De Boor's algorithm: Difference between revisions

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== Introduction ==
 
The general setting is as follows. We would like to construct a curve whose shape is described by a sequence of ''p'' points <math>\vec{d}_0, \vec{d}_1, \dots, \vec{d}_{p-1}</math>, which palysplays the role of a ''control polygon''. The curve can be described as a function <math> \vec{s}(x)</math> of one parameter ''x''. To pass through the sequence of points, the curve must satisfy <math>\vec{s}(u_0)=\vec{d}_0, \dots,
\vec{s}(u_{p-1})=\vec{d}_{p-1}</math>. But this is not quite the case: in general we are satisfied that the curve "approximate" the control polygon. We assume that ''u<sub>0</sub>, ..., u<sub>p-1</sub>'' are given to us along with <math>\vec{d}_0, \vec{d}_1, \dots, \vec{d}_{p-1}</math>.