[an error occurred while processing this directive] Interactive Methods for Visualizable Geometry

Interactive Methods for Visualizable Geometry

Andrew J. Hanson and Tamara Munzner and George Francis

IEEE Computer, Vol. 27, No. 4, pp. 73-83, July 1994.

Introduction

Mathematical visualization is the art of creating a tangible experience with abstract mathematical objects and concepts. While this process has been a cornerstone of the mathematical reasoning process since the times of the ancient geometers, the advent of high-performance interactive computer graphics systems has opened a new era whose ultimate significance can only be imagined.

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The article begins with an overview of mathematical visualization and then turns its attention to some of the visualization methods that have been used to bring computer graphics technology to bear on mathematical problems of low-dimensional topology and geometry. The concluding sections discuss the system design philosophies of various research groups and prospects for the future. Examples of computer-generated images are supplied throughout, and separate sidebars are devoted to a brief glossary, sources of additional background information on visualizable mathematics, and an overview of selected film and video animations concerned with mathematical visualization.

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