论文信息 - A Theoretical Development for the Computer Generation and Display of Piecewise Polynomial Surfaces

A Theoretical Development for the Computer Generation and Display of Piecewise Polynomial Surfaces

Two algorithms for parametric piecewise polynomial evaluation and generation are described. The mathematical development of these algorithms is shown to generalize to new algorithms for obtaining curve and surface intersections and for the computer display of parametric curves and surfaces.

Richard F. Riesenfeld | Jeffrey M. Lane | R. Riesenfeld | J. Lane

[1] Edwin Earl Catmull,et al. A subdivision algorithm for computer display of curved surfaces. , 1974 .

[2] R. Riesenfeld. On Chaikin's algorithm , 1975 .

[3] Donald P. Greenberg,et al. An interactive computer graphics approach to surface representation , 1977, SIGGRAPH '77.

[4] C. D. Boor,et al. On Calculating B-splines , 1972 .

[5] P. Bézier. Numerical control : mathematics and applications , 1972 .

[6] James F. Blinn,et al. Scan line methods for displaying parametrically defined surfaces , 1988, CACM.

[7] M. Cox. The Numerical Evaluation of B-Splines , 1972 .

[8] P. Bézier. MATHEMATICAL AND PRACTICAL POSSIBILITIES OF UNISURF , 1974 .

[9] I. J. Schoenberg,et al. On Pólya frequency functions IV: The fundamental spline functions and their limits , 1966 .

[10] W. J. Gordon,et al. B-SPLINE CURVES AND SURFACES , 1974 .

[11] R. Riesenfeld,et al. The Application of Total Positivity to Computer Aided Curve and Surface Design , 1977 .