METHOD FOR FINDING INTERSECTION OF SCULPTURED SURFACE AND STRAIGHT LINE

摘要

PURPOSE:To calculate all the intersections without missing and efficiently by dividing a sculptured surface crossing with a straight line in lattice shape, making division points into groups based on the positive and negative value of the component of normal vector in a direction of straight line, and finding the intersection with the straight line for each group. CONSTITUTION:The sculuptured surface comprising of a patch 2 and another patch is defined on an XYZ coordinate system with an appropriate method, and similarly, the straight line 4 crossing with the sculptured surface is defined on the XYZ coordinate system. The coordinate system is converted so as to set the direction of the straight line 4 at a coordinate axis from the coordinate system, and the free curved surface crossing with the straight line 4 is divided in the grid shape, and the component of the direction of the coordinate axis in the same direction as that of the straight line 4 of the normal vector N at a lattice point is checked, and the lattice point is made into the groups based on the positive and negative value. Then, the intersection with the straight line 4 can be found at every group. In such a way, it is possible to efficiently find almost all the intersections of the sculuptured surface with the straight line 4.