Spectral Geometry of Shapes

Chapter 2

Background

Abstract

In computational geometry, certain shape can be represented by a differentiable manifold. A differential operator can then be defined on such a manifold based on the local geometry. Within the shape the operator contains intrinsic geometry information. In this chapter, Laplace–Beltrami operator will be introduced to define the shape spectrum on the manifolds. We will review the definition of the operator and its numerical computations.

Keywords

Laplacian spectrum; Riemannian manifold; Laplace–Beltrami operator; Laplace matrix; finite element method; Voronoi area

Chapter Outline

• 2.1  Laplace shape spectrum
• 2.2  Finite element method computation
• 2.3  Discrete Laplace–Beltrami operator

In this book a shape is represented by ...