Exact Geodesic Distance from a Surface Point

The exact backend computes the polyhedral geodesic distance from a source located anywhere on the mesh surface. This compact example places one source at the centroid of a face, colors the mesh by distance, and draws distance isolines.

The source is passed to exact_geodesic_distances_from_points, demonstrating the point-source API without snapping the source to a mesh vertex. The red isolines are extracted from the resulting vertex scalar field with isolines.

What "exact" means here

Exact refers to the algorithm, not to the arithmetic. The shortest path across the polyhedron is computed without algorithmic approximation — no time step, no diffusion, and no dependence on triangle quality — but it is evaluated in double precision under CGAL's Exact_predicates_inexact_constructions_kernel. Geodesic distance is a construction, built from unfoldings and square roots, so the returned numbers carry ordinary floating-point error.

from pathlib import Path

from compas.colors import Color
from compas.colors import ColorMap
from compas.datastructures import Mesh
from compas.geometry import Polyline
from compas_viewer import Viewer
from compas_viewer.config import Config

from compas_cgal.geodesics import exact_geodesic_distances_from_points
from compas_cgal.isolines import isolines

mesh = Mesh.from_off(Path(__file__).parent.parent.parent / "data" / "elephant.off")
mesh.quads_to_triangles()

source = mesh.face_centroid(0)
distances = exact_geodesic_distances_from_points(mesh, [source])
polylines = isolines(mesh, distances, n=10, resample=False)

cmap = ColorMap.from_two_colors(Color.blue(), Color.red())
colors = {vertex: cmap(d, minval=distances.min(), maxval=distances.max()) for vertex, d in zip(mesh.vertices(), distances)}

config = Config()
config.camera.position = [0.0, -1.25, 0.6]
config.camera.target = [0.0, 0.0, 0.0]
config.renderer.show_grid = False
viewer = Viewer(config=config)
viewer.scene.add(mesh, use_vertexcolors=True, vertexcolor=colors, show_lines=False)
viewer.scene.add(source, pointcolor=Color.black(), pointsize=20)
for polyline in polylines:
    viewer.scene.add(Polyline(polyline), linecolor=Color.black(), lineswidth=5)
viewer.show()