An Introduction to Splines for Use in Computer Graphics and Geometric Modeling |
Contents
Introduction 1 | 1 |
Hermite and Cubic Spline Interpolation 9 | 9 |
A Simple Approximation Technique Uniform Cubic Bsplines | 19 |
Copyright | |
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additional algorithm applied approximation arbitrary B-spline curve B₁ B₂ basis functions begin Beta-spline Bézier curve boundary Chapter coefficients Computer consider construction continuity control graph control vertices corresponding course defined derivative derivative vectors Design difference discussion equal equations establish evaluation example expression fact Figure formula four geometric give given Graphics Hence illustrate increasing interpolation interval joint knot knot sequence matrix multiplicity node nonzero Note observation obtain parameter particular patch points polynomials positions produce properties range recurrence refinement represent representation require respect result satisfy segment segment polynomials shape shown in Figure shows simply single space specific spline step subdivision successive surface Table technique tion uniform cubic B-spline V₁ values vertex yields zero