Quad Pillars and Delta Pillars: Algorithms for Converting Dexel Models to Polyhedral Models

In the geometric simulation of multi-axis milling, a dexel representation solid model is frequently used. In this modeling method, the object shape is defined as a collection of vertical segments (dexels) based on a two-dimensional regular square grid in the XY plane. In this paper, the authors propose the quad pillars algorithm and its enhanced version named the delta pillars algorithm for converting a dexel model to an equivalent polyhedral stereolithography (STL) model. These algorithms define a series of vertical pillar shapes for each square cell of the grid to represent the object shape as a bundle of pillars. The final polyhedral model is obtained by performing a simplified Boolean union operation of the pillar shapes. Unlike prior methods, the proposed algorithms are simple and fast and are guaranteed to generate a watertight polyhedral model without holes, gaps, or T-junctions. An experimental system is implemented and conversion tests are performed. The system converted a dexel model based on a high-resolution grid to a polyhedral model in a practical amount of time.