1999 serr et al 2001 and in a phd duong 2003 and

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Unformatted text preview: be used and differential analysis completely rejected. In analytical geometry, every element of which a complex geometric object is composed is in a unique position relation with the Cartesian reference point (the complexity is O ( n ) ). There is no direct topological connection between 2 adjoining elements, except in the eyes of the designer. The extraordinary advantage of the Cartesian reference point is the small number of independent relations to be processed. The major disadvantage is, in point of fact, that there is no relation between 2 adjoining objects, it is up to the user to "propagate" any modifications. It is simple for the machine but difficult for the designer. Therefore, the problem is not properly posed! In declarative geometry, a complex geometric object is perceived as a system of specifications between geometric objects. Each object is potentially in relation with all the others (the complexity is O n 2 ). The vector modelling based on the TTRS () concept, already presented throughout precedent seminars [Clément et al., 1999], [Serré et al., 2001] and in a PhD [Duong, 2003], and the tensor representation will enable the complexity to be reduced to O ( n ) , that is to say, alm...
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