Loop subdivision surface

In computer graphics, the Loop method for subdivision surfaces is an approximating subdivision scheme developed by Charles Loop in 1987 for triangular meshes. Prior methods, namely Catmull-Clark and Doo-Sabin, 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.

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Subdivision surface derived from a triangular mesh

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

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• Geodesic polyhedron
• Catmull-Clark subdivision surface
• Doo-Sabin subdivision surface

References

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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.