保持尖锐特征的隐式曲线绘制算法
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摘要
隐式曲线在生物、医学、气象、地学、石油勘探及物探等领域有着广泛的应用。提出一种绘制带有尖锐特征的平面隐式曲线的算法,能有效地提取隐式曲线的尖锐特征。该算法首先确定曲线的绘制区域,采用自上而下的方式生成绘制区域的四叉树表示,并在四叉树节点表示的每个单元格内生成一个数值场特征点;然后连接特征点生成对偶网格;最后,利用MarchingSquares算法生成曲线。实验结果表明,该算法能在网格较稀松的情况下绘制出隐式曲线,并且可以实现曲线的尖锐特征。
Implicit curve plays an essential role in the fields of medicine, meteorology, geology,petroleum exploration, geophysics and so on. In this paper, we propose an algorithm to visualize implicit curves with sharp features, which can effectively extract the sharp features of such curves.The algorithm first defines the visualizing area of the curve and then adopts a quadtree that generates visualizing area by a top-down method. In each cell, the method produces a feature point of the numerical field, and connects different feature points to generate the dual mesh. Finally, the algorithm employs the Marching Squares algorithm to generate the curves. Experiments show that our method can efficiently extract the sharp features of implicit curves, and it can work with various implicit curves with or without sharp features robustly.
Implicit curve plays an essential role in the fields of medicine, meteorology, geology,petroleum exploration, geophysics and so on. In this paper, we propose an algorithm to visualize implicit curves with sharp features, which can effectively extract the sharp features of such curves.The algorithm first defines the visualizing area of the curve and then adopts a quadtree that generates visualizing area by a top-down method. In each cell, the method produces a feature point of the numerical field, and connects different feature points to generate the dual mesh. Finally, the algorithm employs the Marching Squares algorithm to generate the curves. Experiments show that our method can efficiently extract the sharp features of implicit curves, and it can work with various implicit curves with or without sharp features robustly.
引文
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[8]李华,蒙培生,王乘.医学图像重建MC算法三角片的合并与实现[J].计算机应用,2003,23(6):104-106.
[9]李彩云,朱春钢,王仁宏.参数曲线的分段近似隐式化[J].高校应用数学学报A辑,2010,25(2):202-210.
[10]骆沛,吴壮志,夏春和,等.基于e1范数最小化的非流形曲线族重构[J].计算机学报,2013,36(9):1917-1928.
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[13]李云夕,冯结青,金小刚.基于有向距离场的代数B-样条曲线重建[J].软件学报,2007,18(9):2306-2317.
[14]MAPLE C.Geometric designing and space planning using the marching squares and marching cube algorithms[C]//2003 International Conference on Geometric Modeling and Graphics.New York:IEEEPress,2003:90-95.
[15]MANTZ H,JACOBS K,MECKE K.Utilizing Minkowski functionals for image analysis:a marching square algorithm[J].Journal of Statistical Mechanics Theory and Experiment,2008,12(12):12015.
[16]肖海,章亚男,沈林勇,等.光纤光栅曲线重建算法中的曲率连续化研究[J].仪器仪表学报,2016,17(5):993-999.
[17]CIPOLLETTI M P,DELRIEUX C A,PERILLO G M E,et al.Superresolution border segmentation and measurement in remote sensing images[J].Computers and Geosciences,2012,40(3):87-96.
[18]AKKOUCHE S,GALIN E.Adaptive implicit surface polygonization using marching triangles[J].Computer Graphics Forum,2001,20(2):67-80.
[19]刘颖.复杂的隐式函数曲线绘制算法的研究[D].长春:吉林大学,2006.
[20]范丽鹏,王丽英,庞明勇.平面简单闭合曲线离散采样与重建算法[J].图学学报,2015,36(4):511-515.
[21]JU T,LOSASSO F,SCHAEFER S,et al.Dual contouring of Hermite data[J].ACM Transactions on Graphics,2002,21(3):339-346.
