Titlebook: Computer Graphics and Geometric Modeling Using Beta-splines; Brian A. Barsky Book 1988 Springer-Verlag Berlin Heidelberg 1988 computer gra

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Curve Evaluation and Perturbation with Uniform Shape Parameters,tly evaluate a Beta-spline curve. Observe that all the coefficient functions have a constant denominator of δ. Thus, all the divisions can be performed prior to the actual computation of the Beta-spline basis functions. The following algorithm evaluates the basis functions at . + 1 given values of t

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Curve Evaluation and Perturbation with Continuous Shape Parameters,xpression for the curve will have a denominator of δ(.). It is thus of computational interest to define corresponding sets of coefficient functions and basis functions that are scaled by a factor of δ(.). This would simplify the expressions and eliminate redundant divisions. These scaled coefficient

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Surface Evaluation and Perturbation with Uniform Shape Parameters, involves the computation of points on the surface for many different values of the domain parameters. The determination of a point on the patch requires the evaluation of the surface formulation at an appropriate (.) value. This entails the evaluation of the four basis functions at the value of . a

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Geometrical Interpretation of the Shape Parameters, information specified by the control vertices. These shape parameters have the property that β1 = 1 indicates continuity of the parametric first derivative vector and β1 = 1 with β2 = 0 indicates continuity of the parametric first and second derivative vectors.

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