保持尖锐特征的隐式曲线绘制算法

An Algorithm for Visualizing Implicit Curves with Sharp Features

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.