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H3GraphLayout.java
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H3GraphLayout.java
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//
// The Walrus Graph Visualization Tool.
// Copyright (C) 2000,2001,2002 The Regents of the University of California.
//
// This program is free software; you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation; either version 2 of the License, or
// (at your option) any later version.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this program; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
//
// ######END_HEADER######
//
import java.util.*;
import javax.vecmath.*;
import mpfun.*;
public class H3GraphLayout
{
////////////////////////////////////////////////////////////////////////
// PUBLIC CLASSES
////////////////////////////////////////////////////////////////////////
public interface LayoutState {}
////////////////////////////////////////////////////////////////////////
// CONSTRUCTORS
////////////////////////////////////////////////////////////////////////
public H3GraphLayout(boolean attemptExtended)
{
ATTEMPT_EXTENDED = attemptExtended;
}
////////////////////////////////////////////////////////////////////////
// PUBLIC METHODS
////////////////////////////////////////////////////////////////////////
public LayoutState layoutHyperbolic
(H3Graph graph, boolean useExtendedPrecision)
{
long startTime = 0;
if (DEBUG_PRINT)
{
startTime = System.currentTimeMillis();
System.out.println("layoutHyperbolic.begin[" + startTime +"]");
}
HyperbolicLayout retval = null;
int numNodes = graph.getNumNodes();
if (numNodes > 0)
{
retval = new HyperbolicLayout(numNodes);
computeRadii(graph, retval);
computeAngles(graph, retval);
if (useExtendedPrecision)
{
computeCoordinatesMP(graph, retval);
}
else
{
computeCoordinates(graph, retval);
}
}
if (DEBUG_PRINT)
{
long stopTime = System.currentTimeMillis();
long duration = stopTime - startTime;
System.out.println("layoutHyperbolic.end[" + stopTime + "]");
System.out.println("layoutHyperbolic.time[" + duration + "]");
}
return retval;
}
// Try to calculate the coordinates of the nodes using extended precision.
// Assumes the radii and angles have been computed already.
public void retryHyperbolicLayout(H3Graph graph, LayoutState state)
{
long startTime = 0;
if (DEBUG_PRINT)
{
startTime = System.currentTimeMillis();
System.out.println("retryHyperbolicLayout.begin[" + startTime+"]");
}
if (graph.getNumNodes() > 0)
{
HyperbolicLayout layout = (HyperbolicLayout)state;
computeCoordinatesMP(graph, layout);
}
if (DEBUG_PRINT)
{
long stopTime = System.currentTimeMillis();
long duration = stopTime - startTime;
System.out.println("retryHyperbolicLayout.end[" + stopTime + "]");
System.out.println("retryHyperbolicLayout.time[" + duration + "]");
}
}
public void layoutRandom(H3Graph graph)
{
Random random = new Random();
Point3d p = new Point3d();
for (int i = graph.getNumNodes() - 1; i >= 0; i--)
{
computeRandomPoint(random, p);
graph.setNodeLayoutCoordinates(i, p.x, p.y, p.z, 1.0);
}
}
////////////////////////////////////////////////////////////////////////
// PRIVATE METHODS (hyperbolic layout)
////////////////////////////////////////////////////////////////////////
private void computeRadii(H3Graph graph, HyperbolicLayout layout)
{
computeRadiiSubtree(graph, layout, graph.getRootNode());
}
private void computeRadiiSubtree(H3Graph graph,
HyperbolicLayout layout,
int node)
{
int childIndex = graph.getNodeChildIndex(node);
int nontreeIndex = graph.getNodeNontreeIndex(node);
if (childIndex < nontreeIndex)
{
double HA_p = 0.0;
while (childIndex < nontreeIndex)
{
int child = graph.getLinkDestination(childIndex);
computeRadiiSubtree(graph, layout, child);
HA_p += computeCircleArea(layout.radius[child]);
++childIndex;
}
HA_p *= HEMISPHERE_AREA_SCALE;
layout.radius[node] = computeRadius(HA_p);
}
else
{
layout.radius[node] = LEAF_RADIUS;
}
}
private static double computeCircleArea(double r)
{
return H3Math.TWO_PI * (H3Math.cosh(r / K) - 1.0);
}
private static double computeRadius(double area)
{
return K * H3Math.asinh(Math.sqrt(area / (H3Math.TWO_PI * K * K)));
}
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
private void computeAngles(H3Graph graph, HyperbolicLayout layout)
{
Children children = new Children();
computeAnglesSubtree(graph, layout, children, graph.getRootNode(), 0);
}
private void computeAnglesSubtree(H3Graph graph,
HyperbolicLayout layout,
Children children,
int node, int level)
{
int childIndex = graph.getNodeChildIndex(node);
int nontreeIndex = graph.getNodeNontreeIndex(node);
if (childIndex < nontreeIndex)
{
// We must handle all the children first (or last), so that
// there won't be any contention over the use of {children}.
