Exploiting Subdivision in Modeling and Animation

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Exploiting Subdivision in Modeling and Animation

• David R. Forsey
• The University of British ColumbiaRadical
  Entertainment Inc.

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Topics

• Multiresolution Animation
• What it is.
• How to use it.

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Retrospective

• Hierarchical B-Spline Refinement, SIGGRAPH88
  Forsey/Bartels.

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Motivations for H-Splines

• H-Splines were developed specifically for
  animation.
• Address problems with traditional B-splines
• non-local knot insertion
• the degree-of-freedom problem.

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Local Refinement

• Models rapidly become heavy
• patches in locations they are not needed
• extra rendering overhead
• may affect previously defined animation
• even more points to animate
• Local refinement adds patches to a restricted
  area

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Local Refinement

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Local Refinement

• Created using a multiresolution representation
• Can dramatically reduce the storage requirements

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Multiresolution Editing

• Each resolution procedurally related to the next
  coarsest level
• arbitrary procedure (offset operator) for each
  control point.
• creates a reactive surface

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H-Splines

• Applicable to any surface formulation with
• Local support
• Subdivision that does not alter the shape of the
  limit surface
• polygons
• other splines (including curves deformation
  lattices)
• various subdivision surface formulations
• wavelets (depending upon basis used)

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H-Splines

• Advantages
• Top-down modelling (more like sculpting)
• details maintained during broad-scale editing
• faster/easier to animate complex surfaces
• Efficient representation (compression)
• Refinement only where needed

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Multiresolution Animation

• Available in a limited form commercially
• MetaNURBs (Lightwave)
• Meshsmooth (3DMax)
• Symbolics L-surf (now Nicheman)
• various polygon smoothing packages

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Animating with H-Splines

• Offset Operators
• tangent plane offset
• frame offset (attaches a control vertex to a
  skeletal segment)
• others described later

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Simple Head

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Low-Res Attachment

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Effect on finer resolution

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Example Animation
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Locking down geometry
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Locking Down Geometry, Part II

• Full Detail Lowest Resolution

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Locking Down Geometry, Part II

• Level 1 Level 2

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Locking Down Geometry, Part II

• Full Resolution Bent Full Resolution Straight

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Example Animation
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Multiresolution Animation

• Advantages
• allows top-down approach to surface animation
• easy to mix broad-scale and fine scale effects
• faster to animate
• low-res model always available (for interactive
  speed)
• less worry about high-res model behaviour

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Layered Animation

• Low-res modification High-res effect

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Layered Animation

• Medium-res modification
  High-res effect

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Layered Animation

• Both modifications Both
  modifications, jaw open

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Example Animation
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Level of Detail

• Because the animation occurs at multiple levels
  of detail, low-res models still animate when used
  as low resolution geometry

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Layered Animation

• Animation at each resolution layers deformations
  rather than blending them.
• Makes it easy to combine vertex animation with
  shape interpolation.
• Can combine relative (offset animation) with
  absolute (skeletal attachments) effects easily.
• Provides LOD for animation as well as geometry

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Editing Operations

• Any spline-based tools can be used with H-Splines
• Additional operations possible
• copy level, region (rubber stamp details)
• non-hierarchical editing
• modify offset
• move cv normal/tangent/along parent surface
• move cv along offset
• rotate offset
• move offset origin

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Secondary Motion using Offsets

• Typical spring/mass simulations produce jello
  effects
• Can provide more structure by treating each
  offsets as a rod/mass system.
• prevents motion into surface
• surface details preserved
• fast, easy to calculate

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Secondary Motion using Offsets
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Secondary Motion using Offsets

• Sample animation

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Secondary Motion using Offsets

• Wrinkles
• Uses a behaviour map indicating location of
  wrinkle and dynamic properties (if combined with
  rod/mass simulation).
• value from map used to determine how to alter the
  offset parameterized by change in distance to
  neighbour
• low-res modifications to surface
  increase/decrease size of wrinkle

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Secondary Motion using Offsets

• Wrinkles

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Secondary Motion using Offsets

• Wrinkles

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More Examples
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Surface Approximation

• Problem
• Animators need to control placement of isoparms
• Draw lines directly onto sculptures for
  digitization as a spline control mesh
• Non-locality of knots creates heavier mesh,
  crowded lines
• H-Spline Approach
• Allows mesh to be drawn with areas of higher
  detail

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Variations
Link to paper

• Surface Pasting
• Diagonal features are difficult to model
• Such features are modeled separately and pasted
  onto the low-res surface
• Generalizes H-Splines, but are more
  computationally expensive.
• (Note commercially available in the Houdini
  animation system)

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Surface Pasting

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Surface Pasting

• Overlapping features Underlying parameter space

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Grafting Surfaces

• Arbitrary topology surfaces difficult with
  tensor-product splines
• use Catmull-Clark subdivision surfaces to join
  spline surfaces
• maintain compatibility with B-splines
• minimizes the number of extraordinary points
• maintains a simple U/V mapping for textures and
  attribute maps

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Grafting

• Two grafted cylinders Finger grafts

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Grafting

• Low-res hand with grafts Rendered
  hand

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Multiresolution Simulation

• Problem
• simulations based on simple finite elements
  (spring/mass meshes) are difficult to control
• unclear how to set the parameters for a
  particular behaviour
• stiff systems suffer from numerical instability
  or small step sizes
• very few formulations that deal with micro/macro
  effects in the same model

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Multiresolution Simulation
link to paper

• Animators Solution
• use a multiresolution representation of surface
• propagate a proportion of forces to each
  successive resolution
• similar to multigrid methods, but different
  equation solved at each resolution
• can retain surface details using an offset
  representation

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Multiresolution Simulation
100 of forces applied at lowest resolution
100 of forces applied at highest resolution
Forces applied at multiple resolutions
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Multiresolution Deformations
link to paper

• Uses similar approach, but uses kinematics rather
  than dynamics

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Multiresolution Deformations

• Different behaviours are created by varying the
  amount each resolution accomodates the deformation

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Multiresolution deformations

• Time varying effects are added by delaying the
  change to the position and orientation of the
  offsets

Behaviour during insertion of sphere
Behaviour during withdrawal of sphere
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Summary

• Multiresolution Modeling and Animation
• provides a number of additional tools based on
  offset operators
• fast, easy to use on complex models
• provides good control over complex models
• compatible with tools or simulations that operate
  on spline surfaces
• computations simple enough for real-time