
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 <cap> parameter of Enable, Disable, and IsEnabled,
    and by the <pname> 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