Efficient algorithms for automatic viewer orientation

Abstract

The calculation of a perspective image of an object involves the position and orientation of the viewer. In many graphics applications the viewpoint and object are fixed, and an orientation is sought in which the object is “centered” in the field of view. Previous work has proposed that the viewing direction be the axis of the narrowest circular cone emanating from the viewpoint and containing the object, and has shown how this direction can be calculated based on the viewpoint and a set of n object points which includes the object's extreme points. This paper presents algorithms which efficiently accomplish this task, in O( n) average and O( n log( n)) worst-case time. The orientation problem is converted into a problem in spherical geometry, and the proposed algorithms are based on existing algorithms for the analogous plane geometry problems.