6.52 Transform

Transform { 
  eventIn      MFNode      addChildren
  eventIn      MFNode      removeChildren
  exposedField SFVec3f     center           0 0 0    # (-,)
  exposedField MFNode      children         []
  exposedField SFRotation  rotation         0 0 1 0  # [-1,1],(-,)
  exposedField SFVec3f     scale            1 1 1    # (0,)
  exposedField SFRotation  scaleOrientation 0 0 1 0  # [-1,1],(-,)
  exposedField SFVec3f     translation      0 0 0    # (-,)
  field        SFVec3f     bboxCenter       0 0 0    # (-,)
  field        SFVec3f     bboxSize         -1 -1 -1 # (0,) or -1,-1,-1
} 

The Transform node is a grouping node that defines a coordinate system for its children that is relative to the coordinate systems of its ancestors. See 4.4.4, Transformation hierarchy, and 4.4.5, Standard units and coordinate system, for a description of coordinate systems and transformations.

4.6.5, Grouping and children nodes, provides a description of the children, addChildren, and removeChildren fields and eventIns.

The bboxCenter and bboxSize fields specify a bounding box that encloses the children of the Transform node. This is a hint that may be used for optimization purposes. The results are undefined if the specified bounding box is smaller than the actual bounding box of the children at any time. A default bboxSize value, (-1, -1, -1), implies that the bounding box is not specified and, if needed, shall be calculated by the browser. The bounding box shall be large enough at all times to enclose the union of the group's children's bounding boxes; it shall not include any transformations performed by the group itself (i.e., the bounding box is defined in the local coordinate system of the children). The results are undefined if the specified bounding box is smaller than the true bounding box of the group. A description of the bboxCenter and bboxSize fields is provided in 4.6.4, Bounding boxes.

The translation, rotation, scale, scaleOrientation and center fields define a geometric 3D transformation consisting of (in order):

1. a (possibly) non-uniform scale about an arbitrary point;
2. a rotation about an arbitrary point and axis;
3. a translation.

The center field specifies a translation offset from the origin of the local coordinate system (0,0,0). The rotation field specifies a rotation of the coordinate system. The scale field specifies a non-uniform scale of the coordinate system. scale values shall be greater than zero. The scaleOrientation specifies a rotation of the coordinate system before the scale (to specify scales in arbitrary orientations). The scaleOrientation applies only to the scale operation. The translation field specifies a translation to the coordinate system.

Given a 3-dimensional point P and Transform node, P is transformed into point P' in its parent's coordinate system by a series of intermediate transformations. In matrix transformation notation, where C (center), SR (scaleOrientation), T (translation), R (rotation), and S (scale) are the equivalent transformation matrices,

    P' = T × C × R × SR × S × -SR × -C × P

The following Transform node:

Transform { 
    center           C
    rotation         R
    scale            S
    scaleOrientation SR
    translation      T
    children         [...]
}

is equivalent to the nested sequence of:

Transform {
  translation T 
  children Transform {
    translation C
    children Transform {
      rotation R
      children Transform {
        rotation SR 
        children Transform {
          scale S 
          children Transform {
            rotation -SR 
            children Transform {
              translation -C
              children [...]
}}}}}}}