Adjustment Computations Adjustment Computations: Spatial Data Analysis

SECTION 18.7

Three-Dimensional Conformal Coordinate Transformation

Introduction

The three-dimensional conformal coordinate transformation is also known as the seven-parameter similarity transformation. It is used to transform coordinates in one three-dimensional coordinate system into another by use of a single scale factor (conformality), three rotations, and three translations. This solution requires a minimum of two common points known in horizontal position in both data and three known in vertical. Anymore than the minimum will result in a least square solution.

It is commonly used in photogrammetry and laser-scanning software. For example, the three-dimensional point-cloud image from a laser-scanner is in an arbitrary coordinate system. A three-dimensional coordinate transformation is used to bring this image into a common ground-based datum.

The points and coordinate values for the example data file are contained in the file "Example 18.4.txt". You may modify this file to adjust other data, or create a similar file..

LIBRARY FILE

Parsing the Data File

Parse Control Points

Parse Common Points

Enter initial approximations for unknowns

Rotation matrix function for Equation 18.4

Create J, W, and K matrices

Since nonlinear solution, iterate until convergence

SOLUTION

Transform additional points and propagate errors

 

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