Feature: Curve-mesh intersection and cutting

[ZigaSajovic]

Given a sequence of points on a mesh, connecting them with straight segments doesn't produce a curve that lies on the surface. We need curves that actually follow the mesh.

Intersect module

Project a path onto the mesh surface:

// points may not be exactly on the surface due to numerics
auto surface_curve = tf::make_surface_curve(mesh.polygons(), path_points);

Points are projected onto the mesh first. New points are inserted where the path crosses mesh edges, so that every segment lies entirely within a face. A single mesh edge can have many crossings—naive approaches like scalar field cutting (how VTK does it) don't handle this.

Cut module

Once we have a surface curve, two operations:

Embed the curve into mesh topology (faces split along curve, curve becomes edges):

auto [result_mesh, labels] = tf::embedded_curve(mesh.polygons(), path_points);

Cut the mesh along the curve, classifying regions as inside/outside:

// closed curve defines inside/outside
auto [result_mesh, labels] = tf::cut_by_curve(mesh.polygons(), path_points);

// labels: 0 = outside, 1 = inside (relative to curve winding)

Similar pattern to embedded_isocurves and make_isobands.

Self-intersections

Surface curves often self-intersect after embedding. Should offer ear clipping to remove the loops—these are usually small unintended artifacts.