椭球大地测量计算机代数可视化探究

Visualization of computer algebra of ellipsoid geodesy

针对经典椭球几何大地测量计算中许多计算、推导的可视化效果仍停留在手工计算时代,可视化效果不佳问题,该文利用Mathematica强大的公式推导能力以及可视化功能,对常用纬度之间的关系、常用地图投影及部分椭球大地测量计算内容(渐曲线和渐曲面、法截线和大地线等)进行可视化表达,较好地优化了椭球大地测量学部分概念的可视化性,并有利于增强椭球大地测量学在教学方面的三维展示能力。实验结果表明,该文所绘制示意图是揭示椭球大地测量学计算部分涉及复杂的数学推理、演算结果结论的组成部分,并进一步加强了现代数据处理手段与方法与椭球大地测量计算的可视化分析的联系。

For the problem that the visualization effects of many calculations and derivations in classical elliptic geodesy are still stuck in the era of manual calculation and poor visualization effects,Mathematica's powerful formula derivation ability and visualization function was used to visualize the relationships between common latitude,common map projections,and some elliptic geodesy calculation contents(such as the geodesic and geodesic surface,the normal section line and the geodetic line)in this paper,which optimized the visualization of some concepts in elliptic geodesy and enhanced the three-dimensional display ability of elliptic geodesy in teaching.Experimental results indicated that the diagrams drawn in this paper were a part of revealing the complex mathematical reasoning and calculation results conclusions involved in the computation of ellipsoidal geodesy.Furthermore,it strengthend the connection between modern data processing methods and techniques with the visualization analysis of ellipsoidal geodetic calculations.