Efficient Computation of the Area and Length of a Planar Contour Using Digital Elevation Model Data
Efficient Computation of the Area and Length of a Planar Contour Using Digital Elevation Model Data
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发表时间：
2014
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通讯作者：
H. Goto;Y. Shimakawa
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作者：
H. Goto;Y. Shimakawa
提出了一种计算封闭平面轮廓面积和长度的有效算法。对于给定的连续高程函数z=f(x, y)，我们关注由z=0形成的电路。考虑泰勒展开到二阶，我们用三种曲率近似f（x, y）。电路被分成多个部分，每个部分的结果都是精确或近似圆形的。用三个曲率来计算圆度。面积是通过使用格林定理在一维线积分中累积面积元素来计算的。通过数值实验验证了该方法的有效性。利用日本某岛屿的实际数字高程模型数据，绘制了等高线，并计算了等高线的面积和长度。与现有方法相比，该算法有利于再现光滑轮廓。
We develop an efficient computation algorithm for calculating the area and length of a closed planar contour. For a given continuous elevation function z=f(x, y), we focus on the circuit formed by z=0. Considering the Taylor expansion to second order, we approximate f(x, y) using three types of curvatures. The circuit is partitioned into multiple portions, by which each resultant becomes exactly or approximately round. The roundness is evaluated with the three curvatures. The area is computed by cumulating the area elements in a one-dimensional line integration using the Green’s theorem. An illustrative numerical experiment is performed to validate the proposed method’s effectiveness. Using actual digital elevation model data of an island in Japan, we draw the contours, and calculate the area and length of them. Compared with the existing method, the proposed algorithm is beneficial in reproducing smoothed contours.