Yasumasa Kawashima

A flexible quantitative method for NC machining verification using a space-division based solid model

A geometric-modeling method called Graftree and a system design of an NC (numerical control) machining verifier based on Graftree are proposed. Graftree is constructed by combining Oct-tree and constructive solid geometry (CSG) so as to simulate machining processes precisely in three-dimensional space. Using Graftree, the Boolean operation produces no risk of yielding topological conflicts, which often cause the simulation to stop abnormally. Based on the properties of Graftree, an NC machining verifier is designed to consist of three individual subsystems: data-input operations, geometric simulation, and interactive verification, i.e., visuluatzation of machining scenes and evaluation of the machined product using models of the measuring instruments. This design lets the users watch selectively only the machining steps they want to check precisely, and verify the machining according to dimensional tolerance.

A practical method of constructing surfaces in three-dimensional digitized space

We propose a new, practical algorithm for constructing the surface of a three-dimensional object from its planar cross-sections. This algorithm deals with a general case where each cross-section of the object is given as a two-dimensional digital image and no topological information about these two adjacent cross-sections is assumed. In particular, it can handle the case where there are several connected components with some holes in each cross-section. The algorithms principle is derived from the “region growing” technique. which is well-known in two-dimensional image processing. By combining this algorithm with existing shading techniques, we can obtain a realistic image of a three-dimensional object.

Acceleration of Multi-axis NC Machining Verification

Abstract A method is presented to accelerate solid model based multi-axis NC machining verification. The method includes two steps: ternary logical set operation between a workpiece and cutter-swept volumes; and extraction of the accurate boundary of the finished parts when visualizing or measuring them. In the first step, the cutter-swept volume of each machining block is expressed by a pair of approximated volumes, one actually included in the original volume and the other, possibly in it. The pair is subtracted from the workpiece using ternary logic. The finished part is also obtained as a pair of volumes. A space-division based model, Graftree, is used effectively for the volume expression and set operations. In the second step, an accurate boundary of the finished part is extracted in ray-casting processes. The ray-casting is repeated many times, but a cache technique is applied successfully to save time.