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

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

Overview

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

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

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

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

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

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

Results 1/2 way there

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.

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