Abstract
The rest of the book has led up to being able to design into a scheme exactly the right behaviour in the interior of a long curve, but for practical purposes what happens at the ends of a finite piece of curve, and how that is controlled is of at least equal importance. The previous theory is applicable to finite polygons, provided that they are closed, forming loops. This can be useful, but cannot be called a complete theory. Designers need to be able to create curves which start at one chosen place and finish at another. They also need to be able to influence fairly precisely the derivatives of the curve at those places.
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© 2010 Springer-Verlag Berlin Heidelberg
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Sabin, M. (2010). End Conditions. In: Analysis and Design of Univariate Subdivision Schemes. Geometry and Computing, vol 6. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13648-1_32
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DOI: https://doi.org/10.1007/978-3-642-13648-1_32
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13647-4
Online ISBN: 978-3-642-13648-1
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