====== 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 [[doc:user:geometry:user:operateurs]]. It can be be used for shape optimization ''ShapeValueExtractor'' (see [[doc:user:results:fobj]]), 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 ''[[doc:user:geometry:user: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.