Mesh Triangulation

This example demonstrates how to perform constrained and refined Delaunay triangulation using COMPAS CGAL.

Key Features:

  • Creating polygonal boundary and holes

  • Conforming Delaunay triangulation

  • Refined Delaunay meshing with size constraints

  • Side-by-side visualization of different triangulation methods

../_images/example_triangulation.png 
from compas.datastructures import Mesh
from compas.geometry import Polygon
from compas.geometry import Translation
from compas_viewer import Viewer
from line_profiler import profile

from compas_cgal.triangulation import conforming_delaunay_triangulation
from compas_cgal.triangulation import refined_delaunay_mesh


@profile
def main():
    """Triangulate a mesh with holes."""

    boundary = Polygon.from_sides_and_radius_xy(64, 4)

    hole = Polygon.from_sides_and_radius_xy(128, 1)

    hole1 = hole.transformed(Translation.from_vector([2, 0, 0]))
    hole2 = hole.transformed(Translation.from_vector([-2, 0, 0]))
    hole3 = hole.transformed(Translation.from_vector([0, 2, 0]))
    hole4 = hole.transformed(Translation.from_vector([0, -2, 0]))

    holes = [hole1, hole2, hole3, hole4]

    V, F = conforming_delaunay_triangulation(
        boundary,
        holes=holes,
    )

    cdt = Mesh.from_vertices_and_faces(V, F)

    V, F = refined_delaunay_mesh(
        boundary,
        holes=holes,
        maxlength=0.5,
        is_optimized=True,
    )

    rdm = Mesh.from_vertices_and_faces(V, F)

    return cdt, rdm


cdt, rdm = main()

# ==============================================================================
# Visualize
# ==============================================================================

viewer = Viewer()

viewer.renderer.camera.target = [0, 0, 0]
viewer.renderer.camera.position = [0, -1, 13]

viewer.scene.add(cdt.transformed(Translation.from_vector([-5, 0, 0])))
viewer.scene.add(rdm.transformed(Translation.from_vector([+5, 0, 0])))

viewer.show()