Subdivision Surfaces in Character Animation

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Subdivision Surfaces in Character Animation

• Tony DeRose - Michael Kass - Tien Truong
• - Pixar Animation Studios -

Pierce Groover March 4th, 2003
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Agenda

• Background of subdivision surfaces
• Reasons for use
• Methods and implementation
• Pixar developments
• Conclusion and Geris Game

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Background

• NURBS (Nonuniform Rational B-Splines)
• Easy and Available

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Background

• Problems
• Trimming NURBS is expensive and can have
  numerical errors
• When used in animation, very hard to hide seams

• These problems can be fixed with Subdivision

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Background

• Subdivision
• No Trimming
• Connectivity and smoothness guaranteed
• No hacks needed

• Did not have development like NURBS

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Background

• Pixar needed to develop tools
• Semi-sharp creases
• Based on infinitely sharp creases (Hoppe)
• Physical simulation (ie clothing)
• Collision detection
• Texture mapping

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Background

• But First
• What is Subdivision?

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Subdivision

• Construct a surface from an arbitrary polyhedron
• Subdivide each face of the polyhedron
• The limit will be a smooth surface

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Subdivision

• How to subdivide a face?
• Divide each edge in half
• Average the centroids of each adjacent edge
• Reconnect the two edges with the new vertex

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Subdivision

• Three main methods
• Catmull-Clark (quadrilaterals)
• Loops method (triangles)
• Butterfly method (triangles)

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Subdivision

• Chose Catmull-Clark
• Generalize B-Splines
• Easier to implement with existing software
• Quadrilaterals are better at describing human
  body parts
• Tube-like arms, legs, fingers, etc

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Subdivision Catmull-Clark

• Same as methods as in 2-D
• Start with control mesh
• Split all faces into quadrilaterals
• Apply subdivision rules
• Limit surface is tangent plane smooth no matter
  where the control vertices are placed

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Subdivision
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Pixar Developments

• Semi-sharp creases
• Physical simulation
• Efficient collision detection
• Texture mapping

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Sharp Creases

• Pioneered by Hoppe
• Very useful
• Simply mark a subset of the edges as sharp and
  apply a different set of governing rules
• Easy to model

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Sharp Creases

• But
• Real world objects cannot have infinitely sharp
  creases
• Sometimes necessary to have tightly curved edges
• So..

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Semi-Sharp Creases

• Pixar developed a generalization (semi-sharp)
• Controllable sharpness
• Sharpness (s) 0, smooth
• Sharpness (s) inf, sharp
• Achievable through hybrid subdivision

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Semi-Sharp Creases
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Semi-Sharp Creases
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Physical Simulation

• Model kinematic/dynamic objects
• Specifically, but not limited to, clothing
• Must define an energy functional
• Finite difference approach
• Use springs to model clothing

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Physical Simulation

• Model kinematic/dynamic objects
• Specifically, but not limited to, clothing
• Must define an energy functional
• Finite difference approach
• Use springs to model clothing

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Collision Detection

• Simple solution
• Test each geometric element against all others
• Not practical (N2 Bad)
• Use 2-d or 3-d structure to represent objects
• They used 2-d
• Hierarchy fixed, storage is static, never need
  rebalance

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Collision Detection

• Done mostly in preprocessing
• Hierarchy is made from bottom up
• Start at leaves with control mesh
• Get more detailed as move up
• Root is final surface
• Only need update control vertices positions

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Texture mapping

• Solid color painting is easy, already defined
• Texturing is not so easy
• Using polygonal methods can result in distortion

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Texture mapping

• Treat texture coordinates in same way as
  geometric coordinates and use subdivision
• These are scalar fields
• Used in Geris jacket, ears, nostrils
• Procedural shaders use scalar values to determine
  colors

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Texture mapping

• Scalar values are determined by using
  interpolation at control points using Laplacian
  smoothing
• Sometimes even done manually

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DEMOS!

• 2D
• http//www.subdivision.org/subdivision/demos/2d.js
  p
• 3D
• http//www.subdivision.org/subdivision/demos/demos
  .jsp

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Conclusion

• Subdivision gt NURBS
• More control, accuracy
• Pixar sweet
• Developments make subdivision surfaces very
  practical and useful
• Now part of Renderman

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Geris game

• First definitive work with subdivision
• Crazy old man playing chess against himself
• Enjoy!
• http//www.pixar.com/shorts/gg/theater/short_320.h
  tml

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Thank You

• Pictures and references from
• http//www.subdivision.org
• http//www.3dgraphicsoutpost.com/subdivisionsurfac
  esintro.htm
• http//www.cs.princeton.edu/courses/archive/fall02
  /cs526/lectures/subdivision.pdf
• http//www.pixar.com/
• http//www.scg.uwaterloo.ca/hqle/subdivision/imag
  es/Loop/Loop1.html