Differential Geometry: Computational Differential Geometry of Curves and Surfaces and its Applications - Softcover

Khalifa Saad, Mohamed

Softcover

ISBN 10: 3844315446 ISBN 13: 9783844315448

Publisher: LAP LAMBERT Academic Publishing, 2011

Synopsis

In reverse engineering the detection of special classes of curves and surfaces generated by Computer Aided Curve and Surface Design often is based on the line congruence of normals and the GAUSS-image of such a surface. For surfaces with a ?kinematic generation?, the congruence of normals belongs to a linear complex and this fact allows the detection via a line geometric treatment. Patch detection in case of general spline surfaces is not yet solved successfully. While the patch generation is at most invariant with respect to affine transformation, the normal congruence of the patch is an Euclidean concept. Therefore we can expect that connections between the patch and its congruence turn to be rather complicated already for (algebraic) Bézier surfaces. The analysis of the patch's normal congruence is only the first step of the far more difficult investigation of a reflection or refraction congruence with respect to a given patch. This problem belonging to geometric optics would have explicit industrial applications, but is not the topic of this book. We restrict ourselves to an analysis of the normal congruence of Bézier patches.

About this title

About the Author

M.Khalifa Saad: Lecture of Differential-Computational Geometry, Mathematics Department, Sohag University, Sohag,Egypt

Edition details

• Publisher: LAP LAMBERT Academic Publishing
• Publication date: 2011
• ISBN 10: 3844315446
• ISBN 13: 9783844315448
• Binding: Paperback
• Language: English
• Number of pages: 192