Theories of contact specified by connection matrices

Computer Aided Geometric Design

Volumn 13, Issue 9 SPEC. ISS., 1996, Pages 905-929

  Habib, Ayman W ^a   Goldman, Ron N ^a  

^a Rice University   (United States)

Author keywords

Connection matrices; Contact; Frenet frame; Geometric continuity; Group; Projective invariance; Reparametrization

Indexed keywords

COMPUTATIONAL GEOMETRY; MATHEMATICAL MODELS; MATHEMATICAL TECHNIQUES; SURFACES;

CONNECTION MATRICES; FRENET FRAME;

COMPUTER AIDED DESIGN;

EID: 0030400777     PISSN: 01678396     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-8396(96)00015-5     Document Type: Article

References (18)

1. Barry, P.J., Goldman, R.N. and Micchelli, C.A. (1993), Knot insertion algorithms for piecewise polynomial spaces determined by connection matrices, Adv. Comput. Math. 1, 139-171.
2. Barsky, B.A. and Rose, T.D. (1984), Geometric continuity of parametric curves, Technical Report UCB/CSD 84/205, Department of Electrical Engineering and Computer Science University of California, Berkeley, CA.
3. Barsky, B. A. and Rose, T.D. (1988), Three characterizations of geometric continuity for parametric curves, Technical Report UCB/CSD 88/417, Department of Electrical Engineering and Computer Science, University of California, Berkeley, CA.
4. Bartels, R., Beatty, J. and Barsky, B.A. (1987), An Introduction to Splines for Use in Computer Graphics and Geometric Modeling, Morgan Kaufmann.
5. Boehm, W. (1985), Curvature continuous curves and surfaces, Computer Aided Geometric Design 2(4), 313-323.
6. DeRose, T. (1985), Geometric continuity: A parametrization independent measure of continuity for computer aided geometric design, Ph.D. Thesis, Department of Electrical Engineering and Computer Science, University of California, Berkeley, CA.
7. Dyn, N., Edelmann, A. and Micchelli, C.A. (1987), On locally supported basis functions for the representation of geometrically continuous curves, Analysis 7, 313-341.
8. Dyn, N. and Micchelli, C.A. (1988), Piecewise polynomial spaces and geometric continuity of curves, Numer. Math. 54, 319-337.
9. 2-splines, Computer Aided Geometric Design 2, 325-328.
10. Goldman, R.N. and Barsky, B.A. (1989), Some basic results on beta-continuous functions and their applications to the construction of geometrically continuous curves and surfaces, in: T. Lyche and L. Schumaker, eds., Mathematical Methods in Computer Aided Geometric Design, Academic Press, 299-311.
11. Goldman, R.N. and Micchelli, C.A. (1989), Algebraic aspects of geometric continuity, in: T. Lyche and L. Schumaker, eds., Mathematical Methods in Computer Aided Geometric Design, Academic Press, 313-332.
12. Goodman, T.N.T. (1990), Constructing piecewise rational curves with Frenet frame continuity, Computer Aided Geometric Design 7, 15-31.
13. Gregory, J.A. (1989), Geometric continuity, in: T. Lyche and L. Schumaker, eds., Mathematical Methods in Computer Aided Geometric Design, Academic Press, 353-371.
14. Habib, A.W. (1996), Three approaches to building curves and surfaces in CAGD, Ph.D. Thesis, Department of Computer Science, Rice University, TX, USA.
15. Hagen, H. (1985), Geometric spline curves, Computer Aided Geometric Design 2, 223-227.
16. Hohmeyer, M.E. and Barsky, B.A. (1989), Rational continuity: parametric and geometric continuity of rational polynomial curves, ACM Transactions on Graphics, Special Issue on Computer Aided Geometric Design and Geometric Modeling, 335-359.
17. Pottmann, H. (1989), Projectively invariant classes of geometric continuity for CAGD, Computer Aided Geometric Design 6, 307-321.
18. Seidel, H.P. (1993), Polar forms for geometrically continuous spline curves of arbitrary degree, ACM Transactions on Graphics 12, 1-34.