Umbilics and lines of curvature for shape interrogation

DOI10.1016/0167-8396(95)00018-6zbMath0875.68858OpenAlexW2084106722MaRDI QIDQ1351571

Nicholas M. Patrikalakis, Takashi Maekawa, Franz-Erich Wolter

Publication date: 27 February 1997

Published in: Computer Aided Geometric Design (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-8396(95)00018-6

zbMATH Keywords

CADVisionCAGDPerturbationLines of curvatureMonge formShape recognitionUmbilics

Mathematics Subject Classification ID

Computer graphics; computational geometry (digital and algorithmic aspects) (68U05)

Related Items (18)

Local reparametrization by approximating lines of curvature ⋮ Differential geometry of transversal intersection curves of hypersurfaces in ℝ⁵ ⋮ Interpolation of Surfaces with Line of Curvature ⋮ Self-intersections of offsets of quadratic surfaces. I: Explicit surfaces ⋮ Computing lines of curvature for implicit surfaces ⋮ Ruled surface family with common special curve ⋮ Linear interpolation of shape operators for umbilical points through local parametrization ⋮ An intuitive explanation of third-order surface behavior ⋮ Unnamed Item ⋮ A generalization of surface family with common line of curvature ⋮ Exact solutions for two-dimensional steady flows of a power-law liquid on an incline ⋮ Constructing local controlled developable H-Bézier surfaces by interpolating characteristic curves ⋮ A generalization for surfaces using a line of curvature in Lie group ⋮ Control of lines of curvature for plate forming in shipbuilding ⋮ Ridge extraction of a smooth 2-manifold surface based on vector field ⋮ Lines of curvature and umbilical points for implicit surfaces ⋮ Ovaloids of \(\mathbb{R}^3\) and their umbilics: A differential equation approach ⋮ On integrating lines of curvature

Cites Work

• Cyclides in computer aided geometric design
• Computation of the solutions of nonlinear polynomial systems
• Computation of singularities and intersections of offsets of planar curves
• Describing surfaces
• Umbilic points on Gaussian random surfaces
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