Subdivision I: The Univariate Setting B-Splines (Uniform)

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<strong>Subdivision</strong> SchemesSome properties affine invariance compact support index invariance (topologicsymmetry) local definitionCS175 200519<strong>Subdivision</strong> OperatorProperties compact support affine invariance index invariance/symmetryCS175 200520
Page 1 and 2: Subdivision I:The UnivariateSetting
Page 3 and 4: ConvolutionReminder definition: tra
Page 5: B-Spline RefinementExamples1 2( 1,
Page 8 and 9: Subdivision OperatorExample cubic s
Page 12 and 13: ExamplesSplines linear: quadratic:
Page 14 and 15: AnalysisConvergence define linear i
Page 16 and 17: ExampleCubic B-splines stencils1/84
Page 18 and 19: SmoothnessConsequences 4pt scheme:
Page 20 and 21: So Far, So Good IWhat do we know no
Page 22 and 23: 4pt Scheme IIWeight computation gri
Page 24 and 25: ExampleCubic B-spline 5 control poi
Page 26 and 27: Subdivision MatrixProperties eigen
Page 28 and 29: Necessary ConditionsContinuity at e
Page 30 and 31: ConvergenceLimit position let j go
Page 32: Affine InvarianceSanity condition a

Subdivision I: The Univariate Setting B-Splines (Uniform)

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