Reconstruction of symmetric models composed of analytic curves and surfaces from point cloud

• Published in: Journal of Zhejiang University. A. Science 2008-10, Vol.9 (10), p.1351-1362
• Main Authors: Wang, Qing, Zhu, Wei-dong, Ke, Ying-lin
• Format: Article
• Language: English
• Subjects: Civil Engineering; Classical and Continuum Physics; Engineering; Industrial Chemistry/Chemical Engineering; Mechanical Engineering; 对称性; 模式重造; 约束优化; 逆向工程
• ISSN: 1673-565X; 1862-1775
• DOI: 10.1631/jzus.A0820324

This paper presents a method to reconstruct symmetric geometric models from point cloud with inherent symmetric structure. Symmetry types commonly found in engineering parts, i.e., translational, reflectional and rotational symmetries are considered. The reconstruction problem is formulated as a constrained optimization, where the objective function is the sum of squared distances of points to the model, and constraints are enforced to keep geometric relationships in the model. First, the explicit representations of symmetric models are presented. Then, by using the concept ofparameterized points （where the coordinate components are represented as functions rather than constants）, the distances of points to symmetric models are deduced. With these distance functions, symmetry information, for both 2D and 3D models, is uniformly represented in the process of reconstruction. The constrained optimization problem is solved by a standard nonlinear optimization method. Owing to the explicit representation of symmetry information, the computational complexity of our method is reduced greatly. Finally, examples are given to demonstrate the application of the proposed method.