- #1
irishetalon00
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Homework Statement
I am working in Matlab, and have a 3D plot that I made:
y is parallel to axis labeled "long. dir. (m)"
z is normal to these (right hand coordinate sytem)
The original view was looking parallel with +y. To get the current view, I rotated our viewpoint about the x-axis -15 degrees, then rotated about the ORIGINAL z axis 10 degrees.
How do I calculate the angle that the x-axis now forms on the page?
For comparison, I used image editing software to measure the angle of the axis. It is a rectangle 12 high, 322 wide, so the angle is -2.134 deg.
Homework Equations
The Attempt at a Solution
I attempted to do rotation matrices. I did:
phi = -15deg
theta = 10deg
A =
[cos(theta) sin(theta) 0;
-sin(theta) cos(theta) 0;
0 0 1]
B =
[1 0 0;
0 cos(phi) -sin(phi);
0 sin(phi) cos(phi)]
B*A =
[ cos(theta), cos(phi)*sin(theta), -sin(phi)*sin(theta);
[ -sin(theta), cos(phi)*cos(theta), -cos(theta)*sin(phi);
[ 0, sin(phi), cos(phi)]
And do get the angle that the original x-axis forms with our new viewpoint, I do
r =
[1;
0;
0]
then do:
B*A*r
and I get:
[cos(theta);
-sin(theta);
0]
Which does not give me a correct result. Not only that, there is no way that a rotation in two different axes does not depend on both theta and phi.
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