In my math and physics classes, all the rotation matrices that I have seen have the -sin(theta) term in the bottom left term, and not the upper right. It seems that these two rotation matrices would get different results when applied on the same point/vector.
Is this form the convention in graphics? Why is it not the standard one from math/physics classes?
ananyas
@ljelenak I believe the rotation matrix with -sin(theta) in the upper right indicates a counterclockwise rotation, and with -sin(theta) in the lower left indicates a clockwise rotation.
keenan
@ljelenak Yes, @ananyas is right: the matrix on this slide represents a counter-clockwise rotation by $\theta$. This convention (positive = CCW, negative = CW) is fairly standard across math, graphics, and physics, but it is, of course, just an arbitrary convention.
In my math and physics classes, all the rotation matrices that I have seen have the -sin(theta) term in the bottom left term, and not the upper right. It seems that these two rotation matrices would get different results when applied on the same point/vector.
Is this form the convention in graphics? Why is it not the standard one from math/physics classes?
@ljelenak I believe the rotation matrix with -sin(theta) in the upper right indicates a counterclockwise rotation, and with -sin(theta) in the lower left indicates a clockwise rotation.
@ljelenak Yes, @ananyas is right: the matrix on this slide represents a counter-clockwise rotation by $\theta$. This convention (positive = CCW, negative = CW) is fairly standard across math, graphics, and physics, but it is, of course, just an arbitrary convention.