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Hermite and Cubic Spline Interpolation
A Simple Approximation Technique Uniform Cubic Bsplines
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algorithm approximation arbitrary Barsky basis functions basis segments Bernstein polynomials Beta-spline curve Bezier curve bounding box breakpoint interval C2 continuity Catmull-Rom splines Chapter coefficients collinear Computer Graphics 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 differencing discontinuity discrete B-spline discussion divided difference endfor equations evaluation example formula four geometric continuity given Hermite interpolation interpolation joint knot sequence knot spacing line segment linear combination linearly M,+I matrix multiple knots node nonnegative nonzero notation obtain one-sided basis one-sided power functions parameter range Parametric Curves parametric derivatives patch piecewise polygon properties recurrence refinement represent representation result second derivative vectors Section segment polynomials shown in Figure simply spline surface subdivision techniques Theorem tion triple uniform cubic B-spline uniform knot uniformly-shaped Beta-spline values vector space vertex zero