Abstract
Box splines are density functions of the shadows of higher dimensional polyhe-dra, namely boxes. For example, B-splines with equidistant knots are special univariate box splines, and the surfaces obtained by the averaging algorithm described in Section 15.7 are box spline surfaces over a regular triangular grid. This chapter (an abbreviated version of [Prautzsch & Boehm ′02]) provides a brief introduction to general box splines. It also covers half-box splines. Symmetric half-box splines of degree 3n are more suitable than box splines for the construction of arbitrary G 2n-1 free-form surfaces with triangular patches than box splines.
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© 2002 Springer-Verlag Berlin Heidelberg
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Prautzsch, H., Boehm, W., Paluszny, M. (2002). Box splines. In: Bézier and B-Spline Techniques. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04919-8_17
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DOI: https://doi.org/10.1007/978-3-662-04919-8_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07842-2
Online ISBN: 978-3-662-04919-8
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