Geometry and mesh algorithms

Components

1. 2D Delaunay triangulation by Bowyer-Watson

   delaunay_bowyer_watson

   Triangulate 2D points so that no point lies inside any triangle's circumcircle, using Bowyer-Watson insertion with exact fallback predicates.

   Runs with

   Python 3.10 or later

   Entry points

   delaunay, random_points, triangulation_mesh, build, main

   Code moduleMIT10 files, 215.8 KBreads files, runs commands, writes files

2. 3D convex hull by quickhull

   quickhull_3d

   Compute the convex hull of 3D points as a closed mesh with outward faces, merging coplanar triangles into polygons.

   Runs with

   Python 3.10 or later

   Entry points

   convex_hull, sphere_points, random_points, build, main

   Code moduleMIT10 files, 198.5 KBreads files, runs commands, writes files

3. Ramer-Douglas-Peucker polyline simplification

   douglas_peucker

   Simplify 2D or 3D polylines by keeping only points farther than a tolerance from the simplified line, with a measure of the largest deviation.

   Runs with

   Python 3.10 or later

   Entry points

   simplify, max_deviation, demo_curve, build, main

   Code moduleMIT10 files, 300.3 KBreads files, runs commands, writes files

4. Polygon offset with miter, round or bevel joins

   polygon_offset_2d

   Grow or shrink a simple 2D polygon by a distance with miter, round or bevel joins, refusing offsets that would make it cross itself.

   Runs with

   Python 3.10 or later

   Entry points

   offset_polygon, build, main

   Code moduleMIT10 files, 171.5 KBreads files, runs commands, writes files

5. Catmull-Clark subdivision surface

   catmull_clark_subdivision

   Smooth a polygon cage into a quad mesh by Catmull-Clark subdivision, with B-spline boundary rules and fixed boundary corners.

   Runs with

   Python 3.10 or later

   Entry points

   catmull_clark, cage, build, main

   Code moduleMIT10 files, 226.6 KBreads files, runs commands, writes files

6. Cubic Bezier evaluation, arc length and resampling

   bezier_curve_arc_length

   Evaluate and split cubic Bezier curves by de Casteljau, measure arc length by Gauss-Legendre quadrature and resample paths at even arc-length spacing.

   Runs with

   Python 3.10 or later

   Entry points

   bezier_point, bezier_derivative, split_bezier, arc_length, length_table, parameter_at_length, resample_by_length, demo_path, build, main

   Code moduleMIT10 files, 231.1 KBreads files, runs commands, writes files

7. NURBS curves with exact circles and conics

   nurbs_curve

   Evaluate rational B-spline (NURBS) curves in homogeneous coordinates, with the exact nine-point circle and single-span conic arcs.

   Runs with

   Python 3.10 or later

   Entry points

   nurbs_point, circle, conic_arc, sample_nurbs, build, main

   Code moduleMIT10 files, 249.7 KBreads files, runs commands, writes files

8. Lathe revolution with partial angles

   lathe_revolve

   Revolve an (r, y) profile around the Y axis, fully or through a partial angle with flat cut faces, and compute the exact volume of the polygonal solid.

   Runs with

   Python 3.10 or later

   Entry points

   demo_profile, lathe, revolved_volume, build, main

   Code moduleMIT10 files, 237.5 KBreads files, runs commands, writes files

9. Involute spur gear

   involute_spur_gear

   Generate a spur gear whose tooth flanks are true involutes of the base circle, sized by module, tooth count and pressure angle, extruded around a bore.

   Runs with

   Python 3.10 or later

   Entry points

   involute_function, gear_radii, gear_profile, spur_gear, build, main

   Code moduleMIT10 files, 269.4 KBreads files, runs commands, writes files

10. Conway polyhedron operators

    conway_polyhedron_operators

    Build polyhedra from Conway notation: dual, ambo, kis, truncate, join, expand, ortho, gyro and snub applied to T, C, O, D, I, prisms and antiprisms, with planarizing relaxation.

    Runs with

    Python 3.10 or later

    Entry points

    seed, dual, ambo, kis, gyro, apply_operator, conway, build, main

    Code moduleMIT10 files, 181.8 KBreads files, runs commands, writes files

11. Platonic solids with exact edge length

    platonic_solids

    Generate the five regular convex polyhedra with exact coordinates and polygon faces found as supporting planes.

    Runs with

    Python 3.10 or later

    Entry points

    solid_vertices, hull_faces, platonic_solid, build, main

    Code moduleMIT10 files, 177.7 KBreads files, runs commands, writes files

12. Icosphere by recursive subdivision

    icosphere

    Build an evenly tessellated sphere by splitting a regular icosahedron into four triangles per face and projecting onto the sphere.

    Runs with

    Python 3.10 or later

    Entry points

    icosahedron, icosphere, main

    Code moduleMIT10 files, 200.3 KBreads files, runs commands, writes files