = arr.unbounded_face()->holes_begin()->ptr()->ccb(); + + // find topmost edge (such that "_outer0" will be the topmost region) + while (circ->source()->point().y() != circ->target()->point().y()) ++circ; + + // label outer sea regions in counterclockwise order + int i = 0; + auto curr = circ; + do { + curr->twin()->face()->set_data("_outer" + std::to_string(i++)); + } while (--curr != circ); + + // label remaining sea regions + i = 0; + for (const auto f : arr.face_handles()) + if (!f->is_unbounded() && f->data().empty()) + f->set_data("_sea" + std::to_string(i++)); + + return i; +} + +int triangulate(RegionArrangement &arr, const std::vector> &salientPoints) { + const auto outerPoints = addOuterTriangle(arr); + const auto polygon = arrangementToPolygon(arr); + const StraightSkeleton skeleton = *CGAL::create_interior_straight_skeleton_2(polygon, Exact()); + + // anchors = salientPoints \union outerPoints + std::vector> anchors(salientPoints); + anchors.insert(anchors.end(), outerPoints.begin(), outerPoints.end()); + + std::vector> indexToPoint; + for (auto v : skeleton.vertex_handles()) + if (v->is_skeleton()) + indexToPoint.push_back(v->point()); + + const int numberOfSkeletonPoints = indexToPoint.size(); + + // after this, `indexToPoint` first contains all skeleton points, then all anchor points + indexToPoint.insert(indexToPoint.end(), anchors.begin(), anchors.end()); + + // graph size = no. skeleton vertices + no. anchor vertices + UndirectedGraph graph(indexToPoint.size()); + + // add all inner bisectors and all anchor-incident contour bisectors to the graph + int numberOfBisectorsAdded = 0; + for (auto eit = skeleton.halfedges_begin(); eit != skeleton.halfedges_end(); ++eit) { + const auto p1 = eit->vertex()->point(); + const auto p2 = eit->opposite()->vertex()->point(); + + // (temp) bad, slow + int i1 = 0; + int i2 = 0; + while (i1 < graph.getNumberOfVertices() && indexToPoint[i1] != p1) i1++; + while (i2 < graph.getNumberOfVertices() && indexToPoint[i2] != p2) i2++; + + // immediately skip edges incident to a vertex which is not an anchor or a skeleton vertex + if (std::max(i1, i2) >= graph.getNumberOfVertices()) continue; + + // only process one of each pair of halfedges + if (i1 > i2) continue; + + if (eit->is_inner_bisector()) { + graph.addEdge(i1, i2); + } else if (eit->is_bisector()) { + // so if eit is contour bisector: + if (std::max(i1, i2) >= numberOfSkeletonPoints) { + // so if either p1 or p2 is an anchor: + graph.addEdge(i1, i2); + numberOfBisectorsAdded++; + } + } + } + + // (temp) debug message + std::cerr << "[info] added " << numberOfBisectorsAdded << " bisectors for " << salientPoints.size() << " salient points (and 3 outer points)" << std::endl; + + // remove all non-anchor deg=1 vertices until none are left + // TODO: use queue of candidates to improve runtime + for (int i = 0; i < numberOfSkeletonPoints; i++) { + if (graph.getDegree(i) == 1) { + graph.isolate(i); + i = -1; // there may be new candidates; restart + } + } + + // add all remaining edges to arrangement + for (auto [i1, i2] : graph.getEdges()) { + const auto p1 = indexToPoint[i1]; + const auto p2 = indexToPoint[i2]; + CGAL::insert(arr, Segment(p1, p2)); + } + + return labelSeaRegions(arr); +} + +bool dualIsTriangular(const RegionArrangement &arr) { + return false; +} + +} // namespace cartocrow::mosaic_cartogram diff --git a/cartocrow/mosaic_cartogram/triangulation.h b/cartocrow/mosaic_cartogram/triangulation.h new file mode 100644 index 000000000..6446545c6 --- /dev/null +++ b/cartocrow/mosaic_cartogram/triangulation.h @@ -0,0 +1,26 @@ +#ifndef CARTOCROW_MOSAIC_CARTOGRAM_TRIANGULATION_H +#define CARTOCROW_MOSAIC_CARTOGRAM_TRIANGULATION_H + +#include + +#include "../core/region_arrangement.h" + +namespace cartocrow::mosaic_cartogram { + +/// "Triangulates" \c arr such that its dual is maximal planar. This is achieved by dividing the +/// ocean into sea regions. To this end, we compute a straight skeleton in the ocean, and use the +/// bisectors ending in salient points as sea boundaries. +/// +/// The number of sea regions (excluding the three outer ones) is returned. +/// +/// The current implementation is not particularly efficient. Furthermore, the flow algorithm in +/// \ref HexagonalMap likes to deal with convex-ish regions, but this currently produces many sea +/// regions with sharp angles etc. +int triangulate(RegionArrangement &arr, const std::vector> &salientPoints); + +/// TODO +bool dualIsTriangular(const RegionArrangement &arr); + +} // namespace cartocrow::mosaic_cartogram + +#endif // CARTOCROW_MOSAIC_CARTOGRAM_TRIANGULATION_H diff --git a/cartocrow/mosaic_cartogram/visibility_drawing.cpp b/cartocrow/mosaic_cartogram/visibility_drawing.cpp new file mode 100644 index 000000000..3a8697307 --- /dev/null +++ b/cartocrow/mosaic_cartogram/visibility_drawing.cpp @@ -0,0 +1,119 @@ +#include "visibility_drawing.h" + +#include + +namespace cartocrow::mosaic_cartogram { + +VisibilityDrawing::VisibilityDrawing(const UndirectedGraph &g, int vTop, int vBotL, int vBotR, const std::vector> ¢roids) + : m_graph(g), ost(g, vTop, vBotL, vBotR, centroids) { + // initialize + const int n = g.getNumberOfVertices(); + m_levelVertices.resize(n, -1); + m_levelEdges.resize(n, std::vector(n, -1)); + m_x0.resize(n, -1); + m_x1.resize(n); + m_y0.resize(n); + m_y1.resize(n); + + // compute + m_levelVertices[vTop] = 1; + for (const int v : ost.getVerticesInOrder()) getOrComputeLevel(v); + dfs(vTop, 0, 0); + + // fill grid + const int w = m_x1[vTop]; + const int h = m_y1[vBotL]; + grid.resize(w, std::vector(h, -1)); + for (int i = 0; i < n; i++) + for (int x = m_x0[i]; x < m_x1[i]; x++) + for (int y = m_y0[i]; y < m_y1[i]; y++) + grid[x][y] = i; + + // extend rectangles into empty cells + for (int y = 0; y < h; y++) { + int v = grid[0][y]; + for (int x = 1; x < w; x++) + if (grid[x][y] == -1) + grid[x][y] = v; + else + v = grid[x][y]; + } +} + +std::optional VisibilityDrawing::getUnrelatedNeighborLeft(const int v) const { + const auto &neighbors = m_graph.getNeighbors(v); + const int label = ost.getLabel(v); + + const int n = neighbors.size(); + const int iParent = std::find(neighbors.begin(), neighbors.end(), ost.getParent(v)) - neighbors.begin(); + + int i = iParent; + do { + i = (i-1 + n) % n; + } while (i != iParent && ost.getLabel(neighbors[i]) < label); // i.e., `neighbors[i]` is in U_<(v) + + i = (i+1) % n; + return i == iParent ? std::nullopt : std::optional(neighbors[i]); +} + +std::optional VisibilityDrawing::getUnrelatedNeighborRight(const int v) const { + const auto &neighbors = m_graph.getNeighbors(v); + const int label = ost.getLabel(v); + + const int n = neighbors.size(); + const int iParent = std::find(neighbors.begin(), neighbors.end(), ost.getParent(v)) - neighbors.begin(); + + int i = iParent; + do { + i = (i+1) % n; + } while (ost.getLabel(neighbors[i]) > label && ost.getParent(neighbors[i]) != v); // i.e., `neighbors[i]` is in U_>(v) + + i = (i-1 + n) % n; + return i == iParent ? std::nullopt : std::optional(neighbors[i]); +} + +int VisibilityDrawing::getOrComputeLevel(const int v) { + if (m_levelVertices[v] == -1) { + const auto l = getUnrelatedNeighborLeft(v); + const auto r = getUnrelatedNeighborRight(v); + m_levelVertices[v] = std::max( + // only