alpha-wrap

A clean-room, CGAL-free and copyleft-free implementation of "Alpha Wrapping with an Offset" (Portaneri, Alliez, Hemmer, Birklein, Kobbelt — ACM TOG 2022).

Given an arbitrary input triangle soup (which may be non-manifold, self-intersecting, open, or defective) and two parameters — alpha (the carving-ball radius / level of detail) and offset (the distance-field iso-level / tightness) — it produces a surface mesh that is:

• watertight (closed),
• combinatorially 2-manifold,
• outward-oriented,
• strictly enclosing the input, with vertices ~offset outside it,
• bounded within an O(alpha+offset) band of the offset surface, every facet having circumradius ` soup = /* your input */; aw::WrapStats stats; aw::Mesh m = aw::alpha_wrap(soup, /alpha=/0.05, /offset=/0.002, /manifold=/true, &stats); // m.V : vertices, m.F : outward-oriented triangles

## Python bindings

Install from source (builds the C++ extension via scikit-build-core + nanobind;
needs a C++17 compiler, CMake ≥ 3.16, and network access on first build to fetch
the predicates):

```bash
pip install .
# or straight from GitHub:
pip install "git+https://github.com/alecjacobson/alpha-wrap.git"

Usage — wrap takes a triangle soup (vertices, faces) and returns the wrapped (V, F) as NumPy arrays (float64 and int32):

import numpy as np
import alpha_wrap

V = np.asarray(vertices, float)     # (N, 3)
F = np.asarray(faces, np.int64)     # (M, 3), may be non-manifold / defective

# relative parameters (fractions of the bounding-box diagonal)
W, G = alpha_wrap.wrap(V, F, alpha_rel=1/30, offset_rel=1/900)

# or absolute, and grab the internal stats
W, G, stats = alpha_wrap.wrap(V, F, alpha=0.05, offset=0.002,
                              manifold=True, return_stats=True)

Defaults follow the paper: alpha = diag/20, offset = alpha/30. The output is watertight, outward-oriented, 2-manifold, and strictly encloses the input.

Optional CGAL reference backend

The package can additionally expose alpha_wrap.wrap_cgal(...), which runs CGAL::alpha_wrap_3 for comparison/validation. It is off by default (it fetches Boost + CGAL at build time).