1983 Volume 49 Issue 11 Pages 1561-1566
An interference detection problem among solids in a CAD/CAM system is considered analytically by means of the simplex method. This idea deals directly with the half spaces defining the geometric models, which is appropriate for the constructive solid geometry. The simplex method is applied to a linear inequalities system defining the intersection of two convex polyhedra from two solids in question. Thus an approximation of each solid to a union of convex polyhedra is required. The method makes the followings possible: (1) to check the interference between two convex polyhedra just by manipulating a corresponding matrix, (2) to check the separation at the beginning of the algorithm, (3) to calculate optimally by the simplex criterion, (4) to calculate necessary points for the detection systematically. The implementation indicates that the method functioned well when two polyhedra interpenetrate or separate more than 10-4. The cases of interpenetration and separation less than 10-6 malfunctioned, which is due to the error propagation in the successive calculations of a matrix in the simplex method.
