A control point based curve with two exponential shape parameters
A generalization of a recently developed trigonometric Bézier curve is presented in this paper. The set of original basis functions are generalized also for non-trigonometric functions, and essential properties, such as linear independence, nonnegativity and partition of unity are proved. The new curve—contrary to the original one—can be defined by arbitrary number of control points meanwhile it preserves the properties of the original curve.
KeywordsBlending functions Generalized Bézier curve Shape parameters
Mathematics Subject Classification (2000)68U05 65D18 65D07
- 2.Bressoud, D.M.: Proofs and confirmations: the story of the alternating sign matrix conjecture, pp. 162–164. MAA Spectrum Series. Cambridge University Press, Cambridge (1999)Google Scholar