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.