Generation of CAD Surfaces by using Cubic Spline Curves

Innovative and Intelligent Design Technologies

The latest computation techniques made it possible to simulate complex sculptured surfaces for CAD/CAM applications. The design of mechanical components are becoming more and more complex with the advancement in the speed and the power of computers.
In this research work a cubic spline curve generation algorithm is developed and implemented in a CAD system called Design and Manufacture of Complex Surfaces (DMCS). The technique generates cubic spline curves and these curves are integrated to generate complex surfaces. The cubic spline interpolation technique is developed for CAD applications which require exact shape of the objects. The surfaces produced have enough geometrical information like position, tangent/normal, and curvature so that they may be used in CAM applications. The system is capable of generating and editing the complex surfaces and then producing manufacturing information in CAM package. In this paper complete mathematical algorithm for the cubic spline interpolation technique is given. The working of the DMCS system is also presented by using a case study.

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Submitted by kawan on Fri, 22/06/2007 - 1:17pm.
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drawbacks?

Submitted by LiuH on Tue, 03/07/2007 - 10:53am.

Dear author,

Thanks very much for your contribution to IPROMS2007 and the interesting presentation that has been uploaded on time. One question from me, you mentioned that the spline method described in section 3 has two draw backs. Could your approach overcome them? If yes, can you briefly explain how? Cheers.

Maria

The cubic spline

Submitted by kawan on Tue, 03/07/2007 - 8:07pm.

The cubic spline curve/surface has two drawbacks
i. A local modification involves the re-computation of the entire spline.
ii. A spline, as treated here, will not cope with a vertical tangent.

In the first case, still cubic spline is more efficient as far as surfaces are concern. As only curves are used to define/make surface, mathematical calculations are far less then similar ‘surfaces’ produced using other methods like Bazier or B-spline or conic etc. Although calculation for curves are some what slower as entire curve needs to be calculated. But in our work surfaces are used so cubic spline has distinct advantage. In some future p[publication I will try to compare computation time for different techniques used for generating the surfaces.

In the second case, it is bit tricky. I am checking on every point I am using for vertical tangent to avoid it. It is not very efficient way of doing it but for the time being this is the only way I can figure out. I am still working to get rid of this problem in the algorithm.

Generation of CAD Surfaces by using Cubic Spline Curves

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