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Delve into the world of subdivision surfaces and various modeling techniques such as polygons, splines, and implicit surfaces. Learn about the pros and cons of different methods, including B-splines, NURBS, and implicit surfaces. Discover the motivation for using subdivision surfaces, their terminology, and overview of common schemes. Explore detailed examples and interesting properties, along with discussions on papers and interactive multiresolution mesh editing. Conclude with insights into the applications of subdivision surfaces in character animation and modeling tools.
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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
