Operations research: deterministic optimization models
Operations research: deterministic optimization models
On some geometric optimization problems in layered manufacturing
Computational Geometry: Theory and Applications
Rapid Prototyping and Manufacturing: Fundamentals of StereoLithography
Rapid Prototyping and Manufacturing: Fundamentals of StereoLithography
Removing Zero-Volume Parts from CAD Models for Layered Manufacturing
IEEE Computer Graphics and Applications
A multi-criteria optimization framework for industrial shop scheduling using fuzzy set theory
Integrated Computer-Aided Engineering
Optimising operational costs using Soft Computing techniques
Integrated Computer-Aided Engineering
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Layered manufacturing in rapid prototyping is to fabricate prototypes by using a laser beam to trace the cross-sectional contours of a product layer by layer. Such cross-sections of geometrical objects differ by layers and generally have more than one continuous contour in each layer. In an attempt to facilitate an efficient approach for path planning, the problem is simplified by approximating each of the continuous contours with its minimum circumscribed circle. The tool path planning for traversing all the contours in the same cross-section can then be simplified as the path planning of circles. Finding the shortest path for three circles is fundamental to solving the more general problem. In this paper, the problem of finding the minimum traversal path of three circles is transferred to the problem of finding the minimum traversal path of one circle and two points. By using the concepts of light reflection and accompanied by geometric mathematics, the equation of the minimum traversal path of three circles is derived. By analyzing the initially obtained eight roots, the two-root solution function is derived. This solution function can be used for applications including robotic motion planning and path planning for submarines, ships, and airplanes.