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Journal of Information Science and Engineering, Vol. 23 No. 3, pp. 925-936 (May 2007)

Tunable Bounding Volumes for Elliptic Paraboloids*

Chung-Ming Wang and Yuan-Yu Tsai
Institute of Computer Science
National Chung-Hsing University
Taichung, 402 Taiwan

The tightness of the bounding volume is often difficult to adjust to suit different applications. In this paper, we present a technique to derive a tunable bounding volume for elliptic paraboloids, where the tightness can easily be controlled and altered at several levels. Our technique develops such a tunable bounding volume through the optimization process. Bounding volumes thus developed contain the minimal volume at the corresponding level. We implement a geometric application for the elliptic paraboloid, and analyze the tightness of the bounding volumes at different levels. Finally, we demonstrate the feasibility of using our technique in creating new types of geometries as well as several rendered images.

Keywords: tunable bounding volumes, geometric applications, elliptic paraboloids, modeling, three-dimensional objects

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Received May 11, 2005; revised February 15, 2006; accepted March 17, 2006.
Communicated by H. Y. Mark Liao.
*This paper was supported by the National Science Council (NSC) Taiwan under the grant numbers NSC 94-2213-E-005-022, NSC 94-2218-E-164-001, NSC 93-2213-E-005-018, NSC 93-2815-C-005-019-E, and NSC 92-2213-E-005-021.