1. Deformation techniques
CSE 3541
Matt Boggus

2. Interpolation based animation
Keyframes and inbetweening
Modifying geometry
Morphing between two objects

3. Keyframes and inbetweening
Intermediate three positions are “inbetweens” or “tweens”
Given two mesh objects with the same number of vertices, interpolate the vertex positions to get an “in-between” mesh

4. Correspondence and types
Data/Geometry must “match” to interpolate between
Previously seen how to interpolate between points
Now consider interpolating between
Curves
Polyhedron
Images (and polygons)
Image from

5. Interpolating between two curves
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

6. Interpolating between two curves
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

7. Object (Unity Mesh) Modification
Vertex warping
Modify the vertices directly
2D grid-based deforming
Modify the space the vertices lie in
Free Form Deformations
Skeletal bending
Global transforms

8. Warping
Vertices closer to seed are displaced more

9. For attenuating warping
Power functions
For attenuating warping
k determines how quickly increase in distance decreases the magnitude of warping

10. 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)

11. 2D grid-based deforming
Inverse bilinear mapping
P values at corners known from grid deformation
u and v are known from point’s position in original grid cell

12. 2D grid-based deforming

13. 2D skeleton-based bending

14. 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

15. 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

16. Examples of artist driven deformation
Point based, skeleton based, cage based
Bounded Biharmonic Weights for Real-Time Deformation by Alec Jacobson, Ilya Baran, Jovan Popovic and Olga Sorkine, appearing at SIGGRAPH 2011

17. 3D Free-Form Deformations (FFDs)
2D grid-based deforming
FFDs
2D grid
3D grid
bi-linear interpolation
tri-cubic interpolation

18. FFDs
Animate by passing object through FFD

19. Interpolate between 2 polyhedron
Correspondence problem: what part of one object to maps into what part of the other object

20. Interpolate between 2 polyhedron – difficulties
How to handle objects of different genus?
(roughly speaking: number of holes in the model) 
map to

21. Morphing Image blending Move pixels to corresponding pixels
Example from

22. Morphing

23. Morphing

24. Morphing
Using feature lines instead of grid points

25. Additional Slides

26. Other possible topics of interest
Case studies / implementation of features in:
Adobe After Effects
Snapchat filters
Unity Image Effects