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    $Date: 1997/07/02 23:38:17 $ $Revision: 1.7 $  
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homeprevnext 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.  
homeprevnext New Procedures and Functions
homeprevnext New Tokens
    Accepted by the <cap> parameter of Enable, Disable, and IsEnabled,  
    and by the <pname> parameter of GetBooleanv, GetIntegerv, GetFloatv,  
    and GetDoublev:  
homeprevnext 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  
    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   
    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);  
        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   
    Therefore, if the modelview matrix is M, then the transformed plane equation   
     (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   
            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   
            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 . . . .  
homeprevnext Additions to Chapter 3 of the 1.1 Specification (Rasterization)
homeprevnext Additions to Chapter 4 of the 1.1 Specification (Per-Fragment Operations and the Framebuffer)
homeprevnext Additions to Chapter 5 of the 1.1 Specification (Special Functions)
homeprevnext Additions to Chapter 6 of the 1.1 Specification (State and State Requests)
homeprevnext Additions to the GLX Specification
homeprevnext GLX Protocol
homeprevnext Errors
homeprevnext New State
    Get Value           Get Command     Type    Initial Value    Attribute  
    ---------           -----------     ----    -------------    ---------  
    RESCALE_NORMAL_EXT  IsEnabled      B         FALSE           transform/enable  
homeprevnext New Implementation Dependent State
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