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# Documentation

## Description

PmitError = pmit_create_cadcs(PmitCadCSH* const pmitCadCSHOut, const char* name, const char* nodeID, double rotation[9], double trans[3]) returns an error status PmitError.

With pmit_create_cadcs, you can create an object of PmitCadCSH class to represent a coordinate system in an API CAD model.

## Input Arguments

 name String naming the coordinate system nodeID String uniquely identifying the coordinate system for associativity purposes rotation Double-type real rotation 9-vector specifying rotational transformation of the origin of this coordinate system with respect to its parent CAD model. trans Double-type real 3-vector specifying translation of the origin of this coordinate system with respect to its parent CAD model.

## Output Arguments

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### Orthogonal Matrix

A matrix R is orthogonal if it satisfies the matrix multiplication rule RT*R = R*R T = 1, where 1 is the identity matrix.

### Rotational Transformation: Rotation Matrix and Rotation Vector

The rotation vector input is a 9-vector, defined from the 3-by-3 orthogonal rotation matrix R, that represents the rotational orientation of a CAD model component with respect to its parent CAD model.

$R=\left(\begin{array}{ccc}{R}_{11}& {R}_{12}& {R}_{13}\\ {R}_{21}& {R}_{22}& {R}_{23}\\ {R}_{31}& {R}_{32}& {R}_{33}\end{array}\right).$

You define the rotation 9-vector column-wise:

```rotation = [R(1,1) R(2,1) R(3,1) R(1,2) R(2,2) R(3,2) ...
... R(1,3) R(2,3) R(3,3)]```