1. 3D Morphing using Multiplanar Representation
Anurag Mittal
Mahesh Ramasubramanian
Computer Science Department & Program of Computer Graphics
Cornell University

2. 3D morphing What is 3D morphing ? Why 3D morphing ?
A 3D model of the object is transformed from one shape into another.
Why 3D morphing ?
Morphs are independent of viewing and lighting parameters.
View-dependent effects possible e.g., shadows, highlights, camera can be animated during the morph.
Traditional 2D morphs are inherently “flat” looking.
Features of a Good 3D morphing algorithm
Conceptually Simple
Minimal topological restrictions.
Easy to use user-control

3. Overview

4. 3D model Polygons (triangles) Other parameters (normals, textures)
vertices

5. Multiplanar Representation
Convert model vertices from (x,y,z)
to (ht, theta, radius) space.
Scan convert each triangle.
r1,r2 ht
theta
3D model
(Axis = green) ht r1 r2
“Radius” Images
(brighter = farther
darker = closer to axis
black = no point on object)
theta
Axis

6. 3D to multiplanar representation1b
corrected
Scan-
converted 2a 2b 2a 2b
Using
separation of
planes
(seed-
algo) 3 1a 3 1b 3 3

7. 2D morphing between the planes
For e.g. using Beier & Neely’s technique (1992)

8. Reconstruction Multiplane rep. To model space -ve plane Original torus
Form triangles using adjacent pixels,
take advantage of continuity at boundaries
Multiplanes
Reconstructed torus

9. Different Scenarios E.g. Corresponding planes present
No correspondence for one plane
No correspondence for two planes
(a) Hole in the object
(b) An extruded object

10. Results
1/2 way there

13. Conclusion All the advantages of 3D over 2D morphing are inherited.
Complexity of 3D morphing is not there!
Works for different topologies, as opposed to some existing methods.
All other parameters (textures, normals, colors,...) can be morphed similarly.

15. Boundaries between multiplanes
1. Intermediate object points must have
contribution from both the objects
during dissolving.
(you can’t use 0 as one of the values !!!)
2. Consequence of the above is that you
need to match boundaries exactly.
3. The boundaries of the surfaces which are
connected originally must move
together in the morphing => use related
lines in related images.
Poor morphing + reconstruction