Abstract: Aiming at the problem of solving distance extreme points on trimmed surfaces in collision
detection of rigid bodies which are represented by exact surface, a method is presented to obtain the
initial distance extreme points using the plane vector field, which can avoid the excessive subdivision of
the surface. The differential geometry conditions of the distance extreme points are discussed, and
iterative formulas for obtaining distance extreme points of the analytic surface/parametric surface and
parametric surface/parametric surface are given in this paper. The efficiency and reliability of the
algorithm are verified by an example.

Key words: collision detection, plane vector field, distance extreme points, iteration