1.1 --- a/thesis/cortex.org	Fri Mar 28 21:48:53 2014 -0400
     1.2 +++ b/thesis/cortex.org	Fri Mar 28 22:09:03 2014 -0400
     1.3 @@ -1741,22 +1741,25 @@
     1.4      rotation. The affine transformation from one triangle to another
     1.5      is readily computable if the triangle is expressed in terms of a
     1.6      $4x4$ matrix.
     1.7 -    
     1.8 +
     1.9 +    #+BEGIN_LaTeX
    1.10 +    $$
    1.11      \begin{bmatrix}
    1.12      x_1 & x_2 & x_3 & n_x \\
    1.13      y_1 & y_2 & y_3 & n_y \\ 
    1.14      z_1 & z_2 & z_3 & n_z \\
    1.15      1 & 1 & 1 & 1 
    1.16      \end{bmatrix}
    1.17 +    $$
    1.18 +    #+END_LaTeX
    1.19      
    1.20      Here, the first three columns of the matrix are the vertices of
    1.21      the triangle. The last column is the right-handed unit normal of
    1.22      the triangle.
    1.23      
    1.24 -    With two triangles $T_{1}$ and $T_{2}$ each expressed as a matrix
    1.25 -    like above, the affine transform from $T_{1}$ to $T_{2}$ is
    1.26 -    
    1.27 -    $T_{2}T_{1}^{-1}$
    1.28 +    With two triangles $T_{1}$ and $T_{2}$ each expressed as a
    1.29 +    matrix like above, the affine transform from $T_{1}$ to $T_{2}$
    1.30 +    is $T_{2}T_{1}^{-1}$.
    1.31      
    1.32      The clojure code below recapitulates the formulas above, using
    1.33      jMonkeyEngine's =Matrix4f= objects, which can describe any affine

     2.1 --- a/thesis/rlm-cortex-meng.tex	Fri Mar 28 21:48:53 2014 -0400
     2.2 +++ b/thesis/rlm-cortex-meng.tex	Fri Mar 28 22:09:03 2014 -0400
     2.3 @@ -36,6 +36,7 @@
     2.4  \usepackage{wrapfig}
     2.5  \usepackage{rotating}
     2.6  \usepackage[normalem]{ulem}
     2.7 +\usepackage{mathtools}
     2.8  \usepackage{amsmath}
     2.9  \usepackage{textcomp}
    2.10  \usepackage{marvosym}