Name
EXT_rescale_normal
Name Strings
GL_EXT_rescale_normal
Version
$Date: 1997/07/02 23:38:17 $ $Revision: 1.7 $
Number
27
Dependencies
None
Overview
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.
New Procedures and Functions
None
New Tokens
Accepted by the parameter of Enable, Disable, and IsEnabled,
and by the parameter of GetBooleanv, GetIntegerv, GetFloatv,
and GetDoublev:
RESCALE_NORMAL_EXT 0x803A
Additions to Chapter 2 of the 1.1 Specification (OpenGL Operation)
Section 2.10.3
Finally, we consider how the ModelView transformation state affects
normals. Normals are of interest only in eye coordinates, so the rules
governing their transformation to other coordinate systems are not
examined.
Normals which have unit length when sent to the GL, 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 GL 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 Normal3 command are
normalized after transformation by the model-view inverse matrix and
after rescaling if rescaling is enabled. Normalization and rescaling
are controlled with
void Enable( enum target);
and
void Disable( enum target);
with 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, then the transformed plane equation
is
(n_x' n_y' n_z' q') = ((n_x n_y n_z q) * (M^-1)),
the rescaled normal is
(n_x" n_y" n_z") = f * (n_x' n_y' n_z'),
and the fully transformed normal is
1 (n_x")
____________ (n_y") (2.1)
__________________________________ (n_z")
V (n_x")^2 + (n_y")^2 + (n_z")^2
If rescaling is disabled then f is 1, otherwise f is computed
as follows:
Let m_ij denote the matrix element in row i and column j of M^-1,
numbering the topmost row of the matrix as row 1, and the leftmost
column as column 1. Then
1
__________
f = ________________________________
V (m_31)^2 + (m_32)^2 + (m_33)^2
Alternatively, an implementation my chose to normalize the normal
instead of rescaling the normal. Then
1
__________
f = ________________________________
V (n_x')^2 + (n_y')^2 + (n_z')^2
If normalization is disabled, then the square root in equation 2.1 is
replaced with 1, otherwise . . . .
Additions to Chapter 3 of the 1.1 Specification (Rasterization)
None
Additions to Chapter 4 of the 1.1 Specification (Per-Fragment Operations and
the Framebuffer)
None
Additions to Chapter 5 of the 1.1 Specification (Special Functions)
None
Additions to Chapter 6 of the 1.1 Specification (State and State Requests)
None
Additions to the GLX Specification
None
GLX Protocol
None
Errors
None
New State
Get Value Get Command Type Initial Value Attribute
--------- ----------- ---- ------------- ---------
RESCALE_NORMAL_EXT IsEnabled B FALSE transform/enable
New Implementation Dependent State
None