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August 19th, 2010, 05:47 PM   #1
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Spherical Vector to Cartesian Vector

Hello everyone,

I have what should be a straightforward question. How would I convert a 3D spherical vector into a 3D Cartesian coordinate direction vector.

This may sound confusing at first. ( Or maybe it is just me) But basically, I have a spherical vector defined by <rho,theta,psi> and I would like to convert that vector into a Cartesian vector <x,y,z>.

Thanks,
Taylor S. Amarel
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August 19th, 2010, 08:16 PM   #2
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Re: Spherical Vector to Cartesian Vector

If r is magnitude of the vector, then

x = r*cos{?}

y = r*cos{?}

z = r*cos{?}
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August 20th, 2010, 03:45 AM   #3
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Re: Spherical Vector to Cartesian Vector

I'm not sure that will work, forgive me for questioning your answer. But I with the formula you gave, it appears as if your assuming Rho is an angle. Which in my case it is not. I have the a radius or distance from the origin (rho), an angle, (theta), and another angle (psi). (rho,theta,psi).

I'm trying to get a three dimensional direction vector and it * appears* that your thinking Rho is an angle. (It looks that way because of the trigonometry function associated with Rho in your formula). I could be wrong, I a beginner trying to learn.

Could you please provide some explanation or confirmation?

Thanks,
Taylor S. Amarel
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August 20th, 2010, 07:33 AM   #4
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Re: Spherical Vector to Cartesian Vector

OK. Then I assume that the vector moves through an angle ? with respect to a reference line in the vertical plane. Afterwords it moves horizontally through an angle ? to reach the final position.In that case

x = ?cos?cos?
y = ?cos?sin?
z = ?sin?.
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