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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https://doi.org/10.1007/978-3-642-99434-0In computer graphics, it is of interest to . a Beta-spline, that is, create a realistic two-dimensional image representing three-dimensional Beta-spline objects. This chapter shows several synthetic color images of Beta-spline objects including such features as specular highlights and texture patterns.

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The Parametric Piecewise Representation,The parametric representation of a curve has each component expressed as a separate univariate (single parameter) function while that of a surface has each component defined by a separate bivariate (two parameter) function.

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Geometric Continuity and Shape Parameters,Given the two curves ..(.) and ..(.), consider the joint .. Recalling equation (4.1), continuity of the unit tangent vector is achieved if.that is,.or..

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Explanation of the Surface Representation,A point on the (.). Beta-spline surface patch is a weighted average of the sixteen vertices .., . = ?2, ?1, 0, 1 and . = ?2, ?1,0,1. The mathematical formulation for the patch ..(.) is then

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