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

authored by: Joseph Pegna, Franz Erich Wolter
Abstract: 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.
External Organisation(s): Rensselaer Polytechnic Institute
Type: Article
Journal: Journal of Mechanical Design, Transactions Of the ASME
Volume: 118
Pages: 45-52
No. of pages: 8
ISSN: 1050-0472
Publication date: 03.1996
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Mechanics of Materials, Mechanical Engineering, Computer Science Applications, Computer Graphics and Computer-Aided Design
Electronic version(s): https://doi.org/10.1115/1.2826855 (Access: Closed)

BibTeX

@article{42bf6001a53440278419549f4117c5f4,
title = "Surface Curve Design by Orthogonal Projection of Space Curves Onto Free-Form Surfaces",
abstract = "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.",
author = "Joseph Pegna and Wolter, {Franz Erich}",
year = "1996",
month = mar,
doi = "10.1115/1.2826855",
language = "English",
volume = "118",
pages = "45--52",
journal = "Journal of Mechanical Design, Transactions Of the ASME",
issn = "1050-0472",
publisher = "American Society of Mechanical Engineers(ASME)",
number = "1",
}