Subdivision Surfaces in Character Animation

1
Subdivision Surfaces in Character Animation
Chris DeCoro Presentation of an article by
DeRose, et. Al.
2
Talk outline

• Introduction
• Motivation and applications
• Previous work
• Additional requirements of animation
• Semi-sharp Creases
• Rendering
• Physically-based Modeling
• Conclusion

3
Motivation and Background

• Animation requires smooth surfaces for visual
  appeal
• Traditional Approach NURBS
• However, single patches have limited topology
• Difficult to maintain smoothness during animation
  
• Often require expensive and inaccurate trimming
• Proposed Solution Subdivision Surfaces
• Able to represent arbitrary topology
• No trimming
• No seams always smooth

4
Previous work

• Catmull-Clark Subdivision
• Input is a quadrilateral mesh, M0
• From mesh Mn, reaches Mn1 through subdivision
• Adds additional vertices to make each quad into 4
  subdivided quads
• Limit surface (infinite subdivisions) is smooth
• Infinitely-sharp Creases
• In some locations, the ideal surface is not
  smooth
• For these applications, we require creases
• Sharp edges are manually marked as such
• Algorithm uses special subdivision rules

5
Additional requirements of animation

• Semi-sharp Creases
• An adjustable intermediate between smooth
  surfaces and infinitely sharp creases
• Physical Modeling
• Surfaces pose challenges in representing real
  world movement and collisions
• The article will focus on physical modeling of
  cloth
• Rendering
• NURBS have a direct parameterization for texture
  mapping
• Subdivision surfaces do not

6
Talk outline

• Introduction
• Semi-sharp Creases
• The need for Semi-sharp Creases
• Standard Subdivision
• Infinitely-sharp Creases
• Overall Algorithm
• Rendering
• Physically-based Modeling
• Conclusion

7
The Need for Semi-sharp Creases

• Most sharp edges in nature are smooth at a
  sufficiently close distance
• E.g. the edge of a table top
• Often we wish to control the degree of sharpness
• Shown in the illustrations below

8
Standard Subdivision

• Standard Catmull-Clark Subdivision has three
  types of points in each refined mesh
• Face points
• Vertex points
• Edge points
• Face points centroid of each quad region
• Edge points 0.25(vi ei fJ-1 fJ )
• Vertex points (n-2)/nvi 1/n2sum(ei)
  1/n2sum(fi1)

9
(No Transcript)
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Infinitely-Sharp Creases

• Control vertices and edges are manually tagged as
  sharp
• Face points same as smooth rule
• Edge points place at midpoint of edge
• Vertex points
• One sharp incident edge (dart) same as smooth
  rule
• Two sharp edges (crease) (e1 6vi e2) / 8
• Three or more sharp edges (corner) do not modify
  point

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Overall Algorithm

• For creases with integer sharpness s
• Subdivide using infinitely-sharp rules s times
• For creases with non-integer sharpness s
• Assume creases with sharpness floor(s) and
  ceil(s)
• Determine subdivision points for both cases
• Linearly interpolate to compute points for s
• After previous steps, and for all elements
• Perform standard (smooth) subdivision to the
  limit

12
Talk outline

• Introduction
• Semi-sharp Creases
• Rendering
• Surface texture mapping
• Implementation issues
• Physically-based Modeling
• Conclusion

13
Texture Mapping

• Textures parameterized onto a 2d plane
• Ideal for NURBS
• Not so ideal for Subdivision Surfaces
• Solution Subdivide texture coordinates
• Manually apply texture coordinates to the base
  mesh
• Treat vertex as (x,y,z,s,t) five-tuple
• The texture coordinates are subdivided along with
  the coordinates
• Can be applied to arbitrary attributes
• Normals, arbitrary shader parameters

14
Implementation Issues

• The author is working with the Pixar RenderMan
  system
• Requires geometry be subdivided to sub-pixel
  sized micropolygons
• Each primitive must bound itself, dice into
  micropolygons
• Bounding takes advantage of convex hull property
• Each primitive must dice itself into
  micropolygons
• Locally, surface represents bicubic B-spline
  patch
• Surface is converted into patch, uses less space
  (4x4 grid)
• Regular structure makes easier to dice into
  micropolygons

15
Talk outline

• Introduction
• Semi-sharp Creases
• Rendering
• Physically-based Modeling
• Computing cloth energy functional
• Collision determination
• Conclusion

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Determining Energy Functional

• Basic properties are specified by energy
  functional
• Represents attraction or resistance of material
  to deformation
• Catmull-Clark methods become regular grids
• Ideal for representing woven fabrics
• Energy term represented by
• E(p1,p2) 0.5(p1-p2/p1-p2)2
• p1, p2 are the positions at rest
• This can be used to represent the motion of cloth
• Limited motion along thread directions
• Folds freely along the diagonals

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Collision Determination

• Several approaches stand out
• Test every object against each other
  (impractical)
• Three-D spatial partitioning (not ideal)
• Two-D surface partitioning
• Advantages of surface partitioning
• Hierarchy fixed if connectivity does not change
• All data statically allocated, compute in
  preprocess
• Hierarchy generation through un-subdividing
• Pick a candidate edge e
• Remove faces adjacent to e, merge to
  super-face
• Mark edges adjacent to super-face as
  non-candidates for one iteration (for better
  balancing)
• Store bounding box
• At run time, use precomputed hierarchy to compare
  bounding boxes between object and obstacles

18
Conclusion

• Subdivision surfaces are a better alternative to
  NURBS
• Always smooth, no seams
• No trimming, greater range of topology
• Semi-sharp Creases allow for enhanced control
• Sharpness can range smooth from none to infinite
• Scalar-field texture maps allow for simplified
  texturing
• Directly generated from the base mesh
• Successfully integrated into RenderMan
• Thus has shown to be successful in real-world
  applications
• Collision detection model / Energy functional
• Allows for realistic physics