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subdivision surface
A subdivision surface, in the field of 3D computer graphics, is a method of representing a smooth surface via the specification of a coarser piecewise linear polygon mesh. The smooth surface can be calculated from the coarse mesh as the limit of a recursive process of subdividing each polygonal face into smaller faces that better approximate the smooth surface.
==Overview==
Subdivision surfaces are defined recursively. The process starts with a given 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. The positions of the new vertices in the mesh are computed based on the positions of nearby old vertices. In some refinement schemes, the positions of old vertices might also be altered (possibly based on the positions of new vertices).
This process produces a finer mesh than the original one, containing more polygonal faces. This resulting mesh can be passed through the same refinement scheme again and so on.
The limit subdivision surface is the surface produced from this process being iteratively applied infinitely many times. In practical use however, this algorithm is only applied a limited number of times. The limit surface can also be calculated directly for most subdivision surfaces using the technique of Jos Stam,〔 which eliminates the need for recursive refinement. Subdivision surfaces and T-Splines are competing technologies. Mathematically, subdivision surfaces are spline surfaces with singularities.〔
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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