Преобразования пространственных координат Текст научной статьи по специальности «Медицинские технологии»

УДК 52S.33 Huaan Fan

Department of Geodesy

Royal Institute of Technology (KTH)

Stockholm, Sweden Email: [email protected]

ПРЕОБРАЗОВАНИЯ ПРОСТРАНСТВЕННЫХ КООРДИНАТ

THREE-DIMENSIONAL COORDINATE TRANSFORMATIONS

Abstract

This paper deals with transformations between two three-dimensional coordinate systems using the Helmert-type model. Using given coordinates at four control points defined in two systems, we have derived a new solution for the Helmert transformation parameters which is valid also for large rotations and scale changes. This solution is simple, straight-forward and can be expressed by closed formulas. In a numerical test using simulated coordinates without errors, the direct solution has successfully reproduced the correct transformation parameters. We then study the determination of transformation parameters with three different scale factors. Keywords: Coordinate transformation, translation, rotation, scale.

Huaan Fan

Department of Geodesy

Royal Institute of Technology (KTH)

Teknikringen 72

SE-100 44 Stockholm, Sweden

Tel. +46 S 7907340

Fax: +46 S 7907343

Email: [email protected]

© Huaan Fan, 2008