Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Zippered polygon meshes from range images
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Computer graphics (2nd ed. in C): principles and practice
Computer graphics (2nd ed. in C): principles and practice
Error classification and recovery within CAD model reconstruction
Proceedings of the fifth ACM symposium on Solid modeling and applications
Transfinite interpolation over implicity defined sets
Computer Aided Geometric Design
Meshfree automation of engineering analysis
From geometric modeling to shape modeling
Dual contouring of hermite data
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Numerical Recipes in C: The Art of Scientific Computing
Numerical Recipes in C: The Art of Scientific Computing
Simplification and Repair of Polygonal Models Using Volumetric Techniques
IEEE Transactions on Visualization and Computer Graphics
Robust repair of polygonal models
ACM SIGGRAPH 2004 Papers
Automatic mesh-healing technique for model repair and finite element model generation
Finite Elements in Analysis and Design
Geometrically adaptive numerical integration
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Fixing geometric errors on polygonal models: a survey
Journal of Computer Science and Technology
Repairing CAD model errors based on the design history
Computer-Aided Design
Field modeling with sampled distances
Computer-Aided Design
Finite element analysis in situ
Finite Elements in Analysis and Design
Meshfree natural vibration analysis of 2D structures
Computational Mechanics
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Holes, gaps, dangling boundaries and other imperfections of the geometric models preclude direct application of traditional engineering analysis tools. In such cases geometric inaccuracies have to be removed using a geometry ''healing'' (repair) procedure which results in a valid solid model. Repair procedure applied to the geometric model is computationally expensive and often requires human intervention and supervision. On the other hand, the repair procedure applied to the surface meshes derived from the boundaries of a geometric model may negatively affect the quality of the Finite Element mesh whose construction follows the repair procedure. In this paper we describe a novel numerical technique that enables engineering analysis in imprecise geometric models without reconstructing a valid solid model. At the heart of the proposed method lies a modified geometrically adaptive integration technique. It uses a hybrid geometric model, that consists of a hierarchical space decomposition, boundary representation (B-rep) and distance fields. Hierarchical space decomposition helps to resolve the geometric imperfections, while the original geometric model is used to allocate the integration points in the boundary (geometry) cells. The proposed method uses solution structures that combine together the distance fields to the geometric boundaries, boundary conditions and basis functions to enforce the prescribed boundary conditions. Our approach has been verified on several numerical examples. Our numerical experiments confirm high reliability of the proposed engineering analysis approach for a wide range of geometric imperfections. Despite that the paper presents 2D examples the proposed approach can be generalized in 3D.