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.
Highlights
Straight line drawing is among the important fields of various industries, such as straight-line interpolation [1], stepper motor cooperative control [2], 3D printing [3], 3D model building [4], and image drawing [5]
The most famous is the Bresenham’s algorithm, which is introduced during the 1960s
To draw three-dimensional space straight lines, a novelty method of discriminate regions is proposed in this paper
Summary
Straight line drawing is among the important fields of various industries, such as straight-line interpolation [1], stepper motor cooperative control [2], 3D printing [3], 3D model building [4], and image drawing [5]. To quickly draw straight lines, the speed of the applied algorithm is critical. The most famous is the Bresenham’s algorithm, which is introduced during the 1960s. The advantage of Bresenham’s algorithm is that all the operations are integers, without division or decimals. This approach is efficient at selecting a set of grid points to represent a straight line in a two-dimensional space. Space symmetry and simplifying computation are two major aspects of the algorithm towards high efficiency [14]
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