论文信息 - Interactive methods for visualizable geometry

Interactive methods for visualizable geometry

Interactive computer graphics can provide new insights into the objects of pure geometry, providing intuitively useful images, and, in some cases, unexpected results. Interactive computer graphics systems have opened a new era in the visualization of pure geometry. We demonstrate the fruitful relationship between mathematics and the discipline of computer graphics, emphasizing those areas of low-dimensional geometry and topology where interactive paradigms are of growing importance.<<ETX>>

[1] Kenneth A. Brakke,et al. The Surface Evolver , 1992, Exp. Math..

[2] Mark Phillips,et al. Visualizing hyperbolic space: unusual uses of 4x4 matrices , 1992, I3D '92.

[3] Ulrich Pinkall,et al. Computing Discrete Minimal Surfaces and Their Conjugates , 1993, Exp. Math..

[4] George K. Francis. A Topological Picturebook , 1988 .

[5] Nelson L. Max,et al. Computer animation of the sphere eversion , 1975, SIGGRAPH '75.

[6] David Banks,et al. Interactive manipulation and display of surfaces in four dimensions , 1992, I3D '92.

[7] Andrew J. Hanson,et al. Interactive visualization methods for four dimensions , 1993, Proceedings Visualization '93.

[8] D. Hilbert,et al. Geometry and the Imagination , 1953 .

[9] David A. Hoffman. Adding handles to the helicoid , 1993 .

[10] Charlie Gunn,et al. Discrete groups and visualization of three-dimensional manifolds , 1993, SIGGRAPH.

[11] Pheng-Ann Heng,et al. Illuminating the fourth dimension , 1992, IEEE Computer Graphics and Applications.

[12] Michael J. Callahan,et al. Computer graphics tools for the study of minimal surfaces , 1988, CACM.

[13] Jeffrey R. Weeks,et al. The Shape of Space , 1986 .