For affine transformations, must it follow all rules of linear transformations except that it can move the origin? But all the other rules must be followed?
May I ask two questions? 1) For a LINEAR transformation, is it that the origin must be 0,0 or just that the origin must always stay same? 2) For affine transformation, I heard y = Mx + b is affine transformation but if it is just taking points and creating a line, not mapping lines to lines, how is it a transformation?
May I ask one more question please kind sir: Can a transformation be affine transformation if it has everything you said in video but doesn’t follow the linear transformation rule A) about associativity B) Mapping vector to vector Thank you!
This is probably a year late. But interesting question. Looking at the what changing the individual values of {a....f} in the matrix actually does to the image, I think the 6 DOF's would be (going from a to f): Scale width, shear x, translate x, shear y, scale height, translate y. Rotation could be considered a combination of shears and scaling, do I find it hard to wrap my mind around exactly how that works. This image gives a nice overview though: en.wikipedia.org/wiki/Transformation_matrix#/media/File:2D_affine_transformation_matrix.svg
I program on Khan Acadamy as recreational programming and I want to shear an image, however, I can only use the translate, rotate, and scale commands. how can I achieve a shear with these transformations???
glyn hodges I already know this check out my program called Shear X with quads. I did this there. But I can't apply the same concept on images without manipulating individual pixels which takes too long.
