Surfacemw

Surfacemw is a term used in computational geometry and computer graphics to denote a framework and set of software tools for computing and analyzing the mean width of 3D surfaces. The mean width is a scalar descriptor that captures the size of a body by averaging its width in all directions, and is invariant under rotation.

Surfacemw provides data-structure-agnostic methods for triangulated meshes, point clouds, and voxelized surfaces. It defines a direction sampling strategy on the unit sphere, computes the distance between parallel supporting planes along each direction, and aggregates results to produce the mean width, width distribution, and anisotropy measures. It also supports visualization of width fields on surfaces.

Implementation and usage: It is implemented as a library with a modular API. The core is written in C++ with bindings for Python and other languages, enabling integration into analysis pipelines. It can work with common file formats such as OBJ or PLY, and can export results to JSON, CSV, or visualization-friendly formats.

Applications and limitations: Surfacemw is used in shape analysis, quality control in manufacturing, morphometrics in biology, and digital heritage. Limitations include sensitivity to sampling density of directions and noise in data; results are statistical descriptors rather than exact geometric invariants.

See also: mean width, convex geometry, surface analysis, shape descriptors.