Hello everyone, someoneone bad at maths here asking questions about rotation matrices. Am I correct to assume in rotation matrix we compare the rotation of coordinate system B to A ? For example in row 1 column 2, we compare the coordinate B X-axis to coordinate system A Y-axis ? And the formula on the right is when we rotate the X and Y axis of coordinate system B counterclockwise and we leave axis Z untouched ? That is where we get our corner alpha ? and why zaxis value is 1 for parallel and the others are 0 for being crossed ? Could someone poke me in the right direction if I am wrong here ? And excuse the MSPaint, didnt have anything better at hand.
if I happen to be right, could someone please explain to me how the sines cosines are gotten, in this more simpler 2 axis coordinate system. Thank you
Go back to basic trigonometry. Start with 2-D rotation. Suppose you have a point (x,y) in X-Y Cartesian coordinates. What is the position of the point in polar coordinates, (r,θ)? x = r cos θ y = r sin θ Now rotate the X,Y coordinate system by α-degrees in a counter clockwise direction. The position (x,y) in the new system is r, (θ-α) The new (x,y) coordinates are x = r cos(θ - α) y = r sin(θ - α) Expand these two equations: x = r ( cos θ cos α + sin θ sin α ) y = r ( sin θ cos α - cos θ sin α ) See if you can come up with the rotational matrix for 2-D rotation.
why is it θ-α ? why isnt it x=r*cos(θ-a) y=r*sin(θ+a) in your example and how does this fit into a matrix ? oh man im rly bad at this