高精度曲面建模应用中边界误差解决方案

Method of reducing HASM boundary error

为了降低模拟区域边界误差的影响,进一步提高HASM插值精度,提出借助Laplace方程来模拟区域边界。用此方案计算高斯合成曲面边界,直接验证该方案的插值精度;选取山东省临沂市某试验区作为研究对象,模拟该区域的高程异常曲面,间接验证该方案的可行性。数值模拟结果表明,使用Laplace方程计算的模拟区域边界精度较高,且大幅度提高了HASM实际应用的插值精度。

High accuracy surface modeling （HASM） constructed based on the fundamental theorem of surface is more accurate than the classical methods. However, because of boundary error, location error, etc, HASM has a big accuracy loss in real-world examples. In former researches we solved the location error with Taylor expansion. In order to reduce the HASM boundary error and improve its accuracy further, this paper presents a new method of Laplace interpolation to compute the region boundary value. Gaussian synthetic surface and the real world test region are employed to validate the efficiency of this method. Results show that the boundary value computed with Laplace interpolation is more accurate than the classical methods, which can be regarded as an alternative for boundary value computation.