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one dimensional spline example

The BSpline interpolation is implemented as described in [watt92]. Input
is a set of *n* one dimensional data points *X*_{i}
and
a knot vector
containing *n*+6 knots. A set of
*n*+2 control points *p*_{i} are generated so that a cubic spline
with those control points will fit the data. The control points are such that
*p*_{0}=*p*_{1} and
*p*_{n+1}=*p*_{n+2}. We also subject the curve to
the constraint that
This means that the curve is defined over the interval
This system of equations is then solved to get the control points for the curve.
The curve at time *u* is given by a weighted sum of the control points
The
Blending functions are as follows:

Higher dimensional interpolants can be generated by interpolating each element
independently.

In general, the interpolation of a parameter proceeds as follows:

` `

`control_points = get_control_points(data, knots);`

` `

`interpolant = spline_at(t, control_points);`

*brian martin*

*1999-06-23*