Mathematics of Surfaces XIII

1. Front Matter

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2. Computing Isophotes on Free-Form Surfaces Based on Support Function Approximation

   • M. Aigner, L. Gonzalez-Vega, B. Jüttler, M. L. Sampoli

   Pages 1-18

3. Swept Volume Parameterization for Isogeometric Analysis

   • M. Aigner, C. Heinrich, B. Jüttler, E. Pilgerstorfer, B. Simeon, A. -V. Vuong

   Pages 19-44

4. Numerical Checking of C ¹ for Arbitrary Degree Quadrilateral Subdivision Schemes

   • U. H. Augsdörfer, T. J. Cashman, N. A. Dodgson, M. A. Sabin

   Pages 45-54

5. The Invariant Functions of the Rational Bi-cubic Bézier Surfaces

   • H. E. Bez

   Pages 55-74

6. Crazy Cuts: Dissecting Planar Shapes into Two Identical Parts

   • A. M. Bruckstein, D. Shaked

   Pages 75-89

7. Piecewise Rational Manifold Surfaces with Sharp Features

   • G. Della Vecchia, B. Jüttler

   Pages 90-105

8. Deriving Box-Spline Subdivision Schemes

   • N. A. Dodgson, U. H. Augsdörfer, T. J. Cashman, M. A. Sabin

   Pages 106-123

9. Geometric Characterizations of Graphs Using Heat Kernel Embeddings

   • H. El-Ghawalby, E. R. Hancock

   Pages 124-142

10. Compressive Algorithms—Adaptive Solutions of PDEs and Variational Problems

    • M. Fornasier

    Pages 143-169

11. Symmetry-Aware Mesh Processing

    • A. Golovinskiy, J. Podolak, T. Funkhouser

    Pages 170-188

12. Recent Advances in Computational Conformal Geometry

    • X. D. Gu, F. Luo, S. -T. Yau

    Pages 189-221

13. Finite Curvature Continuous Polar Patchworks

    • K. Karčiauskas, J. Peters

    Pages 222-234

14. A New Approach to Point Membership Classification in B-rep Solids

    • F. Klein

    Pages 235-250

15. Probabilistic Modeling and Visualization of the Flexibility in Morphable Models

    • M. Lüthi, T. Albrecht, T. Vetter

    Pages 251-264

16. Parameterizing Singularities of Positive Integral Index

    • M. Nieser, K. Polthier

    Pages 265-277

17. Two Step Time Discretization of Willmore Flow

    • N. Olischläger, M. Rumpf

    Pages 278-292

18. Surface Triangulation and the Downstream Effects on Flattening

    • S. S. Parwana, R. J. Cripps

    Pages 293-306

19. On Mesh Editing, Manifold Learning, and Diffusion Wavelets

    • R. M. Rustamov

    Pages 307-321

20. Gradient Approximation on Uniform Meshes by Finite Differences and Cubic Spline Interpolation

    • P. Sablonnière

    Pages 322-334

This book constitutes the refereed proceedings of the 13th IMA International Conference on the Mathematics of Surfaces held in York, UK in September 2009. The papers in the present volume include seven invited papers, as well as 16 submitted papers. The topics covered include subdivision schemes and their continuity, polar patchworks, compressive algorithms for PDEs, surface invariant functions, swept volume parameterization, Willmore flow, computational conformal geometry, heat kernel embeddings, and self-organizing maps on manifolds, mesh and manifold construction, editing, flattening, morphing and interrogation, dissection of planar shapes, symmetry processing, morphable models, computation of isophotes, point membership classification and vertex blends. Surface types considered encompass polygon meshes as well as parametric and implicit surfaces.

• Spline
• algorithms
• bezier surfaces
• calculus
• computational geometry
• geometry
• isogeometric analysis
• isophotes
• meshes
• model
• modeling
• quadrilateral subdivision
• rational manifold
• visualization
• willmore flow
• algorithm analysis and problem complexity

• Computer Vision and Pattern Recognition Group,Computer Science, University of York Heslington, York, United Kingdom

  Edwin R. Hancock

• School of Computer Science, Cardiff University, Cardiff, UK

  Ralph R. Martin

• Numerical Geometry Ltd, Cambridge, UK

  Malcolm A. Sabin

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