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 (1978), focused on quad meshes.

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

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.

Applications

Geologists have applied Loop subdivision surfaces to model erosion on mountain faces, specifically in the Appalachians.

See also

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

References

• Charles Loop: Smooth Subdivision Surfaces Based on Triangles, M.S. Mathematics thesis, University of Utah, 1987 (pdf).
• Jos Stam: Evaluation of Loop Subdivision Surfaces, Computer Graphics Proceedings ACM SIGGRAPH 1998, (pdf, downloadable eigenstructures).
• Antony Pugh, Polyhedra: a visual approach, 1976, Chapter 6. The Geodesic Polyhedra of R. Buckminster Fuller and Related Polyhedra