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Deformation using interpolation
CSE 3541Matt Boggus
Interpolation based animation
Keyframe systems – in general
Interpolating shapesDeforming an single shape3D interpolation between two shapesImage morphing
Keyframing
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
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
Object interpolation topics
1. Modify shape of one object
2. Interpolate one object into second object
3. Interpolate one image into second image
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
Warping
Vertices closer to seed are displaced more
Power functionsFor attenuating warping
1
1
)1
0.1(
)1
(0.1)(
k
k
n
in
iiS
0
0
k
k
k determines how quickly increase in distance decreases warping
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)
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
2D grid-based deforming
2D skeleton-based bending
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
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
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
Free-Form Deformations (FFDs)
2D grid-based deforming FFDs
2D grid 3D grid
tri-cubic interpolationbi-linear interpolation
FFDs
Animate by passing object through FFD
Interpolate between 2 objects
Correspondence problem: what part of one object to maps into what part of the other object
Interpolate between 2 objects – difficulties
How to handle objects of different genus?(roughly speaking: number of holes in the model)
map to
Morphing Image blendingMove pixels to corresponding pixels
Example from http://www.mukimuki.fr/flashblog/2009/05/10/morphing/
Morphing
Morphing
Morphing
Using feature lines instead of grid points
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