Smoothing of curves and surfaces

Authors:
Josef Hoschek
Affiliations:
Fachbereich Mathematik, Technische Hochschule Darmstadt, D6100 Darmstadt, Fed. Rep. Germany
Venue:
Computer Aided Geometric Design
Year:
1985

Citing 1
Cited 2

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Abstract

Using Bezier-techniques or B-spline-techniques for interpolation or approximation of curves or surfaces inflection points or changes of sign of the Gaussian curvature occasionally occur. Inflection points or changes of sign of Gaussian curvature are undesired in some applications, notably the fairing of ship lines or the fairing of car body surfaces. In the present contribution we introduce a simple criterion for detecting such undesired domains by using the k-orthotomics. The k-orthotomics are wellknown in optics [Bruce . '84]. Such undesired domains can be smoothed interactively or by using a procedure based on a method from algebraic geometry, the so called Bezout-method [Salmon 1885, Goldman . '85].