In this paper we study the behavior of the beta-spline functions in the case the parameter β2(i) is negative. We prove that a negative value β ̂2(i) exists so that if β2(i) > β ̂2(i) ∀i, the beta-spline functionsNi(u) are positive. Moreover, if the control vertices are such that x0 ≤ ⋯ ≤ xm-1, we have proved that the design curve keeps the properties already proved in the case β2(i) ≥ 0. © 1992.
De Tisi, F., Rossini, M. (1992). Behavior of the beta-splines with values of the parameters beta$2$ negative. COMPUTER AIDED GEOMETRIC DESIGN, 9(6), 419-423.
Behavior of the beta-splines with values of the parameters beta$2$ negative
ROSSINI, MILVIA FRANCESCA
1992
Abstract
In this paper we study the behavior of the beta-spline functions in the case the parameter β2(i) is negative. We prove that a negative value β ̂2(i) exists so that if β2(i) > β ̂2(i) ∀i, the beta-spline functionsNi(u) are positive. Moreover, if the control vertices are such that x0 ≤ ⋯ ≤ xm-1, we have proved that the design curve keeps the properties already proved in the case β2(i) ≥ 0. © 1992.
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