{
for (int i = childIndex; i < nontreeIndex; i++)
{
int child = graph.getLinkDestination(i);
computeAnglesSubtree
(graph, layout, children, child, level + 1);
}
}
children.clear();
{
for (int i = childIndex; i < nontreeIndex; i++)
{
int child = graph.getLinkDestination(i);
children.add(child, layout.radius[child]);
}
}
children.sort();
//computeAnglesNode(graph, layout, children, node);
computeAnglesNode2(graph, layout, children, node, level);
}
}
private void computeAnglesNode(H3Graph graph,
HyperbolicLayout layout,
Children children,
int node)
{
double rp = layout.radius[node];
// Position the first child at the pole.
Children.Child first = children.getChild(0);
layout.theta[first.node] = 0.0;
layout.phi[first.node] = 0.0;
// Position the remaining children.
int numChildren = children.getNumChildren();
if (numChildren > 1)
{
Children.Child second = children.getChild(1);
// deltaPhi: half the phi angle subtended by the current band
// phi: the phi of the center of the current band
// theta: the theta of the beginning of the current child
double deltaPhi = computeDeltaPhi(second.radius, rp);
double phi = computeDeltaPhi(first.radius, rp) + deltaPhi;
double theta = computeDeltaTheta(second.radius, rp, phi);
layout.theta[second.node] = theta;
layout.phi[second.node] = phi;
theta += theta; // advance just past 2nd child
for (int i = 2; i < numChildren; i++)
{
Children.Child child = children.getChild(i);
double deltaTheta = computeDeltaTheta(child.radius, rp, phi);
double centerTheta = theta + deltaTheta;
if (centerTheta + deltaTheta > H3Math.TWO_PI)
{
phi += deltaPhi; // + half the angle of the current band
deltaPhi = computeDeltaPhi(child.radius, rp);
phi += deltaPhi; // + half the angle of the next band
deltaTheta = computeDeltaTheta(child.radius, rp, phi);
centerTheta = deltaTheta;
}
layout.theta[child.node] = centerTheta;
layout.phi[child.node] = phi;
theta = centerTheta + deltaTheta;
}
}
}
private void computeAnglesNode2(H3Graph graph,
HyperbolicLayout layout,
Children children,
int node, int level)
{
final boolean SUBTREE_3_AVG = false;
final boolean SUBTREE_3_CENTROID = true;
final boolean SUBTREE_MORE_4 = true;
final boolean SUBTREE_MORE_4_AVG = false;
final boolean SUBTREE_MORE_4_CENTROID = true;
double rp = layout.radius[node];
// Position the first child at the pole.
