One thing I found very surprising is that transformations can lead to effectively changing the order of triangles. What was once a counterclockwise triangle can easily become a clockwise triangle after transformation.
adampahlavan
What would non-invertible 2x2 matrices look like when treated as transformations? I believe of all the transformations we studied they are invertible b/c the determinants are always non-zero (in 2d coordinates).
m11
I am trying to understand how shear works. For the shear in x the s in the matrix seems to translate the top of the square to the right, how would the matrix look if we wanted to translate the bottom of the square to the right instead?
imm
^ I think we can think of this as a shear using -s instead of s and then translated back over. Not sure if there's a way to do this with a 2x2 matrix since it involves a translation or if we would need to use a matrix in 2D-H
chaonanye
I understand shear in x and y, could anyone explain in intuition way for what the arbitrary shear's doing? They look like 2 totally different shapes.
One thing I found very surprising is that transformations can lead to effectively changing the order of triangles. What was once a counterclockwise triangle can easily become a clockwise triangle after transformation.
What would non-invertible 2x2 matrices look like when treated as transformations? I believe of all the transformations we studied they are invertible b/c the determinants are always non-zero (in 2d coordinates).
I am trying to understand how shear works. For the shear in x the s in the matrix seems to translate the top of the square to the right, how would the matrix look if we wanted to translate the bottom of the square to the right instead?
^ I think we can think of this as a shear using -s instead of s and then translated back over. Not sure if there's a way to do this with a 2x2 matrix since it involves a translation or if we would need to use a matrix in 2D-H
I understand shear in x and y, could anyone explain in intuition way for what the arbitrary shear's doing? They look like 2 totally different shapes.