摘要
针对反距离加权插值算法会出现“牛眼”现象的缺陷问题,本文利用二元泰勒级数展开式,推导出不同幂级数对应的反距离加权插值函数的表达式;通过求取二次幂反距离加权插值函数及偏导数的极限,对二次幂反距离加权插值函数的定义域进行扩充,使得插值函数在控制点位置保持连续,并证明所有控制点均为驻点,指出出现“牛眼”现象的原因。通过设置平滑参数,削减“牛眼”现象的影响,提升插值曲面的平滑程度。利用某矿区地面测绘数据进行数字高程建模试验,通过设置不同的平滑参数值,分析平滑参数对空间插值的影响。结果表明,较大的平滑参数可以增加地形面的平滑程度,但也会导致数字高程模型失真,在建模过程中需要根据实际条件灵活设置。
For the inverse distance-weighted interpolation algorithm,there will be a defect of the"bull′s eye"phenomenon.In this paper,the binary Taylor series expansion is used to derive the expressions of the inverse distance weighted interpolation function of different power series.By finding the limits of the quadratic inverse distance weighted interpolation function and the partial derivative,the definition domain of the quadratic inverse distance weighted interpolation function is expanded,so that the interpolation function remains continuous at the position of the control points,and all control points are proved to be"stationary points",and the reason for the occurrence of the"bull′s eye"phenomenon is obtained.In this paper,the smoothing parameters are set to reduce the influence of the"bull′s eye"phenomenon and improve the smoothness of the interpolated surface.The digital elevation modeling experiment was carried out by using the ground mapping data of a mining area,and the influence of the smoothing parameters on the spatial interpolation was analyzed by setting different smoothing parameter values.The results show that the large smoothing parameter can increase the smoothness of the terrain surface,but it will also make the digital elevation model unrealistic,and it needs to be flexibly set according to the actual conditions in the modeling process.
作者
崔少北
单礼岩
马志华
Cui Shaobei;Shan Liyan;Ma Zhihua(State Key Laboratory of Coal Disaster Prevention and Control,Chongqing 400039,China;China Coal Technology and Engineering Group Chongqing Research Institute,Chongqing 400039,China)
出处
《工程勘察》
2026年第3期74-84,共11页
Geotechnical Investigation & Surveying
基金
中国煤炭科工集团有限公司科技创新创业资金专项重点项目“矿井安全态势融合预警技术”(2023-TD-ZD001-05)
中煤科工集团重庆研究院有限公司自立重点项目“矿井电阻率动态监测关键技术及装备研制”(2022ZDXM06)。
