Shear Matrix as a combination of basic transformation?

Question

I know the transformation matrices for rotation, scaling, translation etc. I also know the matrix for shear transformation. Now, I need to have the shear matrix--

Answer 1

Yup it can be done, a rotation followed by non uniform scaling and reverse rotation. You can find the details here in third question http://www.cs.cmu.edu/~djames/15-462/Fall03/assts/15-462-Fall03-wrAssign1-answer.pdf. you can try the following openGL code as well. It rotates a rectangle by 45 degree then scales in x-axis. and then rotates in -26 degree i.e. atan(0.5). 0.5 comes from finding the angle between x-axis and one side after scaling in x-direction.

glRotatef(-26.0, 0.0, 0.0, 1.0);

glScalef(2,1,1);

glRotatef(45.0, 0.0, 0.0, 1.0);

glRectf(0, 0, 25.0, 25.0);