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Marching along surface⧸surface intersection curves with an adaptive step length

Authors
Journal
Computer Aided Geometric Design
0167-8396
Publisher
Elsevier
Publication Date
Volume
9
Issue
6
Identifiers
DOI: 10.1016/0167-8396(92)90046-r
Keywords
  • Parametric Surfaces
  • Surface⧸Surface Intersection
  • Marching
  • Curvature
  • Chordal Deviation.

Abstract

Abstract A method for generating points on the intersection of two C 2 smooth parametric surfaces is presented. In each generated point the tangent and the curvature of the intersection curve are obtained from the surface positions, first and second derivatives. Initial approximation of the next point lies on a parabola approximating the intersection curve in a vicinity of the last point found. The length of the parabola between the two points is evaluated so that its maximal deviation from the chord joining the points is not greater than a given deviation tolerance. The new point is relaxed to the intersection curve.

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