Degenerations of rational Bezier surface with weights in the form of exponential function

作者：Zhang Yue; Zhu Chun-gang^*; Guo Qing-jie

来源：Applied Mathematics. Series B, A Journal of Chinese Universities, 2017, 32(2): 164-182.

DOI：10.1007/s11766-017-3457-9

• rational Bezier surface
• weights
• regular control surface
• toric degenerations
• exponential function

Rational B,zier surface is a widely used surface fitting tool in CAD. When all the weights of a rational B,zier surface go to infinity in the form of power function, the limit of surface is the regular control surface induced by some lifting function, which is called toric degenerations of rational B,zier surfaces. In this paper, we study on the degenerations of the rational B,zier surface with weights in the exponential function and indicate the difference of our result and the work of GarcA ' A +/- a-Puente et al. Through the transformation of weights in the form of exponential function and power function, the regular control surface of rational B,zier surface with weights in the exponential function is defined, which is just the limit of the surface. Compared with the power function, the exponential function approaches infinity faster, which leads to surface with the weights in the form of exponential function degenerates faster.

• 出版日期2017-6
• 单位大连理工大学