ACM SIGGRAPH 86: course notes, 13th Annual Conference on Computer Graphics and Interactive Techniques, Dallas Convention Center, Dallas, Texas, August 18-22, 1986, Volume 4
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A Simple Approximation Technique Uniform Cubic Bsplines
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algorithm argument basis functions basis segments Be'zier curve Bernstein polynomials bounding boxes breakpoint interval C2 continuity Catmull-Rom splines coefficients collinear compute consider constant constructed continuously-shaped Beta-spline curve control graph convex hull corresponding cubic B-spline curve cubic polynomials curvature vector curve of Figure curve segment curves and surfaces data points definition differencing discontinuity discrete B-splines discretely-shaped Beta-splines discussed divided difference end conditions endpoints equations evaluated example geometric continuity given Hence Hermite interpolation Horner's rule joint knot of multiplicity knot sequence knot spacing legal parameter range linear combination linearly independent matrix multiple knots node nonzero obtain one-sided basis one-sided power functions parametric derivatives patch piecewise quadratic recurrence refinement represented result second derivative vectors segment polynomials shown in Figure simply spline summation tangent vector Theorem tions ui+i uniform cubic B-spline uniform knot values vector space vertex zero