Rational parameterization of quadrics and their offsets

Computing (Vienna/New York)

Volumn 57, Issue 2, 1996, Pages 135-147

  Lu W ^a,b,c  

^a Zhejiang University ^*

^b ZHEJIANG UNIVERSITY   (China)

^c VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

Computational geometry; Quadrics; Rational b zier patches; Rational offsets; Rational parameterization; Triangular and quadrangular patches

Indexed keywords

ALGORITHMS; COMPUTER AIDED DESIGN; COMPUTER GRAPHICS;

QUADRANGULAR PATCHES; QUADRICS; RATIONAL BEZIER PATCHES; RATIONAL OFFSETS; RATIONAL PARAMETERIZATION; TRIANGULAR PATCHES;

COMPUTATIONAL GEOMETRY;

EID: 0030394157     PISSN: 0010485X     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02276876     Document Type: Article

References (24)

1. Abhyankar, S. S., Bajaj, C. L. Automatic parameterization of rational curves and surfaces II: conics and conicoids. Comput. Aided Des. 19, 11-14 (1987).
2. Abhyankar, S. S., Bajaj, C. L.: Automatic parameterization of rational curves and surfaces III: Cubics and cubicoids Comput. Aided Des. 19, 499-502 (1987).
3. Boehm, W : Some remarks on quadrics. Comput. Aided Des. 10, 231-236 (1993).
4. Boehm, W., Hansford, D : Bézier patches on quadrics. In: NURBS for curve and surface design (Farin, G., ed.), pp. 1-14. Philadelphia: SIAM 1991.
5. Dietz, R., Hoschek, J., Jüttler, B.: An algebraic approach to curves and surfaces on the sphere and on other quadrics. Comput. Aided Geom. Des. 10, 211-229 (1993).
6. Dietz, R., Hoschek, J., Jüttler, B.: Rational patches on quadric surfaces. Comput. Aided Des. 27, 27-40 (1995).
7. Farin G.: Triangular Bernstein-Bézier patches. Comput. Aided Geom Des. 3, 83-128 (1994).
8. Farin, G.: Curves and surfaces for computer aided geometric design, 3rd ed. New York: Academic Press 1992.
9. Farin, G., Piper, B., Worsey, A. J.: The octant of a sphere as a non-degenerate triangular Bézier patch. Comput. Aided Geom. Des 4 329-332 (1987).
10. Farouki, R. T.: Pythagorean-hodograph curves in practical use. In: Geometry processing for design and manufacturing (Barnhill, R. E., ed.), pp. 3-33 Philadelphia: SIAM 1992.
11. Farouki, R. T., Sakkalis, T., Pythagorean-hodograph space curves. Adv. Comp. Math. 2, 41-66 (1994).
12. Farouki. R. T., Sederberg, T. W.: Analysis of the offset to a prabola. Comput. Aided Geom. Des. 12, 639-645 (1995).
13. Hansford, D., Barnhill, R. E., Farin, G.: Curves with quadric boundary precision. Comput. Aided Geom Des. 11, 519-531 (1995).
14. Hoschek, J., Lasser. D.: Fundamentals of computer aided geometric design. Wellesley Massachusetts: A. K. Peters, 1993.
15. Joe, B., Wang, W.: Reparameterization of rational triangular Bézier surfaces, Comput. Aided Geom. Des. 11, 345-361 (1994).
16. Lee, E. T. Y.: The rational Bézier representation for conies. In: Geometric modeling: algorithms and new trends (Farm, G. E., ed.). pp. 2-9. Philadelphia: SIAM 1987.
17. Lodha, S., Warren, J.: Bézier representation for quadric surfaces. Comput. Aided Des. 22, 3-19 (1990).
18. Lü, W.: Rationality of the offsets to algebraic curves and surfaces. Appl. Math (A Journal of Chinese Universities) 9 Ser. B. 265-278 (1994).
19. Lü, W.: Offset-rational parameteric plane curves. Comput. Aided Geom. Des. 12, 601-616 (1995).
20. Pottmann, H.: Curve design with rational Pythagorean-hodograph curves. Adv. Comput. Math. 3, 147-170 (1995).
21. Pottmann, H.: Rational curves and surfaces with rational offsets. Comput. Aided Geom. Des. 12, 175-192 (1995).
22. Pottmann, H.: Studying NURBS curves and surfaces with classical geometry. In: Mathematical methods for curves and surfaces (Daehlen, M., Lyche, T., Schumaker, L. L., eds.). pp. 413-438. Nashville: Vanderbilt Press 1995.
23. Salmon, G., A treatise on the analytic geometry of three dimensions. Vol. I and II. New York: Chelsea Publ. 1914.
24. Sederberg, T. W , Anderson, C. D.: Steiner surface patches. IEEE Comput. Graphics Appl. 5, 23-36 (1985).