深圳市3套平面直角坐标系的相互转换——基于Excel多元回归分析的正形变换
Mutual Transformation of Three Plane Rectangular Coordinate Systems in Shenzhen —Orthomorphic Transformation Based on Excel Multiple Regression Analysis
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- Keywords: Shenzhen independent coordinate; CGCS2000 coordinate; BJ54 coordinate; Regression analysis; Excel深圳独立坐标; CGCS2000 坐标; BJ54 坐标; 回归分析; Excel
- Abstract: After the CGCS2000 coordinate system is fully used, it is often necessary to convert Shenzhen independent coordinates, BJ54 coordinates and CGCS2000 coordinates to each other in engineering. Coordinate transformation includes indirect method and direct method. Conformal transformation is one of the direct methods. It has the advantages of isometric transformation and can be used in the transformation of Gaussian projection plane rectangular coordinates of the same sphere and different spheres. In this paper, 67 second order GPS coincidence points in Shenzhen are selected, and a simple Excel multiple linear regression method is used to solve the parameters of orthomorphic transformation. The method is simple and practical, with fast calculation and high conversion accuracy. 在全面启用CGCS2000坐标系后，工程上常常需要对深圳市独立坐标、BJ54坐标、CGCS2000坐标进行相互转换。坐标变换分间接法及直接法。正形变换是直接法之一，它具有等角变换的优点，可通用于同球及异球的高斯投影平面直角坐标变换。本文选用了深圳市67个二等GPS重合点，对正形变换的参数求解采用了简易的Excel多元线性回归方法。方法简单实用，计算快捷，转换精度高。
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土工固结试验压缩模量Es的三次样条插值——基于p-s试验数据的Excel VBA开发
The Cubic Spline Interpolation of Compression Modulus Es of Geotechnical Consolidation Test --Excel VBA Development Based on p-s Test Data
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- Keywords: The Cubic Spline Interpolation of Compression Modulus Es of Geotechnical Consolidation Test —Excel VBA Development Based on p-s Test Data压缩模量; 切线压缩模量; 割线压缩模量; 三次样条函数; Excel VBA
- Abstract: Compression modulus Es is one of the physical and mechanical indexes of soil. The traditional method is to give the curve e-p for manual search [p1, p2] and [e1, e2] , then calculate the compression coefficient av = -Δe/Δp, and then calculate the compression modulus Esv= (1+e0)/av . In this paper, cubic spline function is established by using experimental data (p, ln (h) ) . On this basis, using Excel VBA as a tool, an Es macro is compiled to calculate the tangent compression modulus Es of any point and secant compression modulus Es v of any interval on a PC. 压缩模量Es是土的物理力学指标之一。传统的方法是给出e-p曲线图进行人工查取［ p₁， p₂］及［ e₁， e₂］，然后计算压缩系数 av=-Δ e/Δ p ，再计算压缩模 量Esv =（1+ e 0）/av 。本文利用实验数据（ p，ln（h））建立三次样条函数。在此基础上，以 Excel VBA 为工具，编制了Es宏，实现了在PC机上计算任意点的切线压缩模量Est及任意区间的割线压缩模量Esv。
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三次样条插值三弯矩法（M 法）——以二阶导数为参数
Cubic Spline Interpolation Three Moment Method (M Method) —Taking the Second Derivative as the Parameter
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- Keywords: Cubic spline; Interpolation; Three moment method; M Method; Computational mathematics; Equations; Solution三次样条; 插值; 三弯矩法; M 法; 计算数学; 方程组; 求解
- Abstract: Cubic spline interpolation has important applications in engineering. Generally, there are two methods to establish spline interpolation: the three rotation method with the first derivative as the parameter (m method) and the three bending moment method with the second derivative as the parameter (M method). When the interpolation node equations are established, the m method is more simple to deal with the first kind of boundary conditions, and the M method is more convenient to deal with the second kind of boundary conditions. In order to facilitate the calculation and programming, the establishment and solution of node equations of cubic spline interpolation three moment method (M method) are derived in this paper.三次样条插值在工程中有重要应用。通常，建立样条插值的方法有2 种：以一阶导数为参数的三转角法（m 法）及以二阶导数为参数的三弯矩法（M 法）。在建立插值节点方程组时，m 法对第1 类边界条件的处理较为简洁，M 法对第2 类边界条件的处理较为便捷。为方便计算编程，本文全面整理、详细补充导出了三次样条插值三弯矩法（M 法）节点方程组的建立及其求解方法。
