A class of curves that vary continuously between polynomial Lagrange interpolants and polynomial Bézier curves is discussed. An element in this class is specified by a real number which could be used as a shape parameter for Bézier curves. A geometric derivation of this scheme is given, and the connection to Pólya curves is pointed out. A generalization to the case of tensor product and triangular surface patches is also described.
Bibliographical noteFunding Information:
This research was supportedi n part by Departmento f Energy Contract No. DE-AC02-85ER12046,b y NSF Grant DCR-8502858, and by the CDC Sponsored Research Project 85U101 to The Universityo f Utah. The authors thank D Hansford for creating Figures 4 and 5, N Sapididis for providing the data for Figure 4, and R E Barnhill for many useful comments.
- Bézier curves
- Lagrange interpolation