Differential Geometry: Computational Differential Geometry of Curves and Surfaces and its Applications - Couverture souple

Khalifa Saad, Mohamed

 
9783844315448: Differential Geometry: Computational Differential Geometry of Curves and Surfaces and its Applications
Couverture souple
ISBN 10 : 3844315446 ISBN 13 : 9783844315448
Editeur : 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.

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Présentation de l'éditeur

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.

Biographie de l'auteur

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

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
LAP LAMBERT Academic Publishing
Date d'édition
2011
Langue
anglais
ISBN 10 
3844315446
ISBN 13 
9783844315448
Reliure
Broché
Nombre de pages
192
Coordonnées du fabricant
non disponible
Personne responsable
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