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research-article

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

[+] Author and Article Information
Masatomo Inui

Department of Intelligent Systems Engineering, Ibaraki University 4-12-1, Nakanarusawa, Hitachi, Ibaraki, 316-8511, JAPAN
masatomo.inui.az@vc.ibaraki.ac.jp

Nobuyuki Umezu

Department of Intelligent Systems Engineering, Ibaraki University 4-12-1, Nakanarusawa, Hitachi, Ibaraki, 316-8511, JAPAN
nobuyuki.umezu.cs@vc.ibaraki.ac.jp

1Corresponding author.

ASME doi:10.1115/1.4034737 History: Received August 21, 2014; Revised August 31, 2016

Abstract

In the geometric simulation of multi-axis milling, dexel representation solid model is often used. In this modeling method, the object shape is defined as a collection of vertical segments (dexels) based on a 2 dimensional regular square grid in the xy plane. In this paper, the authors propose quad pillars algorithm and its improvement named delta pillars algorithm for converting a dexel model to an equivalent polyhedral 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 as a result of simplified Boolean union operation of the pillar shapes. Different from the prior methods, proposed algorithms are simple and fast, and they are guaranteed to generate the water-tight polyhedral model without holes, gaps, and T-junctions. An experimental system is implemented and some conversion tests are performed. The system can convert a dexel model based on a high resolution grid to a polyhedral model in a practical amount of time.

Copyright (c) 2016 by ASME
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