Computing intersections of rational patches

• Autorzy: Kiciak P.
• Języki publikacji: EN

Abstrakty

EN

A procedure os finding the intersection of rational patches is developed. It consists of adaptive division of the patches, convex hull test to reject pairs of disjoint pieces, normal vectors test that verifies some condition ensuring a simple enough shape of the pieces, computing end points of common arcs (described in a separate paper, [20]) and computind other points using the Newton method with pseudo-inversion. Some issues concering the reliability of this procedure are discussed.

Słowa kluczowe

EN

rational Bezier patches; intersections of surfaces

• Wydawca: Institute of Information Technology of the Warsaw University of Life Sciences – SGGW
• Czasopismo: Machine Graphics and Vision
• Rocznik: 2002
• Tom: Vol. 11, No. 4
• Strony: 431--454
• Opis fizyczny: Bibliogr. 20 poz.

Twórcy

autor

Kiciak P.

• Institute of Applied Mathematics and Mechanics, Warsaw University, Banacha 2 st., 02-097 Warsaw, Poland,

Bibliografia

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• [2] Barnhill R. E., Farin G., Jordan M., Piper B. R.: Surface/surface intersection. CAGD, 4, 3-16. 1987.
• [3] Sederberg T. W., Meyers R. J.: Loop detection in surface patch intersections. CAGD, 5, 161-171. 1988.
• [4] Cheng F.: Estimating subdivision depths for rational curves and surfaces. ACM Trans. on Graphics, 11(2), 140-204. 1992.
• [5] Kriezis G. A., Patrikalakis N. M., Wolter F.-E.: Topological and differential equation methods for surface intersections. CAD, 24(1), 41-55. 1992.
• [6] Bürger H., Schaback R.: A parallel multistage method for surface/surface intersection. CAGD, 10, 277-291. 1993.
• [7] Farin G.: Curves and surfaces for Computer Aided Geometrie Design . AP. 1993.
• [8] Kiciak P.: Ray tracing for rational Bězier patches. MG&V, 2(3), 193-208. 1993.
• [9] Chang, Bein, Angel: Surface intersection using parallelism. CAGD, 11, 39-69 . 1994.
• [10] Saito T., Wang G.-J., Sederberg T. W.: Hodographs and normals of rational curves and surfaces. CAGD, 12, 417-430. 1995.
• [11] Abdel-Malek K., Yeh H.J.: On the determination of starting points for parametric surface intersections. CAD, 29(1), 21-35. 1997.
• [12] Grandine T. A., Klein F. W.: A new approach to the surface intersection problem. CAGD, 14, 111-134. 1997.
• [13] Hu C.-Y., Maekawa T., Patrikalakis N. M., Ye X.: Robust interval algorithm for surface intersections. Computer-Aided Design, 29(9), 617-627. 1997.
• [14] Kotowski P.: Development and evaluation of algorithms of finding common parts of surfaces for application in NC milling (in Polish). Ph.D. thesis, Warsaw University of Technology, The Faculty of Mechatronics. 1997.
• [15] Krishnan S., Manocha D.: An efficient surface intersection algorithm based on lower-dimensional formulation. ACM Trans. on Graphics, 16(1), 74-106. 1997.
• [16] Cheng K. P.: Using piane vector fields to obtain all the intersection curves of two general surfaces. Strasser W., Seidel H.-P. (Eds.) Theory and Practice of Geometric Modeling, Springer, 187-204. 1998.
• [17] Lukacs G.: The generalized inverse matrix and the surface-surface intersection problem. Strasser W., Seidel H.-P. (Eds.) Theory and Practice of Geometric Modeling, Springer, 167-183. 1998.
• [18] Ye X., Maekawa T.: Differential geometry of intersection curves of two surfaces. CAGD, 16, 767-788. 1999.
• [19] Kiciak P.: Computing normal vector Bezier patches. CAGD, 18, 699-710. 2001.
• [20] Kiciak P.: Solving systems of algebraic equations. MG&V, 11(4), 455-473. 2002.