Spatial Straight-Line Drawing Algorithm Based on Method of Discriminate Regions—A Control Algorithm of Motors

Jianping Wang, Shiguang Xiao, Tao Song, Junqi Yue, Pingyan Bian and Yu Li
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Jianping Wang: School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo 454000, China
Shiguang Xiao: School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo 454000, China
Tao Song: State Grid Jiaozuo Power Supply Company, Jiaozuo 454000, China
Junqi Yue: School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo 454000, China
Pingyan Bian: School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo 454000, China
Yu Li: School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo 454000, China

Energies, 2020, vol. 13, issue 19, 1-16

Abstract: A novelty algorithm of spatial straight-line drawing based on a method of discriminate regions is proposed in this paper based on Bresenham’s algorithm. Three-dimensional space is divided into innumerable three-dimensional meshes according to the given rule; the distance between the start and the end points of the three coordinates is Δx , Δy , and Δz , respectively; the distribution types of spatial straight line and the position of the end point are determined by judging the relationship among Δx , Δy , and Δz ; then, the active-passive directions can be determined. The plane of the ending point of the straight line in a three-dimensional mesh is divided into four regions; then, the discriminant is obtained; and this discriminant determine which region the point is located in The algorithm is verified and analyzed by the method of contrastive analysis; the results show that: the error of the algorithm is related to the step length L; the maximum theoretical error is 0.7071*L. The discriminants are all integers, so the problem of deviation from the theoretical straight line caused by the retention of decimals of significant digits can be avoided. Finally, the algorithm is applied to the cooperative control of multiple motors, and conversion between unit grid number and pulse number of motors is performed.

Keywords: Bresenham’s algorithm; spatial straight line; discriminate regions; integer discriminants (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2020
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