Geometric Analysis and Computer Graphics

1. Front Matter

   Pages i-ix

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2. Multi-functions Mod ν

   • Frederick J. Almgren Jr.

   Pages 1-17

3. Computer Graphics of Solutions of the Generalized Monge-Ampère Equation

   • Alfred Baldes, Ortwin Wohlrab

   Pages 19-30

4. Computer Graphics Tools for Rendering Algebraic Surfaces and for Geometry of Order

   • Thomas F. Banchoff

   Pages 31-37

5. A Low Cost Animation System Applied to Ray Tracing in Liquid Crystals

   • J. R. Bellare, J. A. MacDonald, P. P. Bergstrom, L. E. Scriven, H. T. Davis

   Pages 39-48

6. From Sketches to Equations to Pictures: Minimal Surfaces and Computer Graphics

   • Michael J. Callahan

   Pages 49-61

7. Nonuniqueness and Uniqueness of Capillary Surfaces

   • Paul Concus, Robert Finn

   Pages 63-63

8. Static Theory of Nematic Liquid Crystals

   • J. L. Ericksen

   Pages 65-66

9. The Etruscan Venus

   • George K. Francis

   Pages 67-77

10. Harmonic Mappings, Symmetry, and Computer Graphics

    • Robert Gulliver

    Pages 79-87

11. Video Based Scientific Visualization

    • W. E. Johnston, D. W. Robertson, D. E. Hall, J. Huang, F. Renema, M. Rible et al.

    Pages 89-102

12. Bubbles, Conservation Laws, and Balanced Diagrams

    • Rob Kusner

    Pages 103-108

13. Liquid Menisci in Polyhedral Containers

    • Dieter Langbein, Ulrich Hornung

    Pages 109-118

14. Can One Hear the Shape of a Fractal Drum? Partial Resolution of the Weyl-Berry Conjecture

    • Michel L. Lapidus

    Pages 119-126

15. Steepest Descent as a Tool to Find Critical Points of ∫ k ² Defined on Curves in the Plane with Arbitrary Types of Boundary Conditions

    • Anders Linnér

    Pages 127-138

16. Geometric Data for Triply Periodic Minimal Surfaces in Spaces of Constant Curvature

    • Konrad Polthier

    Pages 139-145

17. Embedded Triply-Periodic Minimal Surfaces and Related Soap Film Experiments

    • Alan H. Schoen

    Pages 147-157

18. The Collapse of a Dumbbell Moving Under Its Mean Curvature

    • J. A. Sethian

    Pages 159-168

19. Geometry Versus Imaging: Extended Abstract

    • Alvy Ray Smith

    Pages 169-174

20. Constant Mean Curvature Tori

    • I. Sterling

    Pages 175-180

This volume derives from a workshop on differential geometry, calculus of vari­ ations, and computer graphics at the Mathematical Sciences Research Institute in Berkeley, May 23-25, 1988. The meeting was structured around principal lectures given by F. Almgren, M. Callahan, J. Ericksen, G. Francis, R. Gulliver, P. Hanra­ han, J. Kajiya, K. Polthier, J. Sethian, I. Sterling, E. L. Thomas, and T. Vogel. The divergent backgrounds of these and the many other participants, as reflected in their lectures at the meeting and in their papers presented here, testify to the unifying element of the workshop's central theme. Any such meeting is ultimately dependent for its success on the interest and motivation of its participants. In this respect the present gathering was especially fortunate. The depth and range of the new developments presented in the lectures and also in informal discussion point to scientific and technological frontiers be­ ing crossed with impressive speed. The present volume is offered as a permanent record for those who were present, and also with a view toward making the material available to a wider audience than were able to attend.

• Impress
• Mean curvature
• Minimal surface
• Volume
• animation
• computer
• computer graphics
• curvature
• development
• fractal
• graphics
• ray tracing
• rendering
• scientific visualization
• visualization

• Lawrence Berkeley Laboratory and Department of Mathematics, University of California at Berkeley, Berkeley, USA

  Paul Concus

• Department of Mathematics, Stanford University, Stanford, USA

  Robert Finn

• Department of Mathematics, University of Massachusetts, Amherst, USA

  David A. Hoffman

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