Artículos de revistas
Marching Along A Regular Surface/surface Intersection With Circular Steps
Registro en:
Computer Aided Geometric Design. Elsevier Science B.v., Amsterdam, Netherlands, v. 16, n. 4, p. 249 - 268, 1999.
1678396
10.1016/S0167-8396(98)00048-X
2-s2.0-0033548985
Autor
Wu S.-T.
Andrade L.N.
Institución
Resumen
This paper presents a simple and elegant algorithm to estimate adaptively the stepping direction and size for tracing a branch of the intersection curve between two regular surfaces without any nonlinear equation system solver. The step is neither along the tangent vector at the current point nor along a parabola in a vicinity of the current point; it is along a circle at the current point. Although no curvature analysis or power series expansions about each point of the intersection curve were used in its construction, we demonstrate that our circle tends to the exact osculating circle, when the distance between two subsequent sampling points tends to zero. Through numerical examples, we also show that the performance of our algorithm by handling singular points, bifurcations, and points on the closely spaced branches, is equivalent to the ones based on embedding schemes. 16 4 249 268 Abdel-Malek, K., Yeh, H.J., Determining intersection curves between surfaces of two solids (1996) Computer-Aided Design, 28, pp. 539-549 Asteasu, C., Intersection of arbitrary surfaces (1988) Computer-Aided Design, 20, pp. 533-538 Blachman, N., (1992) Matematica: A Practical Approach, , Prentice-Hall Inc., New Jersey Bajaj, C.L., Hoffmann, C.M., Hopcroft, J.E., Lynch, R.E., Tracing surface intersections (1988) Computer Aided Geometric Design, 5, pp. 285-307 De Andrade, L.N., (1998) Tracing Along Regular Surface Intersection with Circular Steps, , PhD thesis, FEEC - Unicamp, Campinas (in Portuguese) Kriezis, G.A., Patrikalakis, N.M., Rational polynomial surface intersections (1991) Advances in Design Automation - 1991, 2, pp. 43-52. , Gariele, G.A. ed., Miami, Florida Grandine, T.A., Klein F.W. IV, A new approach to the surface intersection problem (1997) Computer Aided Geometric Design, 14, pp. 111-134 Hoschek, J., Lasser, D., (1993) Fundamentals of Computer Aided Geometric Design, , A K Peters, Ltd., Wellesley, MA, USA. Translation of: Grundlagen der geometrischen Datenverarbeitung, by Schumaker, L.L Houghton, E.G., Emnett, R.F., Factor, J.D., Sabharwal, C.L., Implementation of a divid-and-conquer method for intersection of parametric surfaces (1985) Computer Aided Geometric Design, 2, pp. 173-183 Coxeter, H.S.M., (1989) Introduction to Geometry, , Wiley, Inc., 2nd ed Koparkar, P., Surface intersection by switching from recursive subdivision to iterative refinement (1991) The Visual Computer, 8, pp. 47-63 Mortenson, M.E., (1985) Geometric Modeling, , Wiley, USA, 1st ed Carmo, M.P., (1976) Differential Geometry of Curves and Surfaces, , Prentice-Hall Inc., New Jersey, 1st ed Müllenheim, G., On determining start points for a surface/surface intersection algorithm (1991) Computer Aided Geometric Design, 8, pp. 401-408 Preusser, A., Computing area filling contours for surfaces defined by piecewise polynomials (1986) Computer Aided Geometric Design, 3, pp. 267-279 Barnhill, R.E., Farin, G., Jordan, M., Piper, B.R., Surface/surface intersection (1987) Computer Aided Geometric Design, 4, pp. 3-16 Barnhill, R.E., Kersey, S.N., A marching method for parametric surface/surface intersection (1990) Computer Aided Geometric Design, 7, pp. 257-280 Sederberg, T.W., Meyers, R.J., Loop detection in surface patch intersections (1988) Computer Aided Geometric Design, 5, pp. 161-171 Stoyanov, Tz.E., Marching along surface/surface intersection curves with an adaptative step length (1992) Computer Aided Geometric Design, 9, pp. 485-489