### Table of Contents

# 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 `pointset`

or 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.