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--- doc:user:geometry:user:triedres [2013/07/12 14:09] – external edit 127.0.0.1
+++ doc:user:geometry:user:triedres [2016/03/30 15:23] (current) – external edit 127.0.0.1
@@ Line 1: / Line 1: @@
+====== 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.