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doc:user:geometry:user:triedres

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# Trihedra

## Introduction

A trihedron is a geometric entity which defines a local coordinate system. It can be used to reposition the mesh in another frame using the Geometry/Mesh Operators. It can be be used for shape optimization ShapeValueExtractor (see Fonctions Objectives), where the shape of a meshed entity in a given frame is compared with respect to a desired geometry in another frame.

## Definition

A trihedron is defined by 3 points pt0, pt1 and pt2, which are not on a a same line. pt0 is the origin. The line pt0-pt1 is the direction of the first axis, (local x axis). The third direction (local z axis) is defined by the cross product of the directions pt0-pt1 and pt0-pt2. Finally, the second direction, (local y axis), is defined by the cross product of the local vectors x and z. Syntactically, it is written:

pt0 = Point(0, x0, y0, z0)
pt1 = Point(1, x1, y1, z1)
pt2 = Point(2, x2, y2, z2)
triedre1 = Triedre(pt0, pt1, pt2)

## Note

As for the Axes, points can also be defined in the pointsetor in the meshpointset:

triedre1 = Triedre(pointset(1), pointset(2), pointset(3))
triedre2 = Triedre(meshpointset(1), meshpointset(2), meshpointset(3))

In this case, the trihedron will move if the points are moving.

doc/user/geometry/user/triedres.txt · Last modified: 2016/03/30 15:23 by 127.0.0.1