Machinists often simulate a part program to verify its correctness, since mistakescan cause damage to the part, machine, oneself, or others. A popular approach forpart program simulation involves representing the stock (the material the part is being carved from) as a heightmap. Although this approach is computationally fast and memory efficient, only objects that are representable as functional surfaces (e.g., z = f(x, y)) can be machined. This thesis presents a new heightmap-based datastructure, called a multidirectional heightmap, that does not have this limitation. A multidirectional heightmap, in response to an overhang, recursively subdivides itself until each piece can be represented by an axis-aligned heightmap. More precisely, a multidirectional heightmap is a kD-tree with the property that all cellsare functional: each cell contains a heightmap that represents a functional portion of the stock. To improve accuracy, each regular heightmap can be replaced by a3-Way Heightmap, a new type of heightmap that samples the tool along all threestock axis directions (three ways) rather than just one. The experimental resultsherein suggest that the multidirectional heightmap data structure achieves a goodlevel of performance with respect to memory usage, CPU usage, and approximationerror.
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Software Simulation of 5-Axis CNC Milling using Multidirectional Heightmaps