Least Squares Orthogonal Distance Fitting of Curves and Surfaces in Space

1. Front Matter

   Pages I-XX

   PDF

2. 1. Introduction

   • Sung Joon Ahn

   Pages 1-16

3. 2. Least-Squares Orthogonal Distance Fitting

   • Sung Joon Ahn

   Pages 17-34

4. 3. Orthogonal Distance Fitting of Implicit Curves and Surfaces

   • Sung Joon Ahn

   Pages 35-53

5. 4. Orthogonal Distance Fitting of Parametric Curves and Surfaces

   • Sung Joon Ahn

   Pages 55-73

6. 5. Object Reconstruction from Unordered Point Cloud

   • Sung Joon Ahn

   Pages 75-84

7. 6. Conclusions

   • Sung Joon Ahn

   Pages 85-91

8. Erratum

   • Sung Joon Ahn

   Pages 126-126

9. Back Matter

   Pages 93-125

   PDF

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.

• 2D curves
• 3D
• 3D surfaces
• SPIN
• algorithm
• algorithmic geometry
• algorithms
• computational geometry
• curve fitting
• least squares approximation
• model
• numerical methods
• object reconstruction
• orthogonal distance fitting
• surface fitting
• algorithm analysis and problem complexity

• Fraunhofer IPA, Stuttgart, Germany

  Sung Joon Ahn

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