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Simple subdivision of a cube up to 3 A tessellation pipeline using a subdivision method. A subdivision surface algorithm is recursive in nature. The process starts with a base level polygonal mesh. A refinement scheme is then applied to this mesh. This process takes that mesh and subdivides it, creating new vertices and new faces.
All vertices are valence-6 except the 12 centered at the original vertices which are valence 5 A geodesic polyhedron is a convex polyhedron made from triangles . They usually have icosahedral symmetry , such that they have 6 triangles at a vertex , except 12 vertices which have 5 triangles.
The doubly connected edge list (DCEL), also known as half-edge data structure, is a data structure to represent an embedding of a planar graph in the plane, and polytopes in 3D. This data structure provides efficient manipulation of the topological information associated with the objects in question (vertices, edges, faces).
A simple list of vertices, and a set of polygons that point to the vertices it uses. Winged-edge in which each edge points to two vertices, two faces, and the four (clockwise and counterclockwise) edges that touch them. Winged-edge meshes allow constant time traversal of the surface, but with higher storage requirements. Half-edge meshes
Blender supports Python scripting for the creation of custom tools, prototyping, importing/exporting from other formats, and task automation. This allows for integration with several external render engines through plugins/addons. Blender itself can also be compiled & imported as a python library for further automation and development.
Two vertices connected by a straight line become an edge. Three vertices, connected to each other by three edges, define a triangle , which is the simplest polygon in Euclidean space . More complex polygons can be created out of multiple triangles, or as a single object with more than 3 vertices.
Non-simple (or multiple) - has loops (hyperedges with a single vertex) or repeated edges, which means there can be two or more edges containing the same set of vertices. Simple - has no loops and no repeated edges.
graph join: . Graph with all the edges that connect the vertices of the first graph with the vertices of the second graph. It is a commutative operation (for unlabelled graphs); [2] graph products based on the cartesian product of the vertex sets: