An approach to approximation of curves for shipbuilding applications

Abstract

Numerically controlled flame cutting machines used in shipyards are generally equipped only with line-segment and circle-arc moving capabilities. This paper attacks the problem of how to approximate a given curve of arbitrary shape by a sequence of line-segments and circle-arcs. The given curve is represented by the cubic spline interpolation curve formed by a set of net points on the curve. An efficient method based on the nature of cubic spline is then provided to approximate the interpolation curve by a sequence of linesegments and circle-arcs. This method has been practically employed by the China Shipbuilding Co. in production line. In order to save storage and expedite the approximation, an effective method is also provided for selecting a near minimal set of net points whose cubic spline interpolation curve can adequately represent the actual given curve. Although the techniques are developed for shipbuilding purpose, they can find applications in other fields.

On the Teaching and Learning of Higher Mathematics

“…The teaching process is dull, the explanation is boring, and there is a lack of exploration and students' active participation, and there is a lack of mutual cooperation and communication. The teaching method adopted is still the traditional mode of chalk and blackboard, and the modern teaching methods are not fully utilized [3]. In addition, in terms of homework, the traditional model is still followed, that is, the teacher assigns fixed topics after class → the students complete the assigned topics and hand in the written homework → the teacher gives them to the students and comments on the homework after correcting them.…”

Experimental Study on Cutting Tool Sticking Failure for Stainless Steel lCrl8Ni9Ti

“…Thermal conductivity of stainless steel lCrl8Ni9Ti is low, and extending rate is high which has high temperature strength and hardness [2] , so it's cutting force is big, cutting temperature is high, work-hardening is serious, and the cutting tool wear easily in the process of cutting processing, therefore, it is considered to be the difficult-to-cut material. Because the compatibility between the workpiece material and the cutting tool material, Hard alloy tools in cutting stainless steel lCrl8Ni9Ti makes the problem of Sticking Failure seriously [3], [4] , and therefore, it is necessary to research the thermal condition of Sticking Failure.…”

High-Speed and High-Accuracy Schemes of Coordinate Calculation and End Point Judgment for Elliptic Interpolation

“…Typical interpolation schemes such as Point by Point Comparison method [5,6] and Digital Differential Analyzer method [7,8] or the combination of the two [9] can be used to realize elliptic interpolation, but they are not suitable for the modern CNC system in which advanced micro processor and embedded Operating System are applied and interpolation functions are realized as periodic tasks in software. By contrast, Data Sample method is widely applied in the modern CNC systems [10].…”