Rescaling Normals - HP Workstation zx2000 Implementation Manual

rescaling normals

When normal rescaling is enabled, a new operation is added to the transformation of the normal
vector into eye coordinates. The normal vector is rescaled after it is multiplied by the inverse
modelview matrix and before it is normalized.
The rescale factor is chosen so that in many cases, normal vectors with unit length in object
coordinates will not need to be normalized as they are transformed into eye coordinates.
HP's implementation of OpenGL 1.1 supports the GL_RESCALE_NORMAL_EXT token. It is
accepted by the <cap> parameter of glEnable, glDisable, and glIsEnabled, and by
the <pname> parameter of glGetBooleanv, glGetIntegerv, glGetFloatv, and
glGetDoublev.
Normals that have unit length when sent to the OpenGL, have their length changed by the inverse
of the scaling factor after transformation by the model-view inverse matrix when the model-view
matrix represents a uniform scale. If rescaling is enabled, then normals specified with the Normal
command are rescaled after transformation by the ModelView Inverse.
Normals sent to the OpenGL may or may not have unit length. In addition, the length of the
normals after transformation might be altered due to transformation by the model-view inverse
matrix. If normalization is enabled, then normals specified with the glNormal3 command are
normalized after transformation by the model-view inverse matrix and after rescaling if rescaling
is enabled. Normalization and rescaling are controlled with glEnable and glDisable with
the target equal to NORMALIZE or RESCALE_NORMAL. This requires two bits of state. The
initial state is for normals not to be normalized or rescaled.
Therefore, if the modelview matrix is M, the transformed plane equation is:
the rescaled normal is:
and the fully transformed normal is:
OpenGL implementation guide
programming hints
5–7