Children.Child first = children.getChild(0);
layout.theta[first.node] = 0.0;
layout.phi[first.node] = 0.0;
// Position the remaining children.
int numChildren = children.getNumChildren();
if (numChildren == 2)
{
Children.Child second = children.getChild(1);
double firstPhi = computeDeltaPhi(first.radius, rp);
double secondPhi = computeDeltaPhi(second.radius, rp);
double totalPhi = firstPhi + secondPhi;
layout.phi[first.node] = totalPhi - firstPhi;
layout.phi[second.node] = totalPhi - secondPhi;
double twist = ((level % 2) == 0 ? 0.0 : Math.PI / 2.0);
layout.theta[first.node] = twist;
layout.theta[second.node] = Math.PI + twist;
}
else if (SUBTREE_3_AVG && numChildren == 3)
{
Children.Child second = children.getChild(1);
Children.Child third = children.getChild(2);
double dp1 = computeDeltaPhi(first.radius, rp);
double dp2 = computeDeltaPhi(second.radius, rp);
double dp3 = computeDeltaPhi(third.radius, rp);
// FUDGE * ((dp1 + dp2) / 2 + (dp1 + dp3) / 2) / 2; etc. for rest
final double FUDGE = 1.0;
double firstPhi = FUDGE * 0.25 * (2.0 * dp1 + dp2 + dp3);
double secondPhi = FUDGE * 0.25 * (2.0 * dp2 + dp3 + dp1);
double thirdPhi = FUDGE * 0.25 * (2.0 * dp3 + dp1 + dp2);
double dt1 = computeDeltaTheta(first.radius, rp, dp1);
double dt2 = computeDeltaTheta(second.radius, rp, dp2);
double dt3 = computeDeltaTheta(third.radius, rp, dp3);
double excessTheta = 2.0 * (Math.PI - dt1 - dt2 - dt3) / 3.0;
double firstTheta = dt1;
double secondTheta = firstTheta + dt1 + excessTheta + dt2;
double thirdTheta = secondTheta + dt2 + excessTheta + dt3;
layout.phi[first.node] = firstPhi;
layout.theta[first.node] = firstTheta;
layout.phi[second.node] = secondPhi;
layout.theta[second.node] = secondTheta;
layout.phi[third.node] = thirdPhi;
layout.theta[third.node] = thirdTheta;
}
else if (SUBTREE_3_CENTROID && numChildren == 3)
{
Children.Child second = children.getChild(1);
Children.Child third = children.getChild(2);
m_ternaryLayout.computeLayout(rp, first.radius, second.radius,
third.radius);
layout.theta[first.node] = m_ternaryLayout.getThetaA();
layout.phi[first.node] = m_ternaryLayout.getPhiA();
layout.theta[second.node] = m_ternaryLayout.getThetaB();
layout.phi[second.node] = m_ternaryLayout.getPhiB();
layout.theta[third.node] = m_ternaryLayout.getThetaC();
layout.phi[third.node] = m_ternaryLayout.getPhiC();
}
else if (numChildren == 4)
{
Children.Child second = children.getChild(1);
Children.Child third = children.getChild(2);
Children.Child fourth = children.getChild(3);
double dp1 = computeDeltaPhi(first.radius, rp);
double dp2 = computeDeltaPhi(second.radius, rp);
double dp3 = computeDeltaPhi(third.radius, rp);
double dp4 = computeDeltaPhi(fourth.radius, rp);
// FUDGE * ((dp1 + dp2)/2 + (dp1 + dp3)/2 + (dp1 + dp4)/2) / 3; etc
final double FUDGE = 1.0;
double firstPhi = FUDGE * 0.1667 * (3.0 * dp1 + dp2 + dp3 + dp4);
double secondPhi = FUDGE * 0.1667 * (3.0 * dp2 + dp3 + dp4 + dp1);
double thirdPhi = FUDGE * 0.1667 * (3.0 * dp3 + dp4 + dp1 + dp2);
double fourthPhi = FUDGE * 0.1667 * (3.0 * dp4 + dp1 + dp2 + dp3);
double dt1 = computeDeltaTheta(first.radius, rp, dp1);
double dt2 = computeDeltaTheta(second.radius, rp, dp2);
double dt3 = computeDeltaTheta(third.radius, rp, dp3);
double dt4 = computeDeltaTheta(fourth.radius, rp, dp4);
double excessTheta = 2.0 * (Math.PI - dt1 - dt2 - dt3 - dt4) / 4.0;
double firstTheta = dt1;
