Shape Editing

1. How to represent 3D shape in the Riemann space?

Euclidean space versus Manifold space

Local coordinate system: Laplacian coordinate

2. A few notations of differential geometry and its explanation

3. Deformation matrix and the optimization function

Laplacian shape editing

4. Shape editing in latent space.

represent shape with a latent code, and deform the shape by moving the latent code to a new position in the latent space.

Examples:

• DeformSyncNet
• DualSDF