cortex: thesis/cortex.org comparison

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-:3ec428e096e5
+:5a15611fbb9f
 Triangles are [[http://mathworld.wolfram.com/AffineTransformation.html ][affine]], which means any triangle can be transformed
 into any other by a combination of translation, scaling, and
 rotation. The affine transformation from one triangle to another
 is readily computable if the triangle is expressed in terms of a
 $4x4$ matrix.
+#+BEGIN_LaTeX
+$$
 \begin{bmatrix}
 x_1 & x_2 & x_3 & n_x \\
 y_1 & y_2 & y_3 & n_y \\
 z_1 & z_2 & z_3 & n_z \\
 1 & 1 & 1 & 1
 \end{bmatrix}
+$$
+#+END_LaTeX
 Here, the first three columns of the matrix are the vertices of
 the triangle. The last column is the right-handed unit normal of
 the triangle.
-With two triangles $T_{1}$ and $T_{2}$ each expressed as a matrix
+With two triangles $T_{1}$ and $T_{2}$ each expressed as a
-like above, the affine transform from $T_{1}$ to $T_{2}$ is
+matrix like above, the affine transform from $T_{1}$ to $T_{2}$
+is $T_{2}T_{1}^{-1}$.
-$T_{2}T_{1}^{-1}$
 The clojure code below recapitulates the formulas above, using
 jMonkeyEngine's =Matrix4f= objects, which can describe any affine
 transformation.

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