Geometry processing

branch of mathematics dealing with functions and geometric structures on differentiable manifolds

thumb|upright=0.65|The Klein bottle immersed in three-dimensional space

parametric system of coordinates

branch of computer science

notion in topological vector spaces

topological property

set of data points in three-dimensional space

set of edges, vertices, and polygons which define a 3D model's shape

study of manifolds and maps between them, particularly embeddings of one manifold into another

Type of geometry processing

polygon mesh composed of triangles

analog of the continuous Laplace operator

concepts from applied mathematics, computer science and engineering to design efficient algorithms for complex 3D models.

infinitesimal version of a Lie groupoid: manifold M with vector bundle E, vector bundle map ρ: E→TM, and a Lie bracket on sections of E, so that [s,ft] = (ρ(s)f)t+f[s,t] for any function f: M→ℝ and sections s, t of E

surface in Euclidean space described by an equation