Editing WoW:SetTexCoord Transformations (section)

===SetTexCoord math with matrices===
====T as a matrix====
The first step in figuring out your SetTexCoord parameters is to represent your transformation as a matrix. This wont be covered here, but there are plenty of tutorials online concerning the mathematics of matrix transformations.  You'll end up with a matrix with 6 variables, in the form shown above, and we'll use those for this example.

====Inverting T====
Not all matrices can be inverted, but for this case with the affine restricted 3x3 matrix, any matrix for which (AE-BD) is not zero has an inverse (This value is the 'determinant' of the matrix, and represents the change in area that a shape undergoes when transformed, you cannot reverse a matrix with a zero determinant because it represents a collapse into a single point or line)

 det = AE - BD
 x   = ( EX - BY + (BF-CE)) / det
 y   = (-DX + AY - (AF-CD)) / det

Thus, if we were to make a new matrix for T' it'd be as follows

{|
|(||E/det||-B/det||(BF-CE)/det||)
|-
|(||-D/det||A/det||-(AF-CD)/det||)
|-
|(||0||0||1||)
|}

====Final SetTexCoord results====
To calculate the final image coordinates, we apply T' to each of the corner Texture coordinates:

UL Texture Coordinates (X,Y) = (0,0)
 ULx = ( BF - CE) / det
 ULy = (-AF + CD) / det

LL Texture Coordinates (X,Y) = (0,1)
 LLx = (-B + BF - CE) / det = (-(1-F)B - CE) / det
 LLy = ( A - AF + CD) / det = ( (1-F)A + CD) / det

UR Texture Coordinates (X,Y) = (1,0)
 URx = ( E + BF - CE) / det = ( BF + (1-C)E ) / det
 URy = (-D - AF + CD) / det = ( AF - (1-C)D ) / det

LR Texture Coordinates (X,Y) = (1,1)
 LRx = ( E - B + BF - CE) / det = ( (1-C)E - (1-F)B ) / det
 LRy = (-D + A - AF + CD) / det = (-(1-C)D + (1-F)A ) / det

====Example function====
The function below will take a texture t, and a matrix with 6 variables as its arguments, and apply the transformation to the texture using the SetTexCoord calculations above.
 function setCoords(t, A, B, C, D, E, F)
 	local det = A*E - B*D;
 	local ULx, ULy, LLx, LLy, URx, URy, LRx, LRy;
 	
 	ULx, ULy = ( B*F - C*E ) / det, ( -(A*F) + C*D ) / det;
 	LLx, LLy = ( -B + B*F - C*E ) / det, ( A - A*F + C*D ) / det;
 	URx, URy = ( E + B*F - C*E ) / det, ( -D - A*F + C*D ) / det;
 	LRx, LRy = ( E - B + B*F - C*E ) / det, ( -D + A -(A*F) + C*D ) / det;
 	
 	t:SetTexCoord(ULx, ULy, LLx, LLy, URx, URy, LRx, LRy);
 end
Applying transformations is then rather simple. To apply a rotation to the texture, we can use the rotation matrix below (assuming angle a):
{|
|(||cos(a)||sin(a)||1||)
|-
|(||-sin(a)||cos(a)||1||)
|}
Applying a rotation of 90 degrees can then be done by using:
 local cos, sin = math.cos, math.sin;
 local angle = math.rad(90);
 setCoords(texture, cos(angle), sin(angle), 1, -sin(angle), cos(angle), 1);