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Subdivision Surfaces. Jeff Ballard Nick Rasmussen. Overview. Motivation for Subdivision Surfaces Subdivision Schemes Interesting Properties Discussion of Papers. Traditional Modeling Techniques. Polygons Splines Implicit Surfaces. Polygons - Pro. Fast Arbitrary Topology
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Subdivision Surfaces Jeff Ballard Nick Rasmussen
Overview • Motivation for Subdivision Surfaces • Subdivision Schemes • Interesting Properties • Discussion of Papers
Traditional Modeling Techniques • Polygons • Splines • Implicit Surfaces
Polygons - Pro • Fast • Arbitrary Topology • Easy Stitching
Polygons - Con • C0 Continuity • High Counts for Complex Surfaces • Edits Hard to do Globally
B-Splines - Pro • Mathematically Elegant • Well Understood • C2 Everywhere
B-Splines - Con • Needs ‘Socking’ to Prevent Cracks • Sharp/Curved Edges Hard • High CV Count Creatures
NURBS - Pro • CV Weights => Sharp Edges, Finer Control • Trim Curves • Widespread Support (sort-of :)
NURBS - Con • Trim Curves Susceptible to Numerical Error • Very Hard to Sock with Trim Curves • Difficult to Implement • Greater Sophistication Needed for Modeling Tools
Implicit Surfaces - Pro • ‘Blobby’ Objects • Mathematically Trivial
Implicit Surfaces - Con • Poor Control • Hard to Model Details • Achieving Correct Polyginization
Why Subdivision Surfaces? • Single Surface for All Modeling Operations • Multi-Resolution Edits • Extensions to Support Sharp Edges • Arbitrary Topology • No Cracks
Subdivision Terminology • Vertices: • Regular/Extraordinary • Odd/Even • Face/Edge • Edges: • Boundaries and Creases • Control Mesh
Overview Of Subdivision Schemes • Corner Cutting • Vertex Insertion • Interpolating • Approximating
Corner Cutting • Old Vertices are Discarded • Common Schemes: • Doo-Sabin • Mid-Edge 2 steps 4 steps
Interpolating • Even Vertices Remain Stationary • ‘Inflates’ Out to Limit Surface (bad) • Common Schemes: • Modified Butterfly (triangle based) • Kabbelt (quad based)
Approximating • Even Vertices are Moved • Converges in to Limit Surface • Convergence Faster than Interpolating Schemes • Better Mathematical Properties • Common Schemes: • Loop (triangle based) • Catmull-Clark (quad based)
Subdivision Example:Catmull-Clark • Quad-Based • Approximating Subdivision Surface • Isomorphic to B-Spline Patch Around Regular Vertices
Interesting Properties • Explicit Evaluation • Subdivide Scalar Parameters • ‘Snap’ to Limit Surface
Big ‘Wins’ • No Cracks
Big ‘Wins’ (cont.) • View-Dependant Mesh Refinement • Operate on only one Geometry • Polygon Reduction on Control Mesh • ‘Pawn’ Geometry
Papers • Interactive Multiresolution Mesh Editing • Zorin et. al. • Non-Uniform Recursive Subdivision Surfaces • Sederberg et. al. • Exact Evaluation of Loop Subdivision Surfaces • Jos Stam
Papers (cont.) • Exact Evaluation of Catmull-Clark Subdivision Surfaces • Jos Stam • Subdivision Surfaces in Character Animation • DeRose et. al.
Interactive Multiresolution Mesh Editing • Uniform Editing On All Detail Levels • Edit At One Resolution and Propagate Changes
Interactive Multiresolution Mesh Editing (cont.) • Subdivide Surfaces Only Where it Matters
Non-Uniform Recursive Subdivision Surfaces • Interesting, But Missed the Ball • NURSSes:NURBS as Catmull-Clark:B-Splines • We Don’t Want/Need NURBS
Exact Evaluation of Catmull-Clark Subdivision Surfaces • Subdivision Surfaces Without Subdividing • Precompute Eigenbasis Functions • Produce the Limit Surface Directly
Subdivision Surfaces in Character Animation • Wonderful Overview of Subdivision Surfaces • The Right Way to do Edge Weights • Fits Well With RenderMan