double secondTheta = firstTheta + dt1 + excessTheta + dt2;
double thirdTheta = secondTheta + dt2 + excessTheta + dt3;
double fourthTheta = thirdTheta + dt3 + excessTheta + dt4;
layout.phi[first.node] = firstPhi;
layout.theta[first.node] = firstTheta;
layout.phi[second.node] = secondPhi;
layout.theta[second.node] = secondTheta;
layout.phi[third.node] = thirdPhi;
layout.theta[third.node] = thirdTheta;
layout.phi[fourth.node] = fourthPhi;
layout.theta[fourth.node] = fourthTheta;
}
else if (SUBTREE_MORE_4 && numChildren > 4)
{
double capBottomPhi = 0.0;
if (SUBTREE_MORE_4_AVG)
{
Children.Child second = children.getChild(1);
Children.Child third = children.getChild(2);
double dp1 = computeDeltaPhi(first.radius, rp);
double dp2 = computeDeltaPhi(second.radius, rp);
double dp3 = computeDeltaPhi(third.radius, rp);
// FUDGE * ((dp1 + dp2) / 2 + (dp1 + dp3) / 2) / 2; etc.
final double FUDGE = 1.0;
double firstPhi = FUDGE * 0.25 * (2.0 * dp1 + dp2 + dp3);
double secondPhi = FUDGE * 0.25 * (2.0 * dp2 + dp3 + dp1);
double thirdPhi = FUDGE * 0.25 * (2.0 * dp3 + dp1 + dp2);
double dt1 = computeDeltaTheta(first.radius, rp, dp1);
double dt2 = computeDeltaTheta(second.radius, rp, dp2);
double dt3 = computeDeltaTheta(third.radius, rp, dp3);
double excessTheta = 2.0 * (Math.PI - dt1 - dt2 - dt3) / 3.0;
double firstTheta = dt1;
double secondTheta = firstTheta + dt1 + excessTheta + dt2;
double thirdTheta = secondTheta + dt2 + excessTheta + dt3;
layout.phi[first.node] = firstPhi;
layout.theta[first.node] = firstTheta;
layout.phi[second.node] = secondPhi;
layout.theta[second.node] = secondTheta;
layout.phi[third.node] = thirdPhi;
layout.theta[third.node] = thirdTheta;
capBottomPhi = Math.max(firstPhi + dp1,
Math.max(secondPhi + dp2,
thirdPhi + dp3));
}
else if (SUBTREE_MORE_4_CENTROID)
{
Children.Child second = children.getChild(1);
Children.Child third = children.getChild(2);
m_ternaryLayout.computeLayout(rp, first.radius, second.radius,
third.radius);
layout.theta[first.node] = m_ternaryLayout.getThetaA();
layout.phi[first.node] = m_ternaryLayout.getPhiA();
layout.theta[second.node] = m_ternaryLayout.getThetaB();
layout.phi[second.node] = m_ternaryLayout.getPhiB();
layout.theta[third.node] = m_ternaryLayout.getThetaC();
layout.phi[third.node] = m_ternaryLayout.getPhiC();
double dp1 = computeDeltaPhi(first.radius, rp);
double dp2 = computeDeltaPhi(second.radius, rp);
double dp3 = computeDeltaPhi(third.radius, rp);
capBottomPhi = Math.max(layout.phi[first.node] + dp1,
Math.max(layout.phi[second.node] + dp2,
layout.phi[third.node] + dp3));
}
Children.Child fourth = children.getChild(3);
// deltaPhi: half the phi angle subtended by the current band
// phi: the phi of the center of the current band
// theta: the theta of the beginning of the current child
double deltaPhi = computeDeltaPhi(fourth.radius, rp);
double phi = capBottomPhi + deltaPhi;
double theta = computeDeltaTheta(fourth.radius, rp, phi);
layout.theta[fourth.node] = theta;
layout.phi[fourth.node] = phi;
theta += theta; // advance just past 4th child
boolean positiveTheta = false;
int firstChildInBand = 3;
for (int i = 4; i < numChildren; i++)
{
Children.Child child = children.getChild(i);
double deltaTheta = computeDeltaTheta(child.radius, rp, phi);
double centerTheta = theta + deltaTheta;
if (centerTheta + deltaTheta > H3Math.TWO_PI)
{
// Evenly space out the children in the current band.
