Titlebook: Bézier and B-Spline Techniques; Hartmut Prautzsch,Wolfgang Boehm,Marco Paluszny Textbook 2002 Springer-Verlag Berlin Heidelberg 2002 B-spl

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https://doi.org/10.1057/9781137322067The simple .. joint discussed in 11.7 is too restrictive for modelling smooth regular surfaces of arbitrary shape. Here, we present general ..-conditions and a interpolation scheme that allows to design regular surfaces of arbitrary topology with triangular patches.

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Human Rights and European RemembranceUnder a stationary subdivision scheme, a regular control net is transformed into a regular control net whose vertices are affine combinations of the initial control points. The weights of these affine combinations can be given by masks or algebraically by a characteristic polynomial, as in the case of curve algorithms.

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Geometric fundamentalsThe world can be seen as a space of points while vectors describe the directions and lengths of line segments between pairs of points. The interpretation of the world as a point space, and not as a vector space, has the advantage that any point can may serve as the origin. This fact is also reflected by the symmetry of barycentric coordinates.

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