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Recursively Generated B-Spline Surfaces on Arbitrary Topological Meshes

Edwin Catmull, James Clark

Tech NoteAcademic10 descendantsSkinning

Defines Catmull-Clark subdivision surfaces: recursively refine an arbitrary-topology polygon mesh toward a smooth limit surface, the substrate later adopted for production character meshes.

Abstract

Introduces a recursive refinement scheme that generates a smooth surface from an arbitrary-topology polygonal mesh, generalizing uniform bicubic B-spline surfaces to meshes that are not regular grids. Each step splits faces and repositions points by simple averaging rules, and repeated subdivision converges to a smooth limit surface that behaves well even at extraordinary vertices. Catmull-Clark subdivision became a standard way to model smooth, deformable surfaces of arbitrary topology.

How to read this

Category
Foundational method: Catmull-Clark subdivision surfaces
Contributions
  • Generalizes uniform bicubic B-spline surfaces to meshes of arbitrary topology
  • Simple face-split and averaging rules that converge to a smooth limit surface
  • Handles extraordinary vertices, enabling smooth surfaces on irregular meshes
Context
A root of the smooth-surface substrate lineage; the scheme that Subdivision Surfaces in Character Animation later brought into production.
Correctness
Mathematically sound and now ubiquitous; the subtlety is surface behavior at extraordinary vertices, refined by much later analysis.
Clarity
Short and elegant; the refinement rules are simple to state, the limit-surface analysis is the deeper part.
How to read it
First pass: the split-and-average rules and the idea of a smooth limit from any mesh. Second pass: behavior at extraordinary vertices if you will implement it.

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