Shear Matrix as a combination of basic transformation?
graphics, linear-algebra, matrix, rotational-matrices, transformation
Solution
The x-shear operation for a shearing angle `theta`reduces to rotations and scaling as follows:
(a) Rotate by `theta/2` counter-clockwise.
(b) Scale with `x-scaling factor = sin(theta/2)` and `y-scaling factor = cos(theta/2)`.
(c) Rotate by `45 degree` clockwise.
(d) Scale with `x-scaling factor = sqrt(2)/sin(theta)` , and `y-scaling factor= sqrt(2)`.
Problem
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-- ``` [1 Sx 0] [0 1 0] [0 0 1] ``` in the form of a combination of other aforesaid transformations. Tried searching, tried brainstorming, but unable to strike! Thanks!