Note on curve and surface energies

Energies of curves and surfaces together with their discrete variants play a prominent role as fairness functionals in geometric modeling and computer aided geometric design. This paper deals with a particular discrete surface energy which is expressible in terms of curve energies, and which occurs naturally in the problem of smoothing digital elevation data with tolerance zone constraints. We also discuss geometrically meaningful surface energies in general from the viewpoint of invariant theory, and the role of the Gauss-Bonnet theorem.

• Type: Journal
• Year: 2007
• Where: CAGD
• Authors: Johannes Wallner
• Keywords: CAGD 2007, Energies, Meaningful Surface Energies, Particular Discrete Surface