Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
A Method for Registration of 3-D Shapes
IEEE Transactions on Pattern Analysis and Machine Intelligence - Special issue on interpretation of 3-D scenes—part II
Extracting periodicity of a regular texture based on autocorrelation functions
Pattern Recognition Letters
Hierarchical mesh decomposition using fuzzy clustering and cuts
ACM SIGGRAPH 2003 Papers
A Computational Model for Periodic Pattern Perception Based on Frieze and Wallpaper Groups
IEEE Transactions on Pattern Analysis and Machine Intelligence
A planar-reflective symmetry transform for 3D shapes
ACM SIGGRAPH 2006 Papers
Partial and approximate symmetry detection for 3D geometry
ACM SIGGRAPH 2006 Papers
Image-based procedural modeling of facades
ACM SIGGRAPH 2007 papers
Registration of CAD mesh models with CT volumetric model of assembly of machine parts
The Visual Computer: International Journal of Computer Graphics
Detecting approximate symmetries of discrete point subsets
Computer-Aided Design
Discovering structural regularity in 3D geometry
ACM SIGGRAPH 2008 papers
Extraction of isosurfaces from multi-material CT volumetric data of mechanical parts
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Partial intrinsic reflectional symmetry of 3D shapes
ACM SIGGRAPH Asia 2009 papers
Surface mesh segmentation and smooth surface extraction through region growing
Computer Aided Geometric Design
Detecting design intent in approximate CAD models using symmetry
Computer-Aided Design
Segmenting periodic reliefs on triangle meshes
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Illustrating how mechanical assemblies work
ACM SIGGRAPH 2010 papers
Non-local scan consolidation for 3D urban scenes
ACM SIGGRAPH 2010 papers
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Along with the recent growth of industrial X-ray computerized tomography (CT) scanning systems, it is now possible to non-destructively acquire the entire meshes of assemblies. This technology has the potential to realize an advanced inspection process of an assembly, such as estimation of their assembly errors or examinations of their dynamic behaviors in motion using a model reflecting real assembled situations. However, to realize the process, it is necessary to accurately decompose the mesh and to extract a set of partial meshes, each of which corresponds to a single part, from the entire meshes of assemblies measured from the CT scans. Moreover, it is required to create models that are ready for dynamic behavior simulations. In this paper, we focus on CT scanned meshes of gear assemblies as examples, and propose beneficial methods for establishing such advanced inspections. We first propose a method that accurately decomposes the mesh into partial meshes, each of which corresponds to a single gear, using periodicity recognitions. The key idea is first to accurately recognize the periodicity of each gear, then to extract sets of topologically connected mesh elements where periodicities are valid, and finally to interpolate points in plausible ways from an engineering viewpoint to the area where surface meshes are not generated, especially the contact area between parts in the CT scanning process. We also propose a method for creating kinematic simulation models which can be used for a gear teeth contact evaluation using extracted partial meshes and their periodicities. Such an evaluation of teeth contacts is one of the most important functions in kinematic simulations of gear assemblies for predicting the power transmission efficiency, noise and vibration. The characteristics of the proposed method is that (1) it can robustly and accurately recognize periodicities from noisy scanned meshes, (2) it can estimate the plausible boundaries of neighboring parts without any previous knowledge from single-material CT scanned meshes, and (3) it can efficiently extract partial meshes from large scanned meshes containing millions of triangles in a few minutes. We demonstrate the effectiveness of our method on a variety of artificial and real CT scanned meshes.