double excess = H3Math.TWO_PI - theta;
spreadChildrenEvenly2(layout, children,
firstChildInBand, i, excess,
positiveTheta);
// Move to the next band. - - - - - - - - - - - - - - - -
phi += deltaPhi; // + half the angle of the current band
deltaPhi = computeDeltaPhi(child.radius, rp);
phi += deltaPhi; // + half the angle of the next band
deltaTheta = computeDeltaTheta(child.radius, rp, phi);
centerTheta = deltaTheta;
firstChildInBand = i;
positiveTheta = !positiveTheta;
}
layout.theta[child.node] = centerTheta;
layout.phi[child.node] = phi;
theta = centerTheta + deltaTheta;
}
// Evenly space out the children in the last band.
double excess = H3Math.TWO_PI - theta;
spreadChildrenEvenly2(layout, children,
firstChildInBand, numChildren - 1, excess,
positiveTheta);
}
else if (!SUBTREE_MORE_4 && numChildren > 4)
{
Children.Child second = children.getChild(1);
// deltaPhi: half the phi angle subtended by the current band
// phi: the phi of the center of the current band
// theta: the theta of the beginning of the current child
double deltaPhi = computeDeltaPhi(second.radius, rp);
double phi = computeDeltaPhi(first.radius, rp) + deltaPhi;
double theta = computeDeltaTheta(second.radius, rp, phi);
layout.theta[second.node] = theta;
layout.phi[second.node] = phi;
theta += theta; // advance just past 2nd child
int firstChildInBand = 1;
for (int i = 2; i < numChildren; i++)
{
Children.Child child = children.getChild(i);
double deltaTheta = computeDeltaTheta(child.radius, rp, phi);
double centerTheta = theta + deltaTheta;
if (centerTheta + deltaTheta > H3Math.TWO_PI)
{
// Evenly space out the children in the current band.
double excess = H3Math.TWO_PI - theta;
spreadChildrenEvenly(layout, children,
firstChildInBand, i, excess);
// Move to the next band. - - - - - - - - - - - - - - - -
phi += deltaPhi; // + half the angle of the current band
deltaPhi = computeDeltaPhi(child.radius, rp);
phi += deltaPhi; // + half the angle of the next band
deltaTheta = computeDeltaTheta(child.radius, rp, phi);
centerTheta = deltaTheta;
firstChildInBand = i;
}
layout.theta[child.node] = centerTheta;
layout.phi[child.node] = phi;
theta = centerTheta + deltaTheta;
}
// Evenly space out the children in the last band.
double excess = H3Math.TWO_PI - theta;
spreadChildrenEvenly(layout, children,
firstChildInBand, numChildren - 1, excess);
}
}
private void spreadChildrenEvenly2(HyperbolicLayout layout,
Children children,
int first, int last,
double excess,
boolean positiveTheta)
{
int total = last - first + 1;
for (int i = 1; i < total; i++)
{
double delta = i * excess / total;
Children.Child child = children.getChild(first + i);
layout.theta[child.node] += delta;
if (false && !positiveTheta)
{
layout.theta[child.node] =
H3Math.TWO_PI - layout.theta[child.node];
}
}
}
private void spreadChildrenEvenly(HyperbolicLayout layout,
Children children,
int first, int last,
double excess)
{
int total = last - first + 1;
for (int i = 1; i < total; i++)
{
double delta = i * excess / total;
Children.Child child = children.getChild(first + i);
layout.theta[child.node] += delta;
}
}
private double computeDeltaTheta(double rn, double rp, double phi)
{
return Math.atan(H3Math.tanh(rn / K)
/ (H3Math.sinh(rp / K) * Math.sin(phi)));
}
private double computeDeltaPhi(double rj, double rp)
{
return Math.atan(H3Math.tanh(rj / K) / H3Math.sinh(rp / K));
}
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
private void computeCoordinates(H3Graph graph,
HyperbolicLayout layout)
{
// The root node is always positioned at the origin.
