基於點坐標之三維空間相似轉換尺度因子解算分析

Abstract

三維空間相似轉換是測量應用常見任務，空間資料的收集常藉由不同手法及儀器設備，在各自定義坐標系下進行測量，相同之空間幾何的測量成果必須藉由坐標系的旋轉、平移及尺度縮放整合或轉換至同一坐標系統下。尺度因子影響幾何長度、面積及體積等之度量，三維空間相似轉換模式下的尺度因子可聯合或獨立於其它參數進行解算。而當僅解算尺度因子，其解算程序相對簡易，可採不同模式。尺度因子參數求定之後，對依序解旋轉及平移參數並簡化整個三維空間相似轉換參數計算是十分有幫助的。 基於點坐標的觀測量，本課題針對尺度因子之單獨求解進行探討，並從文獻中收集幾種常用的尺度因子計算方式，詳細檢視方法原理、計算公式以及影響因子，並以定性及定量方式比較及分析方法特性，釐清異同點，供作實務應用尺度因子解算任務之參考。

3D Spatial Similarity Transformation is a common task in geomatics . The collection of spatial data is often performed using various methods and instruments, in respective coordinate systems, to integrate or transform measurements of the same spatial geometry into a unified coordinate system, rotations, translations, and scaling are required. The scale factor of the 3D Spatial Similarity Transformation affects geometric lengths, areas, volumes, and other measurements. The scale factor of the 3D Spatial Similarity Transformation can be solved either jointly with or separately from other parameters. When solely solving for the scale factor, the computation process is relatively simple and can be done using different approaches. Once the scale factor is determined, simplifying the computation of the entire 3D Spatial Similarity Transformation parameters and benefit for sequentially solving for rotation and translation parameters. This study focuses on the individual solution of the scale factor based on point coordinates. Various commonly used methods for scale factor calculation are collected from the literature. The principles, formulas, and influential factors of these methods are examined in detail. A qualitative and quantitative comparison and analysis of the characteristics of these methods are conducted to clarify their similarities and differences, providing a reference for practical applications of scale factor solving tasks.