Unformatted text preview: e. Moreover, not all the usual mathematical operations are valid on these tensors. Inversion, in particular, is an impossible transformation whereas transposition is still valid. Numerical construction of the metric tensor associated with a valid geometric object in our 3D space composed of hundreds of vectors presents no difficultly. However, the terms of this tensor are not independent and are composed of thousands of implicit relations: as a result, the slightest variation of one of them invalidates the 26 P. Serré A. Rivière and A. Clé , ment object. From a mathematical standpoint, it seems that expressing all these terms according to a certain number of independent parameters would be all it takes to vary the object in a straightforward manner. Unfortunately, this is very difficult in practice for a number of reasons, the main one being that you cannot explicitly determine all the Euclidian geometry theorems that apply to the object under consideration and it is therefore almost impossible to know all the constraints linking the geometric elements. 3. NEW MODELLING: PERTURBATION OF A KNOWN OBJECT The solution adopted is not to use the geometric parameters of the object but the parameters...
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This note was uploaded on 08/03/2010 for the course DD 1234 taught by Professor Zczxc during the Spring '10 term at Magnolia Bible.
- Spring '10
- The Land