int rootNode = graph.getRootNode();
graph.setNodeLayoutCoordinates(rootNode, H3Transform.ORIGIN4);
computeCoordinatesSubtree(graph, layout, H3Transform.I4, rootNode);
}
private void computeCoordinatesSubtree(H3Graph graph,
HyperbolicLayout layout,
Matrix4d parentTransform,
int parent)
{
int childIndex = graph.getNodeChildIndex(parent);
int nontreeIndex = graph.getNodeNontreeIndex(parent);
if (childIndex < nontreeIndex)
{
double parentRadiusE =
H3Math.euclideanDistance(layout.radius[parent]);
double lastPhi = 0.0;
Matrix4d rotPhi = H3Transform.I4;
Point4d childCenterAbsolute = new Point4d();
Point4d childPoleAbsolute = new Point4d();
for (int i = childIndex; i < nontreeIndex; i++)
{
int child = graph.getLinkDestination(i);
double childRadiusE =
H3Math.euclideanDistance(layout.radius[child]);
double childPhi = layout.phi[child];
if (childPhi != lastPhi)
{
lastPhi = childPhi;
rotPhi = H3Transform.buildZRotation(childPhi);
}
Matrix4d rot = H3Transform.buildXRotation(layout.theta[child]);
rot.mul(rotPhi);
// compute child's center relative to parent's coord system
childCenterAbsolute.set(parentRadiusE, 0.0, 0.0, 1.0);
rot.transform(childCenterAbsolute);
// compute child's pole relative to parent's coordinate system
double childPoleE =
H3Math.euclideanDistance(layout.radius[parent]
+ layout.radius[child]);
childPoleAbsolute.set(childPoleE, 0.0, 0.0, 1.0);
rot.transform(childPoleAbsolute);
parentTransform.transform(childCenterAbsolute);
parentTransform.transform(childPoleAbsolute);
graph.setNodeLayoutCoordinates(child, childCenterAbsolute);
Matrix4d childTransform = H3Transform
.buildCanonicalOrientation(childCenterAbsolute,
childPoleAbsolute);
if (!ATTEMPT_EXTENDED || H3Math.isFinite(childTransform))
{
computeCoordinatesSubtree(graph, layout,
childTransform, child);
}
else
{
System.out.println("Switching to extended precision"
+ " for subtree at node " + child);
H3Point4d childCenterAbsoluteMP =
new H3Point4d(childCenterAbsolute);
H3Point4d childPoleAbsoluteMP =
new H3Point4d(childPoleAbsolute);
H3Matrix4d childTransformMP = H3Transform
.buildCanonicalOrientation(childCenterAbsoluteMP,
childPoleAbsoluteMP);
computeCoordinatesSubtreeMP(graph, layout,
childTransformMP, child);
}
}
}
}
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
private void computeCoordinatesMP(H3Graph graph,
HyperbolicLayout layout)
{
MPGlobal.setMaximumPrecision(new MPPrecision(30));
// The root node is always positioned at the origin.
