Angles and rotation in GLSL

Zero starts from the right axis, positive rotation is clockwise. If we do fract(atan(y, x)) on the translated UV, we’ll get this:

Matrix multiplication. See also this and this.

To summarize, if you want to apply matrix to a vector, you write it in this order, like in good ol’ math:

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vec3 new_vector = matrix * old_vector;

You can also write it in reverse order, but that will multiply by a transposed matrix. Sadly, some_vec *= matrix will do exactly that.

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vec2 rotated_vector = rotation_matrix * vector;