Abstract
Surface creases have been employed for many useful CG and CAD applications such as shape recognition, quality evaluation, aesthetic shape design, geometric deformations, etc. Especially, the curvature extremum curves, which are defined by extrema of surface principal curvatures along their corresponding lines of curvature, and their subsets called ridge-valley and crest lines have been well studied in connection with geometric surface features. In this research, we introduce a novel subset of curvature extremum curves whose convex and concave lines are dual with respect to spherical inversion transformations. The subset is obtained by calculating the principal curvatures and their derivatives of the transformed surface. The spherical inversion is a conformal transformation which is often used in CG and CAD. Surface creases under inversion transformations have not been studied well compared with rigid motion and scaling of surfaces. We discuss the conformal invariance property of curvature extremum curves, curvature-based surface energies, and cyclides. Also we examined our inversion dual crest lines on several surfaces approximated by triangle meshes.
