B-spline curves - uniform b-splines and de boor algorithm, Computer Graphics

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B-spline curves are piecewise smooth polynomial curves.

B-spline curves are defined over an interval which has been partitioned into sub-intervals. On each subinterval B-spline curve reduces to a polynomial curve. The curve pieces are joined in such a way that the composite curve satisfies certain smoothness conditions specified in terms of matching of derivatives of certain orders. Points defining the partition of the interval are called knots or knot points. This is because at this common domain point of the interval, two polynomial curve segments are joined to make the composite curve.
B-spline curves as well as blending functions are computed using the iterative de Boor algorithm.
B-splines satisfy the important properties suitable for geometric modellling in computer Graphics. Some of these include (i) local control (ii) smoothness (iii) degree of spline curve does not depend on the number of control points (iv) convex hull property (v) convenient blending functions.
Uniform B-splines are B-spline curves with uniform spacing between the knots.
Uniform B-splines give periodic blending functions. This means all blending functions are translated versions of a single B-spline.

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