Ebook: Least Squares Orthogonal Distance Fitting of Curves and Surfaces in Space

Due to the continuing progress of sensor technology, the availability of 3-D c- eras is already foreseeable. These cameras are capable of generating a large set of measurement points within a very short time. There is a variety of 3-D camera - plications in the ?elds of robotics, rapid product development and digital factories. In order to not only visualize the point cloud but also to recognize 3-D object m- els from the point cloud and then further process them in CAD systems, ef?cient and stable algorithms for 3-D information processing are required. For the au- matic segmentation and recognition of such geometric primitives as plane, sphere, cylinder, cone and torus in a 3-D point cloud, ef?cient software has recently been developed at the Fraunhofer IPA by Sung Joon Ahn. This book describes in detail the complete set of ‘best-?t’ algorithms for general curves and surfaces in space which are employed in the Fraunhofer software.

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This book presents in detail a complete set of best-fit algorithms for general curves and surfaces in space. Such best-fit algorithms approximate and estimate curve and surface parameters by minimizing the shortest distances between the curve or surface and the measurement point.

After reviewing the basics for representing curves and surfaces in space and fitting in general, the author presents three algorithms for orthogonal distance fitting combining numerical methods and minimizational methods. These algorithms are applied to implicit and parametric curves and surfaces in 2D and 3D space possessing a broad variety of algorithmic features. Finally, an appendix provides practical information for applying the general orthogonal distance fitting algorithms to fit special model features.

Obvious application areas of the algorithms presented are robot navigation, including the navigation of autonomous vehicles or the grasping of work pieces, as well as factory digitization in general.

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This book presents in detail a complete set of best-fit algorithms for general curves and surfaces in space. Such best-fit algorithms approximate and estimate curve and surface parameters by minimizing the shortest distances between the curve or surface and the measurement point.

After reviewing the basics for representing curves and surfaces in space and fitting in general, the author presents three algorithms for orthogonal distance fitting combining numerical methods and minimizational methods. These algorithms are applied to implicit and parametric curves and surfaces in 2D and 3D space possessing a broad variety of algorithmic features. Finally, an appendix provides practical information for applying the general orthogonal distance fitting algorithms to fit special model features.

Obvious application areas of the algorithms presented are robot navigation, including the navigation of autonomous vehicles or the grasping of work pieces, as well as factory digitization in general.

Content:
Front Matter....Pages -
1. Introduction....Pages 1-16
2. Least-Squares Orthogonal Distance Fitting....Pages 17-34
3. Orthogonal Distance Fitting of Implicit Curves and Surfaces....Pages 35-53
4. Orthogonal Distance Fitting of Parametric Curves and Surfaces....Pages 55-73
5. Object Reconstruction from Unordered Point Cloud....Pages 75-84
6. Conclusions....Pages 85-91
Back Matter....Pages -

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This book presents in detail a complete set of best-fit algorithms for general curves and surfaces in space. Such best-fit algorithms approximate and estimate curve and surface parameters by minimizing the shortest distances between the curve or surface and the measurement point.

After reviewing the basics for representing curves and surfaces in space and fitting in general, the author presents three algorithms for orthogonal distance fitting combining numerical methods and minimizational methods. These algorithms are applied to implicit and parametric curves and surfaces in 2D and 3D space possessing a broad variety of algorithmic features. Finally, an appendix provides practical information for applying the general orthogonal distance fitting algorithms to fit special model features.

Obvious application areas of the algorithms presented are robot navigation, including the navigation of autonomous vehicles or the grasping of work pieces, as well as factory digitization in general.

Content:
Front Matter....Pages -
1. Introduction....Pages 1-16
2. Least-Squares Orthogonal Distance Fitting....Pages 17-34
3. Orthogonal Distance Fitting of Implicit Curves and Surfaces....Pages 35-53
4. Orthogonal Distance Fitting of Parametric Curves and Surfaces....Pages 55-73
5. Object Reconstruction from Unordered Point Cloud....Pages 75-84
6. Conclusions....Pages 85-91
Back Matter....Pages -
....