Ebook: Geometric Analysis and Computer Graphics: Proceedings of a Workshop held May 23–25, 1988

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.

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The meeting at the Mathematical Sciences Research Institute in Berkeley was structured around principal lectures given by Almgren, Callahan, Ericksen, Francis, Gulliver, Hanrahan, Kajiya, Polthier, Sethian, Sterling, Thomas, and Vogel. The divergent backgrounds of these and the many other participants, as reflected in their lectures at the meeting and in the papers presented here, testify to the unifying element of the workshop's central theme. The depth and range of the new developments presented in the lectures point to scientific and technological frontiers being crossed with impressive speed. The present volume is offered as a permanent record for those who were present, and also with a view towards making the material available to a wider audience than were able to attend.

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The meeting at the Mathematical Sciences Research Institute in Berkeley was structured around principal lectures given by Almgren, Callahan, Ericksen, Francis, Gulliver, Hanrahan, Kajiya, Polthier, Sethian, Sterling, Thomas, and Vogel. The divergent backgrounds of these and the many other participants, as reflected in their lectures at the meeting and in the papers presented here, testify to the unifying element of the workshop's central theme. The depth and range of the new developments presented in the lectures point to scientific and technological frontiers being crossed with impressive speed. The present volume is offered as a permanent record for those who were present, and also with a view towards making the material available to a wider audience than were able to attend.
Content:
Front Matter....Pages i-ix
Computer Graphics of Solutions of the Generalized Monge-Amp?re Equation....Pages 1-17
Computer Graphics Tools for Rendering Algebraic Surfaces and for Geometry of Order....Pages 19-30
A Low Cost Animation System Applied to Ray Tracing in Liquid Crystals....Pages 31-37
From Sketches to Equations to Pictures: Minimal Surfaces and Computer Graphics....Pages 39-48
Nonuniqueness and Uniqueness of Capillary Surfaces....Pages 49-61
Static Theory of Nematic Liquid Crystals....Pages 63-63
The Etruscan Venus....Pages 65-66
Harmonic Mappings, Symmetry, and Computer Graphics....Pages 67-77
Video Based Scientific Visualization....Pages 79-87
Bubbles, Conservation Laws, and Balanced Diagrams....Pages 89-102
Liquid Menisci in Polyhedral Containers....Pages 103-108
Can One Hear the Shape of a Fractal Drum? Partial Resolution of the Weyl-Berry Conjecture....Pages 109-118
Geometric Data for Triply Periodic Minimal Surfaces in Spaces of Constant Curvature....Pages 119-126
Embedded Triply-Periodic Minimal Surfaces and Related Soap Film Experiments....Pages 127-138
The Collapse of a Dumbbell Moving Under Its Mean Curvature....Pages 139-145
Geometry Versus Imaging: Extended Abstract....Pages 147-157
Constant Mean Curvature Tori....Pages 159-168
On Deformable Models....Pages 169-174
Periodic Area Minimizing Surfaces in Microstructural Science....Pages 175-180
Types of Instability for the Trapped Drop Problem with Equal Contact Angles....Pages 181-192
....Pages 193-194