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Hermite and Cubic Spline Interpolation
A Simple Approximation Technique Uniform Cubic Bsplines
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algorithm approximation arbitrary basis functions basis segments Bernstein polynomials Beta-spline curve Bezier curve bounding box breakpoint interval C2 continuity Catmull-Rom splines Chapter coefficients collinear construct continuously-shaped Beta-spline control graph control vertices convex hull corresponding cubic B-spline curve cubic polynomials curvature vector curve of Figure curve segment curves and surfaces data points defined differencing discontinuity discrete B-spline divided difference endfor equations evaluation example formula four geometric continuity given Hermite interpolation Horner's rule interpolation joint knot sequence knot spacing line segment linear combination linearly independent m,+i matrix multiple knots node nonzero notation obtain one-sided basis one-sided power functions parameter range parametric derivatives patch Pi and p2 piecewise positive properties quadratic recurrence refinement represent representation result segment polynomials shown in Figure spline surface subdivision techniques Theorem tion ui+k uniform cubic B-spline uniform knot uniformly-shaped Beta-spline values of Pi vector space vertex zero