deformation using interpolation cse 3541 matt boggus
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Deformation using interpolation
CSE 3541Matt Boggus
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Interpolation based animation
Keyframe systems – in general
Interpolating shapesDeforming an single shape3D interpolation between two shapesImage morphing
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Keyframing
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Time-Curve interpolation
Conditions:P(0) maps to Q(0)P(1) maps to Q(1)All of P maps to all of Q
One to one – no two P(u) map to same Q(v)Onto – every Q(v) has a P-1(u) value
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Time-Curve interpolation
Solutions:If P and Q use the same curve formation and # control points, then
generate intermediate curves by interpolating the control points
Supersample: Generate same number of points on P and Q, then interpolate between matching points
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Object interpolation topics
1. Modify shape of one object
2. Interpolate one object into second object
3. Interpolate one image into second image
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Object Modification
Vertex warping
2D grid-based deforming
Skeletal bending
Free Form DeformationsModify the space the vertices lie in
Global transforms
Modify the vertices directly
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Warping
Vertices closer to seed are displaced more
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Power functionsFor attenuating warping
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k determines how quickly increase in distance decreases warping
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2D grid-based deforming
Assumption: easier to deform grid points than object vertices
A (global coordinates): (25.6,14.7)A (local coordinates): (5.6, 2.7)A’s Grid cell (5, 2)A’s position in cell (0.6, 0.7)
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2D grid-based deforming
Inverse bilinear mapping
P values at corners known from grid deformationu and v are known from point’s position in original grid cell
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2D grid-based deforming
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2D skeleton-based bending
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2D skeleton-based bending
For each vertex, determine which line segment (or bone) it is closest to: L2
distance to it: d relative position on the line segment: r = d2/d1
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2D skeleton-based bending
For new vertex position on repositioned (and possibly rescaled) line segment, Interpolate r along line segment Place d units away from the line segment
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Examples of artist driven deformation
• Point based, skeleton based, cage based
• From Bounded Biharmonic Weights for Real-Time Deformation by Alec Jacobson, Ilya Baran, Jovan Popovic and Olga Sorkine, appearing at SIGGRAPH 2011
• http://www.youtube.com/watch?v=P9fqm8vgdB8&feature=related
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Free-Form Deformations (FFDs)
2D grid-based deforming FFDs
2D grid 3D grid
tri-cubic interpolationbi-linear interpolation
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FFDs
Animate by passing object through FFD
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Interpolate between 2 objects
Correspondence problem: what part of one object to maps into what part of the other object
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Interpolate between 2 objects – difficulties
How to handle objects of different genus?(roughly speaking: number of holes in the model)
map to
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Morphing Image blendingMove pixels to corresponding pixels
Example from http://www.mukimuki.fr/flashblog/2009/05/10/morphing/
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Morphing
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Morphing
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Morphing
Using feature lines instead of grid points