Details
| Original language | English |
|---|---|
| Pages (from-to) | 45-52 |
| Number of pages | 8 |
| Journal | Journal of Mechanical Design, Transactions Of the ASME |
| Volume | 118 |
| Issue number | 1 |
| Publication status | Published - Mar 1996 |
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.
ASJC Scopus subject areas
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computer Science Applications
- Computer Science(all)
- Computer Graphics and Computer-Aided Design
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In: Journal of Mechanical Design, Transactions Of the ASME, Vol. 118, No. 1, 03.1996, p. 45-52.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Surface Curve Design by Orthogonal Projection of Space Curves Onto Free-Form Surfaces
AU - Pegna, Joseph
AU - Wolter, Franz Erich
PY - 1996/3
Y1 - 1996/3
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0030104909&partnerID=8YFLogxK
U2 - 10.1115/1.2826855
DO - 10.1115/1.2826855
M3 - Article
AN - SCOPUS:0030104909
VL - 118
SP - 45
EP - 52
JO - Journal of Mechanical Design, Transactions Of the ASME
JF - Journal of Mechanical Design, Transactions Of the ASME
SN - 1050-0472
IS - 1
ER -