Principal curvature ridges and geometrically salient regions of parametric B-spline surfaces

Computational Assessment of Curvatures and Principal Directions of Implicit Surfaces from 3D Scalar Data

“…The subscript notations in (5a) indicate the coordinate system used for the vector decomposition. These expressions are quite similar to those found in the litterature dealing with the computation of crest lines [5,25,33], except we introduce a sign function ζ = ±1 to circumvent degeneracies (see case studies proposed at the end of annex A). Because a wrong choice of u, v may yield to find t 1 = t 2 = 0, we propose a criterion on ζ to ensure that the found vectors are non-null for any arbitrary choice of u, v. Since equation (2b) implies |κ min φ n − φ uu | = |κ max φ n − φ vv |, we propose the following algorithm in order to compute t min and t max associated to κ min and κ max : choose arbitrarily u, v from n; compute φ uu and φ vv with system (15); if |κ min φ n − φ uu | |κ min φ n − φ vv | then choose ζ = +1 to avoid κ 1 φ n − φ uu = −(κ 2 φ n − φ vv ) = 0; compute t min = t 1 and t max = −t 2 with κ min = κ 1 and κ max = κ 2 ; else choose ζ = −1 since |κ max φ n − φ uu | > |κ max φ n − φ vv | 0; compute t min = −t 2 and t max = t 1 with κ max = κ 1 and κ min = κ 2 ; end This algorithm requires to arbitrarily choose (u,v) and compute φ uu and φ vv to determine κ H , κ K , t 1 and t 2 with explicit expressions (2b), (3b), (5a) and (5b).…”

Concurrent Drainage Network Rendering for Automated Pen‐and‐ink Style Landscape Illustration

“…Musuvathy et al. () propose techniques for extracting principal curvature ridges from B‐spline surfaces that may be useful for discovering escarpments on the evaluated PN triangle surfaces used for this project.…”

On k-folding map-germs and hidden symmetries of surfaces in the Euclidean 3-space

“…They play an important role in computer vision and shape recognition (see e.g. [27]) as they can be used to distinguish two shapes (surfaces) from each other and, in some cases, reconstruct the surface.…”

“…At umbilics, the ridge consist of one regular curve or a transverse intersection of three regular curves. (Umbilics and -points are used as seed points for drawing ridges on a given shape, see [27]. )…”