Jim Blinn's Corner: Notation, Notation, Notation

Chapter Thirteen

Inferring Transforms

May-June 1999

In simple 2D texture mapping, you take a 2D image and render it on the screen after some transformation or distortion. To accomplish this, you will need to take each [X, Y] location on the screen and calculate a [U, V] texture coordinate to place there. A particularly common transformation is

$U=\frac{aX+bY+c}{gX+hY+j},V=\frac{dX+eY+f}{gX+hY+j}$

By picking the proper values for the coefficients a … j, we can fly the 2D texture around to an arbitrary position, orientation, and perspective projection on the screen. One can, ...