Surfaces with Natural Ridges

Year: 2015 Authors: David Brander; Steen Markvorsen

Core claim

Given a generic space curve, there is a unique pseudospherical surface with K = -1 containing it as a cuspidal edge.

Topics

surface singularities, constant negative curvature, cuspidal edges, pseudospherical surfaces

Domains

differential geometry, Gaussian curvature, singularity theory, sine-Gordon equation, architecture, natural forms, visual aesthetics, craftbook surfaces

Methods

frontal surface model, Cauchy problem, numerical construction, curve-driven generation

Media

space curves, paperback book, temple roofs, plant leaves

Source status

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