Loop subdivision surface

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Loop subdivision of an icosahedron
Loop subdivision of an icosahedron; refinement steps zero, one, and two

In computer graphics, the Loop method for subdivision surfaces is an approximating subdivision scheme developed by Charles Loop in 1987 for triangular meshes.[1] Prior methods, namely Catmull-Clark[2] and Doo-Sabin,[3] focused on quad meshes.

Loop subdivision surfaces are defined recursively, dividing each triangle into four smaller ones. The method is based on a quartic box spline. It generates C2 continuous limit surfaces everywhere except at extraordinary vertices, where they are C1 continuous.[4]

See also

References

  1. ^ Loop, Charles (1987). Smooth Subdivision Surfaces Based on Triangles (PDF). Retrieved 8 March 2026.
  2. ^ Catmull, E.; Clark, J. (November 1978). "Recursively generated B-spline surfaces on arbitrary topological meshes". Computer-Aided Design. 10 (6): 350–355. doi:10.1016/0010-4485(78)90110-0.
  3. ^ Doo, D.; Sabin, M. (November 1978). "Behaviour of recursive division surfaces near extraordinary points". Computer-Aided Design. 10 (6): 356–360. doi:10.1016/0010-4485(78)90111-2.
  4. ^ Wiliam A. P. Smith (2020). "6. 3D Data Representation, Storage and Processing". 3D Imaging, Analysis and Applications (2nd 2020 ed.). Springer International Publishing. pp. 298–299. ISBN 978-3030440701.

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