| An efficient method for tracing planar implicit curves |
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| 作者姓名： | YU Zheng-sheng CAI Yao-zhi OH Min-jae KIM Tae-wan PENG Qun-sheng |
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| 作者单位： | Department of Naval Architecture and Ocean Engineering Seoul National University Seoul 151-744 Korea，Department of Naval Architecture and Ocean Engineering Seoul National University Seoul 151-744 Korea |
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| 基金项目： | ACKN0WLEDGEMENT This work was completed with the support of the APEC post-doc scholarship by Korea Science and Engineering Foundation （K0SEF）. |
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| 摘 要： | INTRODUCTION Tracing a planar implicit curve f(x, y)=0 on a rectangular region xl, xr]×yb, yt] is of great interest in Computer-Aided Design and Computer Graphics. While parametric curves are easy to plot, plotting implicit curves is a challenging problem. Planar im- plicit curve plotting method can be classified into two categories (Shou et al., 2005; Martin et al., 2002; Lopes et al., 2002). In the first category are subdivi- sion methods (Shou et al., 2005; Martin et al., 2002) …
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| 关 键 词： | 曲线跟踪 连续方法 几何建模 计算机 |
| 收稿时间： | 2006-04-03 |
| 修稿时间： | 2006-04-17 |
An efficient method for tracing planar implicit curves |
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| YU Zheng-sheng CAI Yao-zhi OH Min-jae KIM Tae-wan PENG Qun-sheng.An efficient method for tracing planar implicit curves[J].Journal of Zhejiang University Science,2006,7(7):1115-1123. |
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| Authors: | Zheng-sheng Yu Yao-zhi Cai Min-jae Oh Tae-wan Kim Qun-sheng Peng |
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| Institution: | (1) Computer Science School, Hangzhou Dianzi University, Hangzhou, 310018, China;(2) Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul, 151-744, Korea;(3) Applied Mathematics Department, Zhejiang University, Hangzhou, 310027, China;(4) State Key Laboratory of CAD & CG, Zhejiang University, Hangzhou, 310027, China |
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| Abstract: | This paper presents a method for tracing a planar implicit curve f(x, y)=0 on a rectangular region based on continuation scheme. First, according to the starting track-point and the starting track-direction of the curve, make a new function F(x, y)=0 where the same curve with f(x, y)=0 is defined. Then we trace the curve between the two domains where F(x, y)>0 and F(x, y)<0 alternately, according to the two rules presented in this paper. Equal step size or adaptive step size can be used, when we trace the curve. An irregular planar implicit curve (such as the curve with large curvatures at some points on the curve), can be plotted if an adaptive step size is used. Moreover, this paper presents a scheme to search for the multiple points on the curve. Our method has the following advantages: (1) it can plot C0 planar implicit curves; (2) it can plot the planar implicit curves with multiple points; (3) by the help of using the two rules, our method does not need to compute the tangent vector at the points on the curve, and directly searches for the direction of the tracing curve; (4) the tracing procedure costs only one of two evaluations of function f(x, y)=0 per moving step, while most existing similar methods cost more evaluations of the function. |
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| Keywords: | Planar implicit curve Curve tracing Continuation method Geometric modeling |
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