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三次样条插值三转角法（m 法）——以一阶导数为参数
Cubic Spline Interpolation With Three Rotation Angles (m Method) —Taking the First Derivative as a Parameter
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- Keywords: Cubic spline; Interpolation; Three angle method; m method; Computational mathematics; Equations; Solving三次样条; 插值; 三转角法; m 法; 计算数学; 方程组; 求解
- Abstract: Cubic spline interpolation has important applications in engineering. Generally, there are two methods to establish spline interpolation: the three rotation method with the first derivative as the parameter (m method) and the three bending moment method with the second derivative as the parameter (M method). When the interpolation node equations are established, the m method is more simple to deal with the first kind of boundary conditions, and the M method is more convenient to deal with the second kind of boundary conditions. In order to facilitate the calculation programming, the establishment and solution of the nodal equations of cubic spline interpolation three rotation method (m method) are derived in this paper.三次样条插值在工程中有重要应用。通常，建立样条插值的方法有2 种：以一阶导数为参数的三转角法（m 法）及以二阶导数为参数的三弯矩法（M 法）。在建立插值节点方程组时，m 法对第1 类边界条件的处理较为简洁，M 法对第2 类边界条件的处理较为便捷。为方便计算编程，本文全面整理、详细补充导出了三次样条插值三转角法（m 法）节点方程组的建立及其求解方法。
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平面直角坐标正形变换简易解算方法
A simple solution method for orthomorphic transformation of plane rectangular coordinates
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- Keywords: Beijing 54 coordinates, independent coordinates; CGCS2000 coordinates; nonlinear fitting; optimization; regression analysis; Excel; 1stOpt北京54 坐标; CGCS2000 坐标; 回归分析; 非线性拟合; 1stOpt
- Abstract: After the full use of CGCS2000 coordinate system, it is often necessary to batch convert plane rectangular coordinates such as Beijing 54 coordinates and local independent coordinates into CGCS2000 coordinates. Coordinate transformation is divided into indirect method and direct method. The indirect method takes geodetic coordinates (B, l) as indirect parameters and converts them according to the ellipsoidal projection principle. The theory is rigorous and the conversion is accurate. The direct method is to establish the coordinate transformation equations or numerical approximation model based on the least square method according to the regional common point coordinates. Orthomorphic transformation is one of the direct methods. It has the advantages of equiangular transformation and can be used in rectangular coordinate transformation of Gaussian projection plane of the same sphere and different spheres. In this paper, a simple nonlinear fitting global optimization method and multiple linear regression analysis method are used to solve the parameters of orthomorphic transformation, and the results are the same. The method of multiple linear regression analysis is simple, the calculation is fast, and the conversion accuracy is enough to meet the needs of engineering.在全面启用CGCS2000 坐标系后，常常需要将北京54 坐标及地方独立坐标等平面直角坐标批量转换为CGCS2000 坐标。坐标变换分间接法及直接法。间接法是以大地坐标（B，L）作为间接参数，根据椭球投影原理进行转换，理论严密，转换精准。直接法是直接根据区域公共点坐标，以最小二乘法为基础建立坐标 变换方程组或数值逼近模型，转换近似。正形变换是直接法之一，它具有等角变换的优点，可通用于同球及异球的高斯投影平面直角坐标变换。本文对正形变换的参数求解采用了简易的非线性拟合全局最优化方法以及多元线性回归分析方法，两者解算结果完全相同。多元线性回归分析，方法简单，计算快捷，转换精度足以满足工程需要。
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