the root doesn't have both, but its level was already set in advance + l ? getOrComputeLevel(*l, v) : -1, + r ? getOrComputeLevel(v, *r) : -1 + ); + } + return m_levelVertices[v]; +} + +int VisibilityDrawing::getOrComputeLevel(const int u, const int v) { // assert: u.label < v.label + if (m_levelEdges[u][v] == -1) { + const auto w = m_graph.getNextNeighbor(v, u).value(); // assert: w has value + m_levelEdges[u][v] = 1 + std::max( + w == ost.getParent(u) ? getOrComputeLevel(w) : getOrComputeLevel(u, w), + w == ost.getParent(v) ? getOrComputeLevel(w) : getOrComputeLevel(w, v) + ); + } + return m_levelEdges[u][v]; +} + +int VisibilityDrawing::dfs(const int curr, int x, int y) { + m_x0[curr] = x; + m_y0[curr] = y; + m_y1[curr] = y = m_levelVertices[curr]; + + const auto &children = ost.getChildren(curr); + if (children.empty()) { + // `curr` is leaf + x += 1; + } else { + // `curr` is internal node + for (const int next : children) + if (m_x0[next] == -1) // skip if `next` was already visited + x = dfs(next, x, y); + } + + m_x1[curr] = x; + return x; +} + +} diff --git a/cartocrow/mosaic_cartogram/visibility_drawing.h b/cartocrow/mosaic_cartogram/visibility_drawing.h new file mode 100644 index 000000000..34e5cd1ba --- /dev/null +++ b/cartocrow/mosaic_cartogram/visibility_drawing.h @@ -0,0 +1,48 @@ +#ifndef CARTOCROW_MOSAIC_CARTOGRAM_VISIBILITY_DRAWING_H +#define CARTOCROW_MOSAIC_CARTOGRAM_VISIBILITY_DRAWING_H + +#include +#include + +#include "../core/core.h" +#include "graph.h" +#include "orderly_spanning_tree.h" + +namespace cartocrow::mosaic_cartogram { + +/// Computes a 2-visibility drawing using an orderly-spanning tree like the +/// original paper on mosaic cartograms (Cano et al., 2015) describes. +/// Also refer to section 4 (page 935) of Chiang et al., 2005. +class VisibilityDrawing { + public: + // adjacencies of graph must be in clockwise order + VisibilityDrawing(const UndirectedGraph &g, int vTop, int vBotL, int vBotR, const std::vector> ¢roids); + + const OrderlySpanningTree ost; + std::vector> grid; + + private: + const UndirectedGraph &m_graph; + + // memoization + // level is similar (but not identical) to Chiang (2005), page 935 + std::vector m_levelVertices; + std::vector> m_levelEdges; // only for edges in Δ-T + + std::vector m_x0, m_x1; + std::vector m_y0, m_y1; + + /// Returns the first vertex in the block \f$U_<(v)\f$, if it's not empty. + std::optional getUnrelatedNeighborLeft(const int v) const; + /// Returns the last vertex in the block \f$U_>(v)\f$, if it's not empty. + std::optional getUnrelatedNeighborRight(const int v) const; + + int getOrComputeLevel(const int v); + int getOrComputeLevel(const int u, const int v); // label(u) < label(v) + + int dfs(const int curr, int x, int y); +}; + +} // namespace cartocrow::mosaic_cartogram + +#endif //CARTOCROW_MOSAIC_CARTOGRAM_VISIBILITY_DRAWING_H diff --git a/cartocrow/necklace_map/CMakeLists.txt b/cartocrow/necklace_map/CMakeLists.txt index 1eca8b993..88f2df7fa 100644 --- a/cartocrow/necklace_map/CMakeLists.txt +++ b/cartocrow/necklace_map/CMakeLists.txt @@ -60,6 +60,7 @@ set(HEADERS add_library(necklace_map ${SOURCES}) target_link_libraries(necklace_map + PUBLIC core PRIVATE glog::glog ) diff --git a/cartocrow/necklace_map/necklace_map.h b/cartocrow/necklace_map/necklace_map.h index a28ef8bdd..8995a42e5 100644 --- a/cartocrow/necklace_map/necklace_map.h +++ b/cartocrow/necklace_map/necklace_map.h @@ -120,7 +120,7 @@ class NecklaceMap { /// Constructs a necklace map with the given regions and no necklaces. /// /// This does not compute the necklace map: use \ref compute() to run the - /// computation. Modifying the RegionList passed here after the necklace + /// computation. Modifying the RegionMap passed here after the necklace /// map has been constructed results in undefined behavior. NecklaceMap(const std::shared_ptr map); diff --git a/cartocrow/renderer/geometry_renderer.h b/cartocrow/renderer/geometry_renderer.h index 731ea3aa4..76b90bb42 100644 --- a/cartocrow/renderer/geometry_renderer.h +++ b/cartocrow/renderer/geometry_renderer.h @@ -22,6 +22,7 @@ along with this program. If not, see . #include "../core/bezier.h" #include "../core/core.h" +#include "../core/ellipse.h" #include "../core/region_map.h" #include "../core/polyline.h" @@ -96,6 +97,10 @@ class GeometryRenderer { virtual void draw(const PolygonWithHoles& p) = 0; /// Draws a circle with the currently set style. virtual void draw(const Circle& c) = 0; + /// Draws a circle with the currently set style. + void draw(const Circle& c); + /// Draws an ellipse with the currently set style. + virtual void draw(const Ellipse& e) = 0; /// Draws a Bézier spline with the currently set style. void draw(const BezierCurve& c); /// Draws a Bézier spline with the currently set style. diff --git a/cartocrow/renderer/geometry_widget.cpp b/cartocrow/renderer/geometry_widget.cpp index c0b429f18..d2ddf141c 100644 --- a/cartocrow/renderer/geometry_widget.cpp +++ b/cartocrow/renderer/geometry_widget.cpp @@ -32,6 +32,8 @@ along with this program. If not, see . #include #include +#include + namespace cartocrow::renderer { GeometryWidget::Editable::Editable(GeometryWidget* widget) : m_widget(widget) {} @@ -535,6 +537,16 @@ void GeometryWidget::draw(const Circle& c) { m_painter->drawEllipse(rect); } +void GeometryWidget::draw(const Ellipse& e) { + setupPainter(); + const auto p = e.parameters(); + m_painter->save(); + m_painter->translate(convertPoint(Point(p.x0, p.y0))); + m_painter->rotate(-p.angle * 180 * std::numbers::inv_pi); // clockwise! + m_painter->drawEllipse(QPointF(), p.a * zoomFactor(), p.b * zoomFactor()); + m_painter->restore(); +} + void GeometryWidget::draw(const BezierSpline& s) { setupPainter(); QPainterPath path; diff --git a/cartocrow/renderer/geometry_widget.h b/cartocrow/renderer/geometry_widget.h index a700408aa..6fa52e851 100644 --- a/cartocrow/renderer/geometry_widget.h +++ b/cartocrow/renderer/geometry_widget.h @@ -163,6 +163,7 @@ class GeometryWidget : public QWidget, public GeometryRenderer { void draw(const Polygon& p) override; void draw(const PolygonWithHoles& p) override; void draw(const Circle& c) override; + void draw(const Ellipse& e) override; void draw(const BezierSpline& s) override; void draw(const Line& l) override; void draw(const Ray& r) override; @@ -297,7 +298,7 @@ class GeometryWidget : public QWidget, public GeometryRenderer { /// The editable in \ref m_editables that the user is currently interacting /// with, or `nullptr` if no such interaction is going on. Editable* m_activeEditable = nullptr; - + /// The current drawing style. GeometryWidgetStyle m_style; /// A stack of drawing styles, used by \link pushStyle() and \link diff --git a/cartocrow/renderer/ipe_renderer.cpp b/cartocrow/renderer/ipe_renderer.cpp index 8ae25e825..d4fd2563e 100644 --- a/cartocrow/renderer/ipe_renderer.cpp +++ b/cartocrow/renderer/ipe_renderer.cpp @@ -207,6 +207,22 @@ void IpeRenderer::draw(const Circle& c) { m_page->append(ipe::TSelect::ENotSelected, m_layer, path); } +void IpeRenderer::draw(const Ellipse& e) { + const auto m = e.parameters().matrix(); + ipe::Matrix matrix { + // transposed linear map: (i.e., to make it column-major) + m(0, 0), m(1, 0), + m(0, 1), m(1, 1), + // translation: + m(0, 2), m(1, 2) + }; + ipe::Ellipse* ellipse = new ipe::Ellipse(matrix); + ipe::Shape* shape = new ipe::Shape(); + shape->appendSubPath(ellipse); + ipe::Path* path = new ipe::Path(getAttributesForStyle(), *shape); + m_page->append(ipe::TSelect::ENotSelected, m_layer, path); +} + void IpeRenderer::draw(const BezierSpline& s) { ipe::Curve* curve = new ipe::Curve(); for (BezierCurve c : s.curves()) { diff --git a/cartocrow/renderer/ipe_renderer.h b/cartocrow/renderer/ipe_renderer.h index e1f050567..487d3ea9b 100644 --- a/cartocrow/renderer/ipe_renderer.h +++ b/cartocrow/renderer/ipe_renderer.h @@ -86,6 +86,7 @@ class IpeRenderer : public GeometryRenderer { void draw(const Polygon& p) override; void draw(const PolygonWithHoles& p) override; void draw(const Circle& c) override; + void draw(const Ellipse& e) override; void draw(const BezierSpline& s) override; void draw(const Line& l) override; void draw(const Ray& r) override; diff --git a/cartocrow/renderer/painting_renderer.cpp b/cartocrow/renderer/painting_renderer.cpp index 007529fae..2263b1553 100644 --- a/cartocrow/renderer/painting_renderer.cpp +++ b/cartocrow/renderer/painting_renderer.cpp @@ -37,6 +37,8 @@ void PaintingRenderer::paint(GeometryRenderer& renderer) const { renderer.draw(std::get>(object)); } else if (std::holds_alternative>(object)) { renderer.draw(std::get>(object)); + } else if (std::holds_alternative(object)) { + renderer.draw(std::get(object)); } else if (std::holds_alternative(object)) { renderer.draw(std::get(object)); } else if (std::holds_alternative>(object)) { @@ -77,6 +79,10 @@ void PaintingRenderer::draw(const Circle& c) { m_objects.push_back(c); } +void PaintingRenderer::draw(const Ellipse& e) { + m_objects.push_back(e); +} + void PaintingRenderer::draw(const BezierSpline& s) { m_objects.push_back(s); } diff --git a/cartocrow/renderer/painting_renderer.h b/cartocrow/renderer/painting_renderer.h index f8d83b007..13c734ff9 100644 --- a/cartocrow/renderer/painting_renderer.h +++ b/cartocrow/renderer/painting_renderer.h @@ -41,6 +41,7 @@ class PaintingRenderer : public GeometryPainting, public GeometryRenderer { void draw(const Polygon& p) override; void draw(const PolygonWithHoles& p) override; void draw(const Circle& c) override; + void draw(const Ellipse& e) override; void draw(const BezierSpline& s) override; void draw(const Line& l) override; void draw(const Ray& r) override; @@ -74,8 +75,9 @@ class PaintingRenderer : public GeometryPainting, public GeometryRenderer { }; using Label = std::pair, std::string>; using DrawableObject = std::variant, Segment, Polygon, - PolygonWithHoles, Circle, BezierSpline, - Line, Ray, Polyline, Label, Style>; + PolygonWithHoles, Circle, Ellipse, + BezierSpline, Line, Ray, + Polyline, Label, Style>; std::vector m_objects; Style m_style; }; diff --git a/data/europe-manual-sea.ipe b/data/europe-manual-sea.ipe new file mode 100644 index 000000000..074ae0bfc --- /dev/null +++ b/data/europe-manual-sea.ipe @@ -0,0 +1,2943 @@ + + + + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-0.8 0 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-0.8 0 l +-1 -0.333 l +h + + + + +0.6 0 0 0.6 0 0 e +0.4 0 0 0.4 0 0 e + + + + +0.6 0 0 0.6 0 0 e + + + + + +0.5 0 0 0.5 0 0 e + + +0.6 0 0 0.6 0 0 e +0.4 0 0 0.4 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"mosaic_cartogram", + "map": "europe-manual-sea.ipe", + "data": { + "RUS": 122412000, + "TUR": 85279553, + "DEU": 83783942, + "GBR": 67886011, + "FRA": 65273511, + "ITA": 60461826, + "ESP": 46754778, + "UKR": 43733762, + "POL": 37846611, + "ROU": 19237691, + "NLD": 17134872, + "BEL": 11589623, + "CZE": 10708981, + "GRC": 10423054, + "PR1": 10196709, + "SWE": 10099265, + "HUN": 9660351, + "BLR": 9449323, + "AUT": 9006398, + "CHE": 8654622, + "BGR": 6948445, + "SRB": 6647003, + "DNK": 5792202, + "FIN": 5540720, + "SVK": 5459642, + "NOR": 5421241, + "IRL": 4937786, + "HRV": 4105267, + "MDA": 4033963, + "BIH": 3280819, + "ALB": 2877797, + "LTU": 2722289, + "MKD": 2083374, + "SVN": 2078938, + "LVA": 1886198, + "KOS": 1761985, + "EST": 1326535, + "CYP": 923272, + "MNE": 628066, + "LUX": 625978, + "MLT": 441543, + "CYN": 382836, + "ISL": 341243, + "JEY": 173863, + "IMN": 85033, + "AND": 77265, + "FRO": 48863, + "MCO": 39242, + "LIE": 38128, + "SMR": 33931, + "VAT": 801 + }, + "parameters": { + "drawBorders": true, + "manualSeas": true, + "tileArea": 100, + "unitValue": 680000 + } +} diff --git a/data/europe-population-mosaic.json b/data/europe-population-mosaic.json new file mode 100644 index 000000000..668562cf4 --- /dev/null +++ b/data/europe-population-mosaic.json @@ -0,0 +1,62 @@ +{ + "type": "mosaic_cartogram", + "map": "europe-ne-110m-salient-points.ipe", + "data": { + "RUS": 122412000, + "TUR": 85279553, + "DEU": 83783942, + "GBR": 67886011, + "FRA": 65273511, + "ITA": 60461826, + "ESP": 46754778, + "UKR": 43733762, + "POL": 37846611, + "ROU": 19237691, + "NLD": 17134872, + "BEL": 11589623, + "CZE": 10708981, + "GRC": 10423054, + "PR1": 10196709, + "SWE": 10099265, + "HUN": 9660351, + "BLR": 9449323, + "AUT": 9006398, + "CHE": 8654622, + "BGR": 6948445, + "SRB": 6647003, + "DNK": 5792202, + "FIN": 5540720, + "SVK": 5459642, + "NOR": 5421241, + "IRL": 4937786, + "HRV": 4105267, + "MDA": 4033963, + "BIH": 3280819, + "ALB": 2877797, + "LTU": 2722289, + "MKD": 2083374, + "SVN": 2078938, + "LVA": 1886198, + "KOS": 1761985, + "EST": 1326535, + "CYP": 923272, + "MNE": 628066, + "LUX": 625978, + "MLT": 441543, + "CYN": 382836, + "ISL": 341243, + "JEY": 173863, + "IMN": 85033, + "AND": 77265, + "FRO": 48863, + "MCO": 39242, + "LIE": 38128, + "SMR": 33931, + "VAT": 801 + }, + "parameters": { + "drawBorders": true, + "tileArea": 100, + "unitValue": 680000 + } +} diff --git a/doc/Doxyfile b/doc/Doxyfile index 0bce9114a..2120536b1 100644 --- a/doc/Doxyfile +++ b/doc/Doxyfile @@ -16,7 +16,7 @@ EXTRACT_PRIVATE = YES EXTRACT_PACKAGE = YES EXTRACT_STATIC = YES -INPUT = "cartocrow/core" "cartocrow/renderer" "cartocrow/necklace_map" "cartocrow/isoline_simplification" "cartocrow/flow_map" "doc/pages" +INPUT = "cartocrow/core" "cartocrow/renderer" "cartocrow/necklace_map" "cartocrow/isoline_simplification" "cartocrow/flow_map" "cartocrow/mosaic_cartogram" "doc/pages" FILE_PATTERNS = *.cpp *.h *.inc *.md RECURSIVE = YES diff --git 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a/doc/images/mosaic-cartogram-guiding-shapes.svg b/doc/images/mosaic-cartogram-guiding-shapes.svg new file mode 100644 index 000000000..b06e03ea9 --- /dev/null +++ b/doc/images/mosaic-cartogram-guiding-shapes.svg @@ -0,0 +1,249 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/doc/pages/main_page.md b/doc/pages/main_page.md index aa8dceba2..7e32b7046 100644 --- a/doc/pages/main_page.md +++ b/doc/pages/main_page.md @@ -42,7 +42,7 @@ CartoCrow consists of the following modules. ### Utilities -* The **core** module contains the basic primitives and utilities that are in use throughout the library. This includes a list of type aliases for basic [CGAL](https://cgal.org) types (\ref cartocrow::Point "Point", \ref cartocrow::Circle "Circle", \ref cartocrow::Polygon "Polygon", etc.) and tools to read maps from Ipe files (\ref cartocrow::RegionList "RegionList"). +* The **core** module contains the basic primitives