Rotation matrix for azimuth and zenith angles

[lightningbolt]

I have a shape with spherical coordinate (r, theta, phi) which I can convert to Cartesian. I want to apply rotation to the shape by incrementing theta & phi.
I figured out the matrix for rotating azimuth angle is
{
{cos(theta), -sin(theta), 0}
{sin(theta), cos(theta), 0}
{ 0, 0, 1}
}
How to find the rotation matrix for Zenith angle?.
Thanks.

 

[SonyAD]

Why don't you increment θ and φ as you wish then convert to Cartesian?

 

[lightningbolt]

@SonyAD,
If you change θ and φ in spherical coordinates and convert to Cartesian, it won't result in the change you expect. It gives garbage values.
i.e I can't just add 5 degree to θ or φ, if i want to rotate the shape 5 degree.
Thanks.

 

[SonyAD]

I don't think I understand what you're after.

If it is rotation equations inside a Cartesian system you're after:

v1 = calf*xi+salf*zi;
v2 = calf*zi-salf*xi;
v3 = cbet*yi+sbet*v2;

zr = cbet*v2-sbet*yi;
xr = cgam*v1+sgam*v3;
yr = cgam*v3-sgam*v1;

salf = $$\sin(\alpha)$$;
calf = $$\cos(\alpha)$$;
etc.

In case you're making a mistake converting to Cartesian, I've worked out how to do it and http://en.wikipedia.org/wiki/Spherical_coordinate_system#Cartesian_coordinates":

x = radius · sin(θ) · cos(φ)
y = radius · sin(θ) · sin(φ)
z = radius · cos(θ)

In case the spherical coordinate system isn't doing what you expect it to, when you increment θ and φ this is what actually happens:

You rotate the initial point around the absolute Y axis.
You rotate the transformed point around the absolute Z axis.

Are you trying to interpret mouse input?

 

[blue_raver22]

I would like to commend you for taking the initiative to find the rotation matrix for your spherical coordinates. It is essential to have a solid understanding of coordinate systems and their transformations in order to accurately represent and manipulate data in various fields of science.

To answer your question, the rotation matrix for the zenith angle can be found by using the same approach as the azimuth angle. The zenith angle, also known as the polar angle, is the angle measured from the positive z-axis to the vector representing the point in spherical coordinates.

To rotate the shape by incrementing the zenith angle, we can use the following matrix:

{
{cos(phi), 0, sin(phi)}
{0, 1, 0}
{-sin(phi), 0, cos(phi)}
}

This matrix represents a rotation around the y-axis, which is perpendicular to the z-axis and passes through the origin. This rotation will change the value of the zenith angle while keeping the azimuth angle constant.

It is important to note that the order in which these rotations are applied matters. If you first apply the rotation for the azimuth angle and then the rotation for the zenith angle, the resulting shape will be different from if you apply the rotations in the opposite order. This is due to the fact that rotations are not commutative, meaning the order of operations affects the final outcome.

I hope this helps in your understanding of rotation matrices for spherical coordinates. Keep up the good work in exploring and understanding coordinate systems in your scientific endeavors.