I.2.2.2 Three “initWithOViVj” methods

The three methods are “initWithOV1V2”, “initWithOV2V3”, “initWithOV3V1”, “initWithOV2V1”, “initWithOV3V2” and “initWithOV1V3”. They produce CoordSys objects defined by their origin and two direction vectors corresponding to vector $e_i$ and to the orientation of vector $e_j$ respectively.

The six arguments of these methods are:

• A string argument corresponding to the type of coordinate system being build. Three values are accepted: ‘CORDC”, “CORDR” and “CORDS”.
• A DataBase argument that provides the information needed to complete the definition of the coordinate system.
• An integer argument corresponding to the reference coordinate system (coordinate system wrt which the origin and direction vectors are specified).
• A vector containing the coordinates of the origin. This origin is specified with an Array of three real values corresponding to the components of O wrt the reference coordinate system identified with the integer argument.
• A vector (Array of three real values) corresponding to the direction $i$ of the coordinate system. The components of the vector are given wrt to the reference coordinate system (estimated at point $0$ if the reference coordinate system is curvilinear).
• A vector (Array of three real values) corresponding to the orientation of base vector $j$ of the coordinate system. The components of the vector are given wrt to the reference coordinate system (estimated at point $0$ if the reference coordinate system is curvilinear).

Note that the orientation vector $e_j$ is not necessarily orthogonal to $e_i$. If the vectors are not orthogonal, then $i$ is a unit vector parallel to $e_i$, and vector $j$ is the unit vector perpendicular to $i$ closest to $e_j$. The last vector $k$ of the coordinate system is a unit vector perpendicular to both $i$ and $j$.

Here again, no check is made in a DataBase to ensure that the data are consistent. (For example, checking that the reference coordinate system exists.)