int rootNode = graph.getRootNode();
graph.setNodeLayoutCoordinates(rootNode, H3Transform.ORIGIN4);
computeCoordinatesSubtreeMP
(graph, layout, H3Transform.I4_MP, rootNode);
}
private void computeCoordinatesSubtreeMP(H3Graph graph,
HyperbolicLayout layout,
H3Matrix4d parentTransform,
int parent)
{
int childIndex = graph.getNodeChildIndex(parent);
int nontreeIndex = graph.getNodeNontreeIndex(parent);
if (childIndex < nontreeIndex)
{
double parentRadiusE =
H3Math.euclideanDistance(layout.radius[parent]);
double lastPhi = 0.0;
Matrix4d rotPhi = H3Transform.I4;
Point4d childCenterAbsolute = new Point4d();
Point4d childPoleAbsolute = new Point4d();
Point4d p = new Point4d();
H3Point4d childCenterAbsoluteMP = new H3Point4d();
H3Point4d childPoleAbsoluteMP = new H3Point4d();
for (int i = childIndex; i < nontreeIndex; i++)
{
int child = graph.getLinkDestination(i);
double childRadiusE =
H3Math.euclideanDistance(layout.radius[child]);
double childPhi = layout.phi[child];
if (childPhi != lastPhi)
{
lastPhi = childPhi;
rotPhi = H3Transform.buildZRotation(childPhi);
}
Matrix4d rot = H3Transform.buildXRotation(layout.theta[child]);
rot.mul(rotPhi);
// compute child's center relative to parent's coord system
childCenterAbsolute.set(parentRadiusE, 0.0, 0.0, 1.0);
rot.transform(childCenterAbsolute);
// compute child's pole relative to parent's coordinate system
double childPoleE =
H3Math.euclideanDistance(layout.radius[parent]
+ layout.radius[child]);
childPoleAbsolute.set(childPoleE, 0.0, 0.0, 1.0);
rot.transform(childPoleAbsolute);
childCenterAbsoluteMP.set(childCenterAbsolute);
childPoleAbsoluteMP.set(childPoleAbsolute);
parentTransform.transform(childCenterAbsoluteMP);
parentTransform.transform(childPoleAbsoluteMP);
convertToDoubleCoordinates(p, childCenterAbsoluteMP);
graph.setNodeLayoutCoordinates(child, p);
H3Matrix4d childTransform = H3Transform
.buildCanonicalOrientation(childCenterAbsoluteMP,
childPoleAbsoluteMP);
computeCoordinatesSubtreeMP(graph, layout,
childTransform, child);
}
}
}
private void convertToDoubleCoordinates(Point4d lhs, H3Point4d rhs)
{
lhs.x = rhs.x.doubleValue();
lhs.y = rhs.y.doubleValue();
lhs.z = rhs.z.doubleValue();
lhs.w = rhs.w.doubleValue();
}
////////////////////////////////////////////////////////////////////////
// PRIVATE METHODS (random layout)
////////////////////////////////////////////////////////////////////////
// NOTE: The points generated by this algorithm aren't very uniformly
// distributed within the unit sphere (there is a concentration
// of points near the poles). However, it is good enough for
// our purposes.
private void computeRandomPoint(Random random, Point3d p)
{
double x = 2.0 * random.nextDouble() - 1.0; // -1.0 <= x <= 1.0
double y = 2.0 * random.nextDouble() - 1.0; // -1.0 <= y <= 1.0
y *= Math.sqrt(1.0 - x*x); // | y | <= sqrt(1-x^2)
double z = 2.0 * random.nextDouble() - 1.0; // -1.0 <= z <= 1.0
z *= Math.sqrt(1.0 - x*x - y*y); // | z | <= sqrt(1-x^2-y^2)
p.x = x;
p.y = y;
p.z = z;
}
////////////////////////////////////////////////////////////////////////
// PRIVATE FIELDS (all layouts)
////////////////////////////////////////////////////////////////////////
private static final boolean DEBUG_PRINT = true;
// Whether extended precision calculations should be tried automatically
// when needed. This value is set in the constructor.
