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Research Papers

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

[+] Author and Article Information
Masatomo Inui

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

Contributed by the Computers and Information Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received August 21, 2014; final manuscript received August 31, 2016; published online February 16, 2017. Editor: Bahram Ravani.

J. Comput. Inf. Sci. Eng 17(3), 031001 (Feb 16, 2017) (9 pages) Paper No: JCISE-14-1257; doi: 10.1115/1.4034737 History: Received August 21, 2014; Revised August 31, 2016

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.

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Figures

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Fig. 1

Dexel representation of a solid model

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Fig. 2

Outline of quad pillars algorithm

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Fig. 3

Dexel lists on four adjacent grid points

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Fig. 4

Section of dexel models with overhangs and their conversion to pillars

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Fig. 6

Expansion of gray zones by shifting borders of the black and white zones

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Fig. 7

Dexels representing a horizontally placed box and their corresponding zones

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Fig. 8

Selection of the highest endpoint in a WGB gray zone for each dexel list

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Fig. 10

Removal of overlapping portions of the wall trapezoids in quad pillars algorithm

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Fig. 11

Necessary Boolean subtraction of trapezoids in quad pillars algorithm

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Fig. 12

Impossible configuration of trapezoids

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Fig. 13

T-junctions on an edge

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Fig. 14

Triangulation process of remaining trapezoid in sidewall

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Fig. 15

Construction of a triangular pillar shape using three dexel lists

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Fig. 16

Selection rules of type A, B, C, and D triangular pillars

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Fig. 17

Removal of overlapping portions of wall-side trapezoids in delta pillars algorithm

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Fig. 18

Conversion results using quad pillars and delta pillars algorithms

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Fig. 19

Conversion result of sample model A

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Fig. 20

Conversion result of sample model B

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Fig. 21

Relationship between number of dexels and required time for conversion

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