Catmull-Clark Subdivision Algorithm

The Catmull-Clark algorithm is a subdivision surface method in three-dimensional computer graphics that Edwin Catmull and Jim Clark developed in 1978 as a way to extend bicubic uniform B-spline surfaces to meshes of arbitrary topology, not just to the regular rectangular grids that ordinary B-spline surfaces require. Starting from a polygonal mesh, each refinement step computes a new face point for every face as the average of that face's original vertices, a new edge point for every edge as the average of the edge's two endpoints and the face points of its two neighboring faces, and a new position for every original vertex from a weighted average of the surrounding face points, edge midpoints and the vertex's own original position; repeating this process produces a sequence of meshes made entirely of quadrilaterals that grows progressively smoother and converges toward a bicubic B-spline surface. The weights used in the vertex-repositioning step were chosen mainly because they produced visually pleasing results rather than being derived from a theoretical requirement, and in 2005 the Academy of Motion Picture Arts and Sciences recognized Catmull, together with Tony DeRose and Jos Stam, with a Technical Achievement Award for the invention and application of subdivision surfaces in character animation.