A novel method of combined interval analysis and homotopy continuation in indoor building reconstruction

Abstract

ABSTRACTIn this article, several mathematical and statistical methods for uncertainty modelling in indoor buildings are investigated. To reduce the time and cost of the indoor building data-acquisition process, the Trimble LaserAce 1000 rangefinder is used. The accuracy of the rangefinder is evaluated and a simple spatial model is reconstructed. The rangefinder has been used for forest applications to measure the height of trees. In this article, the rangefinder is used for indoor building environment data collection and mapping. The rangefinder was calibrated using a least squares adjustment algorithm and a novel method of interval-valued homotopy as a continuous deformation that reconstructs straight lines or algebraic curves between any pair of three-dimensional data. Homotopy gives better results in term of root mean square error than conventional surveying engineering methods where, in some cases, cubic homotopy gives results 11 times better than conventional methods.