3D Parameterizer II : gradient constraints

Richard Cognot. ( 2001 )
in: 21st gOcad Meeting, ASGA

Abstract

To parametrize a 3D volume, it is necessary to define a mapping from the normal(x,y,z) space, called the modeling space, to a (u,v,w) parametric space. For this new space to conform with the definition of a parametric space, the (u,v,w) properties must meet some important criteria. Among these, the three parameters should be kept as orthogonal as possible to each other. In our case, we will focus on a special case of a 3D parametrization, where only the(u,v) parametric coordinates are used, and the w parameter is assumed equal to the modeling coordinate. Thus, forthe orthogonality criterion to be met, we will need two basic constraints. Of course, these constraints will be defined so that they are in a suitable form to be used within the D.S.I. method ([Mallet 1992]).

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    BibTeX Reference

    @inproceedings{CognotRM2001,
 abstract = { To parametrize a 3D volume, it is necessary to define a mapping from the normal(x,y,z) space, called the modeling space, to a (u,v,w) parametric space. For this new space to conform with the definition of a parametric space, the (u,v,w) properties must meet some important criteria. Among these, the three parameters should be kept as orthogonal as possible to each other. In our case, we will focus on a special case of a 3D parametrization, where only the(u,v) parametric coordinates are used, and the w parameter is assumed equal to the modeling coordinate. Thus, forthe orthogonality criterion to be met, we will need two basic constraints. Of course, these constraints will be defined so that they are in a suitable form to be used within the D.S.I. method ([Mallet 1992]). },
 author = { Cognot, Richard },
 booktitle = { 21st gOcad Meeting },
 month = { "june" },
 publisher = { ASGA },
 title = { 3D Parameterizer II : gradient constraints },
 year = { 2001 }
}