Surface Curve Design by Orthogonal Projection of Space Curves Onto Free-Form Surfaces

[+] Author and Article Information
Joseph Pegna

Department of Mechanical Engineering, Aeronautical Engineering and Mechanics, Rensselaer Polytechnic Institute, Troy, New York 12180-3590

Franz-Erich Wolter

Universität Hannover, Institut Für Informatik, FG Graphische Datenverarbeitung Welfengarten 1 30167 Hannover Germany

J. Mech. Des 118(1), 45-52 (Mar 01, 1996) (8 pages) doi:10.1115/1.2826855 History: Received February 01, 1991; Revised February 01, 1992; Online December 11, 2007


A novel technique for designing curves on surfaces is presented. The design specifications for this technique derive from other works on curvature continuous surface fairing. Briefly stated, the technique must provide a computationally efficient method for the design of surface curves that is applicable to a very general class of surface formulations. It must also provide means to define a smooth natural map relating two or more surface curves. The resulting technique is formulated as a geometric construction that maps a space curve onto a surface curve. It is designed to be coordinate independent and provides isoparametric maps for multiple surface curves. Generality of the formulation is attained by solving a tensorial differential equation formulated in terms of local differential properties of the surfaces. For an implicit surface, the differential equation is solved in three-space. For a parametric surface the tensorial differential equation is solved in the parametric space associated with the surface representation. This technique has been tested on a broad class of examples including polynomials, splines, transcendental parametric and implicit surface representations.

Copyright © 1996 by The American Society of Mechanical Engineers
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