to find the intersection curves of the two given surfaces , is required in many operation such as nc machining and solid geometric modeling surface creation . normally , the intersection of two surfaces is not unique . in order to generate a proper tool path or to create a correct boundary surface , all the intersection curves must be found . a new method of finding all the intersection curves of two surfaces has been developed . this new method is based on the use of a plane vector field vf induced by the two given surfaces . the system constructs the 2d vector field vf and uses the integral curves of vf to locate the first intersection curve sc . after the first intersection curve has been found , the system locates all the initial points on sc . then , it follows the connecting curves of the initial points to locate the other intersection curves . furthermore , the initial points on the newly found curves will lead the system to other intersection curves . by following all the connecting curves , the system will find them all . once all the intersection curves are found , the system is able to select the desired tool path or construct the correct surface . additionally , the absolute distance d between two surfaces can be calculated by using the same method . the value d is used for checking the clearance of moving a cutter along a tool path .