使用多段Bezier曲线模型的地质等值线光滑算法

A Smoothed Contours Generating Algorithm for the Multi-Segment Bezier Curve

在等值线自动生成过程中,如果仅仅将追踪到的等值点依次用线连接起来,那么将会生成一幅折线式的等值线图。文章提出使用多段三次Bezier曲线拟合模型对得到的等值线进行拟合,首先利用三次Bezier曲线的拟合公式和最小二乘法得到首段Bezier曲线的四个控制点,然后依据Bezier曲线拼接的光滑条件和首段Bezier曲线的控制点,再次使用最小二乘法得到次段Bezier曲线的四个控制点,依此类推,从而得到由多段Bezier曲线组成的光滑的等值线图。除此之外,本文给出构建网格较小情况下的多段Bezier曲线拟合模型特例。实验结果证实,本文提出的方法易理解,可行性好,光滑效果显著。

In the process of generating contours automatically, it generates a polyline type of contour map if we connect the tracked point with the line. This paper proposes using the multi-segment Bezier curve model to fit the contours. At first we use three Bezier curves fitting formula and least-squares to get the four control points of the first segment of the Bezier curve. Then based on the smooth conditions of the Bezier curve and the acquired control points, we get the four sub-segment control points with least-squares. According to above ideas, we get the smooth contours. In addition, this paper proposes building the special case of the multi-segment Bezier curve model in the condition of a smaller grid. Experiments show the proposed method is easy and feasible, and it has good visual effect.