| 杨学顺,陈煜烽,胡贺松,赖志丹,刘海飞,张宇豪,李小强,刘春明.融合趋势面函数的多重二次曲面法恢复图形数字化数据[J].矿产勘查,2024,15(9):1750-1756 |
| 融合趋势面函数的多重二次曲面法恢复图形数字化数据 |
| Restoration of digitized graphic data with multiquadric method incorporating trend surface function |
| 投稿时间：2024-07-23 修订日期：2024-09-25 |
| DOI：10.20008/j.kckc.202409020 |
| 中文关键词: 趋势面函数 多重二次曲面函数 二维插值 |
| 英文关键词: trend surface function multiquadric function two-dimentional interpolation |
| 基金项目:本文受广州市建筑集团科技计划项目（2023-KJ032、2022-KJ005、2022KJ004、2022KJ003、2022-KJ015）和广东省住建厅科技计划项目（No.2022-K29-384697）联合资助。 |
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| 中文摘要: |
| 为方便对一些老的纸质等值线图件进行数据再处理，首先需要对图件进行数字化，然后再进行二维网格化，网格化数据质量直接影响后续数据的处理效果。由于等值线图的数字化数据具有不均匀的特点，网格化后容易产生数据畸变的问题，本文提出了融合趋势面函数的多重二次曲面网格化方法。该方法首先根据已知离散点构建低阶趋势面函数，然后利用已知离散点与低阶趋势面函数的差构建多重二次曲面函数，再将低阶趋势面与多重二次曲面叠加构造出新曲面，两者结合可较好地消除多重二次曲面函数在数据稀疏区的畸变效应。通过对磁法等值线图数字化数据进行插值测试，验证了融合趋势面函数的多重二次曲面插值方法具有良好的保真性。 |
| 英文摘要: |
| In order to facilitate the reprocessing of older paper contour maps， it is necessary to digitize the maps first， followed by a two-dimensional grid generation， and the quality of this gridded data significantly influences subsequent data processing outcomes. Given the uneven nature of digitized data from contour maps， issues of data distortion often arise during grid generation. This paper introduces a method for grid generation that integrates global multiquadric （MQ） method with trend surface functions. The approach begins by constructing low-order trend surface functions based on known discrete points. Subsequently， it utilizes the difference between known discrete points and low-order trend surface functions to formulate a MQ function. This involves superimposing the low-order trend surface with the MQ function to create a novel surface. This method effectively mitigates the distortion effects of MQ function in data-sparse regions. Interpolation tests conducted on model data， elevation data and digitized data from magnetic contour maps validate the fidelity of this grid generation method， showcasing its effectiveness in preserving data accuracy. |
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