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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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Technik der Maschinen-Buchhaltung 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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Bach to Rock, A Musical OdysseyThe underlying concept of this work is the synthesis of two useful concepts: the application of . to a shape; and the study of the . and . of a parametrically defined shape as fundamental geometric measures.
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https://doi.org/10.1007/978-94-009-9900-8The 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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Heidegger’s Philosophy of TechnologyConsider a space curve (in three dimensions) parametrized with respect to an arbitrary parameter . [8, 9, 10, 15, 24]. The unit tangent vector has the same direction and sense as the parametric first derivative vector, but it is normalized.
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https://doi.org/10.1007/978-3-663-04316-4An important observation is that β1.(.) and β2.(.) (equation (14.3)) can each be written as a pair of equations of similar form; specifically,.where . and . were defined in equation (14.3).
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