This is a supplement to our previous research note [3]. In [3], we gave a characterization of biharmonic curves in Minkowski 3-space. More precisely, we pointed out that every biharmonic curves with nonnull principal normal in Minkowski 3-space is a helix, whose curvature κ and torsion τ satisfy κ2 = τ2. In the classification of biharmonic curves in Minkowski 3-space due to Chen and Ishikawa [1...

Dupin cyclides are surfaces characterized by the property that all their curvature lines are circles or lines. Spheres, circular cylinders, cones and tori are particular examples. We introduce a bilinear rational Bézier-like formula with quaternion weights for parametrizing principal patches of Dupin cyclides. The proposed construction is not affine invariant but it is Möbius invariant, has low...

Using the visual search method, we show that stimuli that contain curvature discontinuities (i.e., points where the second derivative along an image contour is not defined) are easily found among stimuli containing only smooth changes in curvature. Curved stimuli that lack curvature discontinuities, however, are difficult to find among distractors that have them. These results suggest that the ...

This article presents a new definition of Branson’s Q-curvature in even dimensional conformal geometry. The Q-curvature is a generalization of the scalar curvature in dimension 2: it satisfies an analogous transformation law under conformal rescalings of the metric and on conformally flat manifolds its integral is a multiple of the Euler characteristic. Our approach is motivated by the recent w...

Estimating principal curvatures and principal directions of a smooth surface represented by a triangular mesh is an important step in many CAD or graphics related tasks. This paper presents a new method for curvature tensor estimation on a triangular mesh by replacing flat triangles with triangular parametric patches. An improved local interpolation scheme of cubic triangular Bézier patches to ...