Based on the concept of gauge function, the pseudo minimum translational distance (PMTD) between two convex objects is defined in this paper. PMTD not only provides a measure of the clearance between two separating ob...Based on the concept of gauge function, the pseudo minimum translational distance (PMTD) between two convex objects is defined in this paper. PMTD not only provides a measure of the clearance between two separating objects, but also quantifies the penetration of two objects intersecting each other. It is proved that the PMTD is differentiate almost everywhere w. r.t. the configuration variable of the objects. Algorithms for calculating PMTD and its derivative are also presented.展开更多
基金the National Natural Science Foundation of China (Grant Nos. 59805004, 59990470) the National Distinguished Youth Foundation (Grant No. 59725514).
文摘Based on the concept of gauge function, the pseudo minimum translational distance (PMTD) between two convex objects is defined in this paper. PMTD not only provides a measure of the clearance between two separating objects, but also quantifies the penetration of two objects intersecting each other. It is proved that the PMTD is differentiate almost everywhere w. r.t. the configuration variable of the objects. Algorithms for calculating PMTD and its derivative are also presented.