[22]RAMAN S,WENGER R.Quality isosurface mesh generation using an extended marching cubes look up table[J].Computer Graphics Forum,2010,27(3):791-798.
[2]BLOOMENTHAL J.An implicit surface polygonizer[M].San Diego:Academic Press,1994:324-349.
[3]SHELBERG M C,MOELLERING H,LAM N.Measuring the fractal dimensions of empirical cartographic curves[M].Rome:Food and Agriculture Organization of the United Nation,1982:481-490.
[4]赵伟,赵卓宁,李五生.一种有效的离散数据场等值线生成方法[J].成都信息工程学院学报,2007,22(1):116-121.
[5]温维亮,郭新宇,陆声链,等.隐式曲面在三维植物建模中的应用研究综述[J].图学学报,2010,31(3):1-10.
[6]SUNDARAMOORTHI G,YEZZI A,MENNUCCI A.Coarse-to-fine segmentation and tracking using Sobolev active contours[J].IEEE Transactions on Pattern Analysis&Machine Intelligence,2008,30(5):851-864.
[7]寿华好,何苹,缪永伟.自动微分在隐式曲线绘制中的应用[C]//第四届全国几何设计与计算学术会议.北京:中国工业与应用数学学会,2009:150-153.
[8]李华,蒙培生,王乘.医学图像重建MC算法三角片的合并与实现[J].计算机应用,2003,23(6):104-106.
[9]李彩云,朱春钢,王仁宏.参数曲线的分段近似隐式化[J].高校应用数学学报A辑,2010,25(2):202-210.
[10]骆沛,吴壮志,夏春和,等.基于e1范数最小化的非流形曲线族重构[J].计算机学报,2013,36(9):1917-1928.
[11]LAGUARDIA J J,CUETO E,DOBLARE M.A natural neighbour Galerkin method with quadtree structure[J].International Journal for Numerical Methods in Engineering,2006,15(5):529-548.
[12]ZHU X J,JI L X,JIN X B.Fitting and reconstruction of three-dimensional curve based on orthogonal curvature[C]//2009 9th International Conference on Electronic Measurement and Instruments.New York:IEEE Press,2009:323-328.
[13]李云夕,冯结青,金小刚.基于有向距离场的代数B-样条曲线重建[J].软件学报,2007,18(9):2306-2317.
[14]MAPLE C.Geometric designing and space planning using the marching squares and marching cube algorithms[C]//2003 International Conference on Geometric Modeling and Graphics.New York:IEEEPress,2003:90-95.
[15]MANTZ H,JACOBS K,MECKE K.Utilizing Minkowski functionals for image analysis:a marching square algorithm[J].Journal of Statistical Mechanics Theory and Experiment,2008,12(12):12015.
[16]肖海,章亚男,沈林勇,等.光纤光栅曲线重建算法中的曲率连续化研究[J].仪器仪表学报,2016,17(5):993-999.
[17]CIPOLLETTI M P,DELRIEUX C A,PERILLO G M E,et al.Superresolution border segmentation and measurement in remote sensing images[J].Computers and Geosciences,2012,40(3):87-96.
[18]AKKOUCHE S,GALIN E.Adaptive implicit surface polygonization using marching triangles[J].Computer Graphics Forum,2001,20(2):67-80.
[19]刘颖.复杂的隐式函数曲线绘制算法的研究[D].长春:吉林大学,2006.
[20]范丽鹏,王丽英,庞明勇.平面简单闭合曲线离散采样与重建算法[J].图学学报,2015,36(4):511-515.
[21]JU T,LOSASSO F,SCHAEFER S,et al.Dual contouring of Hermite data[J].ACM Transactions on Graphics,2002,21(3):339-346.
[22]RAMAN S,WENGER R.Quality isosurface mesh generation using an extended marching cubes look up table[J].Computer Graphics Forum,2010,27(3):791-798.
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