Least Squares Orthogonal Distance Fitting of Curves and Surfaces in Space (Lecture Notes in Computer Science, 3151)

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.

asynchronous Javascript And Xml (ajax) Is A Web Technique Used To Transfer Data Between A Browser And Server Asynchronously Without Posting The Web Page To The Server. Asynchronously Implies That The Processing Of The Web Page Continues While The Ajax Request Is Sent To The Server And A Response Is Received From The Server. The Web Page, Or Section(s) Of The Web Page, Is Refreshed With The Ajax Response Without Reposting The Web Page. Ajax Has The Following Advantages Over Non-ajax Web Applications.

- Reduced Response Time And Reduced Server Load, As The Complete Web Page Is Not Reposted.

- Reduced Bandwidth Of Web Applications As Only Data Is Transferred And The Html Format Is Applied In The Browser.

- Separation Of Data, Format And Style.

the Book Covers Web Search And Rss Feed With Ajax As Well As Form Validation With Ajax Frameworks For Java, Jsp, Jsf, And Php. It Discusses Using Ajax In Oracle Jdeveloper And Is Ide Based. Jdeveloper Has The Following Advantages Over Eclipse Ide.

- Jdeveloper 11g Provides An Integrated Javascript Editor For Ajax/web Development.

- It Also Provides A Php Extension.

- Jdeveloper Has A Built-in Support For Jsf And For Jdbc.

Asynchronous JavaScript and XML (Ajax) is a web technique used to transfer data between a browser and server asynchronously without posting the web page to the server. "Asynchronously" implies that the processing of the web page continues while the Ajax request is sent to the server and a response is received from the server. The web page, or section(s) of the web page, is refreshed with the Ajax response without reposting the web page. Ajax has the following advantages over non-Ajax web applications. - Reduced response time and reduced server load, as the complete web page is not reposted. - Reduced bandwidth of web applications as only data is transferred and the HTML format is applied in the browser. - Separation of data, format and style. The book covers web search and RSS Feed with Ajax as well as form validation with Ajax frameworks for Java, JSP, JSF, and PHP. It discusses using Ajax in Oracle JDeveloper and is IDE based. JDeveloper has the following advantages over Eclipse IDE. - JDeveloper 11g provides an integrated JavaScript Editor for Ajax/Web development. - It also provides a PHP extension. - JDeveloper has a built-in support for JSF and for JDBC. Cover Page 1 Title Page 4 ISBN 3540239669 5 Foreword 6 Preface 8 Table of Contents (with page links) 10 1. Introduction 10 2. Least-Squares Orthogonal Distance Fitting 10 3. Orthogonal Distance Fitting of Implicit Curves and Surfaces 10 4. Orthogonal Distance Fitting of Parametric Curves and Surfaces 11 5. Object Reconstruction from Unordered Point Cloud 11 6. Conclusions 11 References 11 Index 11 A. Implementation Examples 11 B. CMM Software Tools Fulfilling ISO 10360-6 12 C. FHG Matrix of Superellipse and Superellipsoid 12 List of Figures 14 List of Tables 16 List of Symbols 18 1. Introduction 22 2. Least-Squares Orthogonal Distance Fitting 38 3. Orthogonal Distance Fitting of Implicit Curves and Surfaces 56 4. Orthogonal Distance Fitting of Parametric Curves and Surfaces 76 5. Object Reconstruction from Unordered Point Cloud 96 6. Conclusions 106 References 114 Index 118 A. Implementation Examples 122 C. FHG Matrix of Superellipse and Superellipsoid 144 B. CMM Software Tools Fulfilling ISO 10360-6 128

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.

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 processing 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 Due to the continuing progress of sensor technology, the availability of 3-D cameras is already foreseeable. These cameras are capable of generating a large set of measurement points within a very short time. There are a variety of 3-D camera applications in the fields of robotics, rapid product development and digital factories. In order to not only visualize the point cloud but also to recognize 3-D object models from the point cloud and then further process them in CAD systems, efficient and stable algorithms for 3-D information processing are required. For the automatic segmentation and recognition of such geometric primitives as plane, sphere, cylinder, cone and torus in a 3-D point cloud, efficient software has recently been developed at the Fraunhofer IPA by Sung Joon Ahn. This book describes in detail the complete set of ‘best-fit’ algorithms for general curves and surfaces in space which are employed in the Fraunhofer software. Asynchronous JavaScript and XML (Ajax) is a web technique to transfer data between a browser and server asynchronously without posting the web page to the server. Asynchronously implies that the processing of the web page continues while the Ajax request is sent to the server and a response received from the server. Sections of the web page get refreshed with the Ajax response without reposting the web page. Ajax has the following advantages over non-Ajax web applications: Reduced response time and reduced server load as the complete web page is not reposted - Reduced bandwidth of web applicat Front Matter....Pages I-XX 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 Erratum....Pages 126-126 Back Matter....Pages 93-125