Fast and Faithful Geometric Algorithm for Detecting Crest Lines on Meshes

A new geometry-based finite difference method for a fast and reliable detection of perceptually salient curvature extrema on surfaces approximated by dense triangle meshes is proposed. The foundations of the method are two simple curvature and curvature derivative formulas overlooked in modern differential geometry textbooks and seemingly new observation about inversion-invariant local surface-based differential forms. Problem setting and solution This paper is inspired by two simple but beautiful formulas of classical differential geometry and a seemingly new observation about inversion-invariant local surface-based differential forms. The formulas and observation are the key ingredients of our approach to fast and reliable detection of the so-called crest lines [30], salient subsets of the extrema of the surface principal curvatures along their corresponding curvature lines. Related work. The full set of such extrema, frequently called ridges [25], corresponds to the edges of regre...

• Type: Conference
• Year: 2007
• Where: PG
• Authors: Shin Yoshizawa, Alexander G. Belyaev, Hideo Yokota, Hans-Peter Seidel
• Keywords: Computer Graphics, Curvature Derivative Formulas, PG 2007, Reliable Detection, Salient Curvature Extrema