Journal for Geometry and Graphics 29 (2025), No. 1, 107--123
Copyright by the authors licensed under CC BY SA 4.0
Fitting Curves to Point Clouds: Targeted Approximation Methods for HBIM
Larysa Ivanova
(1) University of Technology, Dresden, Germany
(2) National University of Construction and Architecture, Kyiv, Ukraine
ivanova.ls@knuba.edu.ua
This study focuses on the reconstruction and fitting of curves to 2D and 3D scanned point clouds in the context of HBIM applications. The paper begins by analyzing the distinctive characteristics of the input data, such as inherent noise, outliers, non-uniform sampling, and variable point density. Recognizing the critical impact of these factors on the choice of approximation methods, a classification system is proposed to evaluate both input data attributes and modeling objectives.
The key aspect of selecting a method is defined by the modeling objectives, namely the required accuracy and level of detail of the reconstructed curves. The author emphasizes that aligning method selection with this classification enables optimization of computational resources and processing time.
The methods proposed in this study varies depending on the specified criteria and includes the Normal Vector method, the Crawling method, the Trend method, and the Gravity method. Each technique is briefly described in terms of its core principles and applicability based on the proposed classification.
This task-oriented approach aims to achieve a balance between reconstruction quality and computational efficiency. To validate the proposed methods, a comparative evaluation is conducted. The results demonstrate satisfactory accuracy in curve reconstruction combined with optimal processing time. Overall, the proposed approximation methods significantly enhance the processing and analysis of 2D and 3D scanned point clouds. Their ability to handle noise, outliers, and variable point densities -- along with their computational efficiency -- makes them valuable tools for applications in architecture and industrial design.
Keywords: Point cloud approximation, curve fitting, heritage building information modeling, approximation types, data features.
MSC: 68W25; 65D10, 65D17, 68W40
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