Author： Tien H. L. Hansuebsai D. Phien H. N.
Publisher： Taylor & Francis Ltd
ISSN： 1464-5211
Source： International Journal of Mathematical Education in Science and Technology, Vol.30, Iss.2, 1999-03, pp. : 243-257
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Abstract
Although Bezier curves have been used as a base model for curve modeling in computer graphics, computer-aided design (CAD) and computer-aided geometric design (CAGD), generalized Ball curves have been found to be more suitable in some circumstances. The present study introduces rational Ball curves which are obtained from generalized Ball curves by appropriately introducing the weights. It is shown that a rational Ball curve is a rational Bezier curve of the same degree and vice versa. By means of the polar form approach, the weights and control points of a rational curve in one model are shown to be obtained from the weights and control points of the other model. The relationship established in this paper allows one to go from one model to the other to make use of the good properties of each model in practical situations.
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