1988 | OriginalPaper | Chapter
The Bernstein Approximation
Author : Professor Fujio Yamaguchi
Published in: Curves and Surfaces in Computer Aided Geometric Design
Publisher: Springer Berlin Heidelberg
Included in: Professional Book Archive
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As explained in Chap. 3, curves and surfaces based on Hermite interpolation position vectors of 2 points Q0and Q1 and the tangent vectors at those points $$ {\dot Q_0} $$ and $$ {\dot Q_1} $$ (Chap. 3): 5.1$$ P\left( t \right) = \left[ {\begin{array}{*{20}{c}} {{t^3}}&{{t^2}}&t&1 \end{array}} \right]\left[ {\begin{array}{*{20}{r}} 2&{ - 2}&1&1 \\ { - 3}&3&{ - 2}&{ - 1} \\ 0&0&1&0 \\ 1&0&0&0 \end{array}} \right]\left[ {\begin{array}{*{20}{l}} {{Q_0}} \\ {{Q_1}} \\ {{{\dot Q}_0}} \\ {{{\dot Q}_1}} \end{array}} \right]. $$