Page 281 - DMTH402_COMPLEX_ANALYSIS_AND_DIFFERENTIAL_GEOMETRY

Complex Analysis and Differential Geometry Sachin Kaushal, Lovely Professional University

Notes Unit 23: Developable Surface Fitting to Point Clouds

CONTENTS
Objectives
Introduction

23.1 Contribution of the Article
23.2 The Blaschke Model of Oriented Planes in R 3
23.2.1 Incidence of Point and Plane
23.2.2 Tangency of Sphere and Plane
23.2.3 The Tangent Planes of a Developable Surface
23.3 The Classification of Developable Surfaces according to their Image on B
23.3.1 Cones and Cylinders of Revolution

23.4 Recognition of Developable Surfaces from Point Clouds
23.4.1 Estimation of Tangent Planes
23.4.2 A Euclidean Metric in the Set of Planes
23.4.3 A Cell Decomposition of the Blaschke Cylinder
23.4.4 Analysis and Classification of the Blaschke Image
23.5 Reconstruction of Developable Surfaces from Measurements

23.5.1 Curve fitting on the Blaschke cylinder B
23.5.2 Biarcs in the Space of Planes
23.5.3 A Parametrization of the Developable Surface
23.5.4 Fitting Developable Surfaces to nearly Developable Shapes
23.5.5 Singular Points of a Developable Surface
23.5.6 Conclusion
23.6 Summary

23.7 Keywords
23.8 Self Assessment
23.9 Review Questions
23.10 Further Readings

Objectives

After studying this unit, you will be able to:
Discuss The Blaschke Model of Oriented Planes in R 3

Explain Incidence of Point and Plane

Define Tangency of Sphere and Plane


274 LOVELY PROFESSIONAL UNIVERSITY