ISO 10303-214:2010(E)
An Axis2_placement_3d represents the location and orientation in three-dimensional space of two mutually perpendicular axes. An axis2_placement_3d is defined in terms of a point, (inherited from the placement supertype), and two (ideally orthogonal) axes. It can be used to locate and orientate a non axis-symmetric object in space and to define a placement coordinate system. The entity includes a point which forms the origin of the placement coordinate system. Two direction vectors are required to complete the definition of the placement coordinate system.
NOTE Let z be the placement Z axis direction
and a be the approximate placement X axis direction. There are two methods,
mathematically identical but numerically different, for calculating the
placement X and Y axis directions.
a.
The vector a is projected onto
the plane defined by the origin point P and the vector z to give the placement
X axis direction as x = (a -(a.z)z). The placement Y axis direction is then
given by y = (z x x).
b.
The placement Y axis direction
is calculated as y = (z x a) and then the placement X axis direction is given
by x = (y x z).
The first method is likely to be the more numerically stable
of the two, and is used here.
A placement coordinate system referenced by the parametric equations is derived from the axis2_placement_ 3d data for conic curves and elementary surfaces.
The data associated with an Axis2_placement_3D are the following:
The axis specifies the exact direction of the local Z axis.
The ref_direction specifies the direction used to determine the direction of the local X axis. If necessary an adjustment is made to maintain orthogonality to the axis direction. If axis and/or ref_direction is omitted, these directions are taken from the geometric coordinate system.
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