Interpolation on quadric surfaces with rational quadratic spline curves

Computer Aided Geometric Design

Volumn 14, Issue 3, 1997, Pages 207-230

  Wang, Wenping ^a   Barry, Joe ^b  

^a UNIVERSITY OF HONG KONG   (Hong Kong)

^b UNIVERSITY OF ALBERTA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL GEOMETRY; INTERPOLATION; PROBLEM SOLVING; SURFACES;

QUADRIC SURFACE;

COMPUTER AIDED DESIGN;

EID: 0031123712     PISSN: 01678396     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0167-8396(96)00030-1     Document Type: Article

References (25)

1. Bézier, P. (1972), Numerical Control, John Wiley & Sons, London.
2. Bolton, K.M. (1975), Biarc curves, Computer-Aided Design 7, 89-92.
3. Bookstein, F.L. (1979), Fitting conic sections to scattered data, Comput. Graph. Image Process. 9, 56-71.
4. Dietz, R., Hoschek, J. and Juttler, B. (1993), An algebraic approach to curves and surfaces on a sphere and on other quadrics, Computer Aided Geometric Design 10, 211-229.
5. Dietz, R., Hoschek, J. and Juttler, B. (1995), Rational patches on quadric surfaces, Computer-Aided Design 27, 27-40.
6. Farin, G. (1989), Curvature continuity and offsets for piecewise conics, ACM Trans. on Graph. 8, 89-99.
7. Fuhs, W. and Stachel, H. (1988), Circular pipe-connections, Computer & Graphics 12, 53-57.
8. Golub, G.H. and Van Loan, C.F. (1989), Matrix Computations, 2nd ed., The Johns Hopkins University Press.
9. Hoschek, J. and Seeman, G. (1992), Spherical splines, Mathematical Modelling and Numerical Analysis 26, 1-22.
10. Kim, M.J., Kim, M.S. and Shin, S.Y. (1995), A general construction for unit quaternion curves with simple high order derivatives, in: Proceedings of SIGGRAPH '95, 369-376.
11. Lee, E.T.Y. (1987), The rational Bézier representation for conics, in: Farin, G., ed., Geometric Modeling: Algorithms and New Trends, SIAM, Philadelphia, 3-19.
12. Nutbourne, A.W. and Martin, R.R. (1988), Differential Geometry Applied to Curve and Surface Design, Vol. 1: Foundations, Ellis Horwood Limited, England.
13. Patterson, R.R. (1986), Projective transformations of the parameter of a Bernstein-Bézier curve, ACM Trans. on Graph. 4, 276-290.
14. Pavlidis, T. (1983), Curve fitting with conic splines, ACM Trans. on Graph. 2, 1-31.
15. Pletinckx, D. (1989), Quaternion calculus as a basic tool in computer graphics, The Visual Computer 5, 2-13.
16. Pratt, V. (1985), Techniques for conic splines, in: Proceedings of SIGGRAPH '85, 151-159.
17. Rossignac, J.R. and Requicha, A.A. (1987), Piecewise-circular curves for geometric modeling, IBM J. Res. Develop. 31, 296-313.
18. Sabin, M. (1976), The use of piecewise forms for the numerical description of shape. Ph.D. Thesis, Hungarian Academy of Sciences.
19. Semple, J.G. and Kneebone, G.T. (1952), Algebraic Projective Geometry, Oxford University Press, London.
20. Sharrock, T.J. (1987), Biarcs in three dimensions, in: Martin, R.R., ed., The Mathematics of Surfaces II, Clarendon Press, Oxford, 395-411.
21. Shoemake, K. (1985), Animation rotation with quaternion curves, in: Proceedings of SIGGRAPH '85, 245-254.
22. Wilkinson, J.H. (1965), The Algebraic Eigenvalue Problem, Clarendon Press, Oxford.
23. Xu, Y.C. (1965), Introduction to Algebra. Shanghai Science and Technology Press.
24. Wang, W. and Joe, B. (1992), Classification and properties of space biarcs, in: SPIE Vol. 1830: Curves and Surfaces in Computer Vision and Graphics III, 184-195.
25. Wang, W. and Joe, B. (1993), Orientation interpolation in quaternion space using spherical biarcs, in: Proceedings of Graphics Interface '93, 24-32.