工程设计中直纹面生成的三维曲线等距方法
A 3D Curve Offset Approach for Ruled Surface Generation in Engineering Design
摘要：
直纹面在工程设计中有着广泛的应用，如注塑模分型面设计、检具面设计等，通常都是通过对三维曲线进行偏置来生成直纹面。然而，在三维曲线等距中，往往存在着断裂、干涉和重叠等问题，现有的CAD软件无法自动解决这些问题。针对直纹曲面生成中的三维曲线等距算法，提出了三项关键技术：改进的曲线分割方法，减小了等距距离和曲率变化对等距精度的影响;在此基础上，提出了一种曲线过渡方法，提高了曲线在断点和相交/重叠区域的偏移质量，其中提出了一种新的正权球面有理四次Bezier曲线生成算法，直纹面最后通过分型面和校核面两个设计实例表明，该方法可以提高直纹面生成的效率和质量。
英文摘要：
Ruled surface is widely used in engineering design such as parting surface design of injection mold and checking surface design of checking fixture, which are usually generated by offsetting 3D curves. However, in 3D curve offset, there often exist break,interaction and overlapping problems which can't be solved by current CAD software automatically. This paper is targeted at developing a 3D curve offsetting algorithm for ruled surface generation, and three key technologies are introduced in details: An improved curve division method is proposed to reduce the offset accuracy error resulted from different offset distances and curvatures; An offsetting curve overlapping detection and elimination method is proposed; And then, a curve transition method is presented to improve curve offsetting quality for the break and intersection/overlapping regions, where a new algorithm for generating positive weights spherical rational quartic Bezier curve is proposed to bridge the breaks of offset curves to create a smooth ruled surface. Finally, two practical design cases, parting surface and checking surface generation, show that the proposed approach can enhance the efficiency and quality for ruled surface generation in engineering design.
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