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xi | |
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xv | |
Foreword |
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xvii | |
Preface |
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xix | |
Teaching and Reading Guides |
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xxiii | |
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1 | (36) |
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1.1 Curve representation and drawing |
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2 | (3) |
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1.2 Free-form parametric curves |
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5 | (6) |
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1.3 From subdivision to basis functions |
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11 | (5) |
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1.4 Wavelet subdivision and editing |
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16 | (13) |
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29 | (3) |
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32 | (5) |
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2 Basis Functions for Curve Representation |
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37 | (38) |
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2.1 Refinability and scaling functions |
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39 | (7) |
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2.2 Generation of smooth basis functions |
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46 | (6) |
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52 | (4) |
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2.4 Stable bases for integer-shift spaces |
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56 | (6) |
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2.5 Splines and polynomial reproduction |
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62 | (5) |
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67 | (8) |
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3 Curve Subdivision Schemes |
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75 | (58) |
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3.1 Subdivision matrices and stencils |
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76 | (9) |
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3.2 B-spline subdivision schemes |
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85 | (10) |
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3.3 Closed curve rendering |
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95 | (11) |
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106 | (23) |
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129 | (4) |
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4 Basis Functions Generated by Subdivision Matrices |
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133 | (36) |
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4.1 Subdivision operators |
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134 | (4) |
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4.2 The up-sampling convolution operation |
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138 | (3) |
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4.3 Scaling functions from subdivision matrices |
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141 | (13) |
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4.4 Convergence of subdivision schemes |
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154 | (6) |
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4.5 Uniqueness and symmetry |
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160 | (3) |
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163 | (6) |
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169 | (36) |
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5.1 Sum-rule orders and discrete moments |
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170 | (3) |
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5.2 Representation of Polynomials |
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173 | (5) |
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5.3 Characterization of sum-rule orders |
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178 | (4) |
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182 | (16) |
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198 | (7) |
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6 Convergence and Regularity Analysis |
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205 | (66) |
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206 | (5) |
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6.2 Sufficient conditions for convergence |
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211 | (7) |
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218 | (7) |
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6.4 Positive refinement sequences |
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225 | (8) |
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6.5 Convergence and regularity governed by two-scale symbols |
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233 | (11) |
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6.6 A one-parameter family |
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244 | (11) |
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6.7 Stability of the one-parameter family |
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255 | (5) |
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260 | (11) |
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7 Algebraic Polynomial Identities |
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271 | (24) |
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7.1 Fundamental existence and uniqueness theorem |
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272 | (8) |
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7.2 Normalized binomial symbols |
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280 | (8) |
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7.3 Behavior on the unit circle in the complex plane |
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288 | (3) |
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291 | (4) |
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8 Interpolatory Subdivision |
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295 | (44) |
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8.1 Scaling functions generated by interpolatory refinement sequences |
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296 | (6) |
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8.2 Convergence, regularity, and symmetry |
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302 | (10) |
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8.3 Rendering of closed and open interpolatory curves |
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312 | (10) |
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8.4 A one-parameter family of interpolatory subdivision operators |
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322 | (11) |
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333 | (6) |
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9 Wavelets for Subdivision |
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339 | (72) |
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9.1 From scaling functions to synthesis wavelets |
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340 | (11) |
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9.2 Synthesis wavelets with prescribed vanishing moments |
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351 | (13) |
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9.3 Robust stability of synthesis wavelets |
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364 | (6) |
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370 | (15) |
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9.5 Interpolation wavelets |
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385 | (16) |
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9.6 Wavelet subdivision and editing |
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401 | (5) |
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406 | (5) |
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411 | (34) |
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10.1 Control nets and net refinement |
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413 | (9) |
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10.2 Box splines as basis functions |
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422 | (5) |
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10.3 Surface subdivision masks and stencils |
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427 | (10) |
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10.4 Wavelet surface subdivision |
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437 | (5) |
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442 | (3) |
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445 | (4) |
Supplementary Readings |
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449 | (2) |
Index |
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451 | |