Geometric Computing for Industrial Design, Manufacturing and Management
Date Issued
2014
Date
2014
Author(s)
Dai, Bang-Sin
Abstract
This dissertation addresses the geometric computing problems in industrial application from an algorithmic perspective. The practical issues encountered in the fields of industrial design, manufacturing, and management are formulated as algorithmic problems by mathematical abstraction. We present both the algorithmic results and the hardness proofs with theoretical guarantees and also the combinatorial bounds in the aspect of combinatorics to jointly compose a comprehensive study for the entire research.
In terms of industrial design and manufacturing, we consider the solid moulding problem, which is formulated from the optimization point of view in the design and manufacturing process of moulding technology. From the theoretical perspective, the solid moulding problem is also fundamental in visibility, one of the most classical topics in computational geometry. We present both the algorithmic results and the hardness proofs for the problems addressed in this dissertation, and the gap between the problem complexity and the algorithm complexity contained in our main results is nearly closed. In the aspect of combinatorics, we provide the tight combinatorial bounds. Our algorithms are efficient in practice.
In terms of industrial management, we consider the time convex hull problem, which arises from path planning and further extensions of the shortest path problem, in the presence of high-speed transportation networks. For transportation business, to minimize the transportation time and cost is among the most important objectives. We explore shortest time-path planning and the generalization of convex hull into which the time-based concept is introduced. The main result is an optimal time algorithm for the problem under the general Lp metrics, in the presence of a straight-line highway. Our results in some sense have closed the study of this problem in the particular network topology.
Subjects
計算幾何
可視性
固體鑄模
路徑規劃
時間凸包
Type
thesis
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