Subdivision Surface
A subdivision surface ( German: subdivision surface ) in the computer graphics, a smooth (in the first or multiple derivation continuous) surface that has been output from a grid ( also referred to as control mesh ) produced. A subdivision surface is originally defined as the limit ( limit ) an infinite, recursive refinement scheme. This refinement scheme is also called a subdivision scheme; the limit as the limit surface.
Development
Refinement schemes
Refinement schemes can be broadly classified into two categories: interpolating and approximating. Interpolating schemes are used when the limit surface will interpolate the points of the starting grid. Approximating schemes not afford this; the limit surface may come to lie inside or outside the starting grid. At appoximierenden schemes is often the starting grid, the convex hull of the limit surface. In general, most of the known approximating schemes produce more aesthetically pleasing Limes surfaces.
The other distinguishing criterion is also used, the categorization in Schemeta that exist only on lattices of polygons with a certain score. Some such schemes require, for example, an output grid that consists only of triangles or quadrilaterals.
Many schemes are also defined on manifold outlet grilles.
Approximating schemes
Approximating thinks that the limit surface approximates the output grid ( approximate ) and the newly generated points at each Rekursionschritt usually do not lie on the limit surface. Examples of approximating schemes are:
- Catmull -Clark
- Doo - Sabin
- Loop
- Mid- Edge
- V3
Interpolating schemes
Interpolating means that the output grid points and the points through each recursion step the newly generated always lie on the limit surface. Examples of interpolating schemes are:
- Butterfly Subdivision Surfaces: The butterfly subdivision surface is an interpolating subdivision scheme for triangle meshes. This new points and edges are generated to refine the network per iteration for each triangle.
- Kobbelt