private final boolean ATTEMPT_EXTENDED;
////////////////////////////////////////////////////////////////////////
// PRIVATE FIELDS (hyperbolic layout)
////////////////////////////////////////////////////////////////////////
// Some good combinations of HEMISPHERE_AREA_SCALE and LEAF_AREA:
// 6.0 & 0.1, 7.0 & 0.1, 7.0 & 0.005, 7.0 & 0.0025
//
// 7.0 & 0.0025 seems good for large trees (~100K nodes)
// 6.0 & 0.0025 also seems good for large trees, though bushier
// 5.0 & 0.0025 seems tolerable for large trees and very bushy
private static final double K = 2.0;
private static final double HEMISPHERE_AREA_SCALE = 7.2;
private static final double LEAF_AREA = 0.005;
private static final double LEAF_RADIUS = computeRadius(LEAF_AREA);
private TernaryTreeLayout m_ternaryLayout = new TernaryTreeLayout();
////////////////////////////////////////////////////////////////////////
// PRIVATE CLASSES (hyperbolic layout)
////////////////////////////////////////////////////////////////////////
private class TernaryTreeLayout
{
public void computeLayout(double rp, double rA, double rB, double rC)
{
m_radiusParent = rp;
m_radiusA = rA;
m_radiusB = rB;
m_radiusC = rC;
computeEuclideanCenters();
computeCircleCentroid();
computeHyperbolicAngles();
}
public double getThetaA()
{
return m_thetaA;
}
public double getThetaB()
{
return m_thetaB;
}
public double getThetaC()
{
return m_thetaC;
}
public double getPhiA()
{
return m_phiA;
}
public double getPhiB()
{
return m_phiB;
}
public double getPhiC()
{
return m_phiC;
}
private void computeHyperbolicAngles()
{
final double phiRadiusScale = 1.0;
// - - - - - - - - - - - - - - - - - - - - -
double dC = m_center.distance(m_centerC);
double dEC = H3Math.euclideanDistance(dC);
m_phiC = 2.0 * computeDeltaPhi(phiRadiusScale * dEC,
m_radiusParent);
m_thetaC = 0.0;
// - - - - - - - - - - - - - - - - - - - - -
double dB = m_center.distance(m_centerB);
double dEB = H3Math.euclideanDistance(dB);
m_phiB = 2.0 * computeDeltaPhi(phiRadiusScale * dEB,
m_radiusParent);
m_thetaB = computeAngle(dB, dC, m_radiusB + m_radiusC);
// - - - - - - - - - - - - - - - - - - - - -
double dA = m_center.distance(m_centerA);
double dEA = H3Math.euclideanDistance(dA);
m_phiA = 2.0 * computeDeltaPhi(phiRadiusScale * dEA,
m_radiusParent);
m_thetaA = -computeAngle(dA, dC, m_radiusA + m_radiusC);
}
private void computeCircleCentroid()
{
double mA = m_radiusA * m_radiusA;
double mB = m_radiusB * m_radiusB;
double mC = m_radiusC * m_radiusC;
double total = mA + mB + mC;
double x = mA * m_centerA.x + mB * m_centerB.x + mC * m_centerC.x;
double y = mA * m_centerA.y + mB * m_centerB.y + mC * m_centerC.y;
m_center.x = x / total;
m_center.y = y / total;
m_center.z = 0.0;
}
private void computeEuclideanCenters()
{
double a = m_radiusB + m_radiusC;
double b = m_radiusA + m_radiusC;
double c = m_radiusA + m_radiusB;
double x = (b * b + c * c - a * a) / (2.0 * b);
double y = Math.sqrt(c * c - x * x);
m_centerA.x = 0.0;
m_centerA.y = 0.0;
m_centerA.z = 0.0;
m_centerB.x = x;
m_centerB.y = y;
m_centerB.z = 0.0;
m_centerC.x = b;
m_centerC.y = 0.0;
m_centerC.z = 0.0;
}
private void makeAcute()
{
double a = m_radiusB + m_radiusC;
double b = m_radiusA + m_radiusC;
double c = m_radiusA + m_radiusB;
double a2 = a * a;
double b2 = b * b;
double c2 = c * c;
if (a2 + b2 < c2)
{