and utilities that are in use throughout the library. This includes a list of type aliases for basic [CGAL](https://cgal.org) types (\ref cartocrow::Point "Point", \ref cartocrow::Circle "Circle", \ref cartocrow::Polygon "Polygon", etc.) and tools to read maps from Ipe files (\ref cartocrow::RegionMap "RegionMap"). _Author: Willem Sonke_ * The **renderer** module implements an interface that can be used to render maps. Each map type provides a \ref cartocrow::renderer:GeometryPainting "GeometryPainting", which can be handed to a \ref cartocrow::renderer::GeometryRenderer "GeometryRenderer" to draw it. In particular, the \ref cartocrow::renderer::IpeRenderer "IpeRenderer" renders the painting to an [Ipe](https://ipe.otfried.org) drawing, while the \ref cartocrow::renderer::GeometryWidget "GeometryWidget" renders the painting to a \ref QWidget for inclusion in a Qt application. diff --git a/frontend/CMakeLists.txt b/frontend/CMakeLists.txt index fa99da52e..0194a0943 100644 --- a/frontend/CMakeLists.txt +++ b/frontend/CMakeLists.txt @@ -12,6 +12,7 @@ target_link_libraries( ${COMMON_CLA_TARGET} core flow_map + mosaic_cartogram necklace_map isoline_simplification renderer diff --git a/frontend/cartocrow.cpp b/frontend/cartocrow.cpp index ccb3e0283..d020eb2c6 100644 --- a/frontend/cartocrow.cpp +++ b/frontend/cartocrow.cpp @@ -40,6 +40,9 @@ Created by tvl (t.vanlankveld@esciencecenter.nl) on 10-09-2019 #include "cartocrow/isoline_simplification/ipe_isolines.h" #include "cartocrow/isoline_simplification/isoline_simplifier.h" #include "cartocrow/isoline_simplification/simple_isoline_painting.h" +#include "cartocrow/mosaic_cartogram/mosaic_cartogram.h" +#include "cartocrow/mosaic_cartogram/painting.h" +#include "cartocrow/mosaic_cartogram/parameters.h" #include "cartocrow/necklace_map/circle_necklace.h" #include "cartocrow/necklace_map/necklace_map.h" #include "cartocrow/necklace_map/painting.h" @@ -118,6 +121,48 @@ int main(int argc, char* argv[]) { flow_map::Painting::Options options; painting = std::make_shared(map_ptr, tree, options); + } else if (projectData["type"] == "mosaic_cartogram") { + const std::filesystem::path ipeFilename = projectFilename.parent_path() / projectData["map"]; + RegionMap map = ipeToRegionMap(ipeFilename); + auto map_ptr = std::make_shared(map); + + // read data values + std::unordered_map> dataValues; + for (auto &[key, val] : projectData["data"].items()) { + if (dataValues.contains(key)) { + throw std::logic_error("More than one data value is specified for region \"" + key + '"'); + } + dataValues[key] = val; + } + + // initialize cartogram + auto cartogram = std::make_shared( + map_ptr, + std::move(dataValues), + ipeToSalientPoints(ipeFilename) + ); + + // read parameters + const auto &p = projectData["parameters"]; + auto ¶msComputation = cartogram->parameters(); + mosaic_cartogram::Painting::Options paramsPainting; + + paramsComputation.manualSeas = p.value("manualSeas", false); // optional + paramsComputation.unitValue = p.value("unitValue", -1); // required + paramsPainting.drawBorders = p.value("drawBorders", false); // optional + paramsPainting.tileArea = p.value("tileArea", 1); // optional + + paramsComputation.validate(); + paramsPainting.validate(); + + // compute cartogram + cartogram->compute(); + + // initialize painting + painting = std::make_shared( + cartogram, + std::move(paramsPainting) + ); } else if (projectData["type"] == "isoline_simplification") { auto isolines = isoline_simplification::ipeToIsolines(projectFilename.parent_path() / projectData["isolines"]); isoline_simplification::IsolineSimplifier simplifier(isolines);