pointinsimplex
Pointinsimplex is a term that appears primarily in computational geometry and numerical analysis, referring to a simple algorithmic process for determining whether a given point lies within a simplex in a multidimensional space. A simplex is the generalization of a triangle or tetrahedron to arbitrary dimensions; in n dimensions it is the convex hull of n+1 affinely independent points. The point‑in‑simplex test is fundamental for mesh generation, finite element analysis, and collision detection.
The most common implementation of pointinsimplex evaluates barycentric coordinates. For a simplex defined by vertices v0,
In computer graphics, pointinsimplex tests enable texture mapping and rendering by determining which triangle or tetrahedron
The algorithm’s complexity is linear in the number of dimensions, making it efficient for high‑dimensional problems