Changes between Version 11 and Version 12 of MousePicking

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Author:
bhook (IP: 64.207.62.170)
Timestamp:
05/18/06 16:10:37 (13 years ago)
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  • MousePicking

    v11 v12  
    143143 
    144144=== Clipping Space to View Space === 
     145A point in view space is transformed to clipping space with the {{{GL_PROJECTION}}} matrix: 
     146 
     147{{{ 
     148#!latex-math-hook 
     149\begin{eqnarray*} 
     150{\boldsymbol P}{\boldsymbol v}&=&{\boldsymbol c} \\ 
     151\text{where} \\ 
     152{\boldsymbol P}&=&\text{projection matrix} \\ 
     153\boldsymbol{v} &=& \text{point in view space} \\ 
     154\boldsymbol{c} &=& \text{point in clip space} \\ 
     155\end{eqnarray*} 
     156}}} 
     157 
     158Given this we can do the opposite by multiplying the clipping space coordinate by the inverse of the {{{GL_PROJECTION}}} matrix.  This isn't as bad as it sounds since we can avoid computing a true 4x4 matrix inverse if we just construct the inverse projection matrix at the same time we build the projection matrix. 
     159 
     160A typical OpenGL projection matrix takes the form: 
     161