How do I translate a spherical coordinate to a Cartesian one?

Question

Could someone point me in the right direction as to how this might be achieved? 3D math / geometry often throws me.

I'm looking for something like this (ideally in C#):

public Vector3 getCartesianFor(float elevation, float asimuth, float polar)
{
   return ????;
}

Answer 1

http://blog.nobel-joergensen.com/2010/10/22/spherical-coordinates-in-unity/

public static void SphericalToCartesian(float radius, float polar, float elevation, out Vector3 outCart){
    float a = radius * Mathf.Cos(elevation);
    outCart.x = a * Mathf.Cos(polar);
    outCart.y = radius * Mathf.Sin(elevation);
    outCart.z = a * Mathf.Sin(polar);
}


public static void CartesianToSpherical(Vector3 cartCoords, out float outRadius, out float outPolar, out float outElevation){
    if (cartCoords.x == 0)
        cartCoords.x = Mathf.Epsilon;
    outRadius = Mathf.Sqrt((cartCoords.x * cartCoords.x)
                    + (cartCoords.y * cartCoords.y)
                    + (cartCoords.z * cartCoords.z));
    outPolar = Mathf.Atan(cartCoords.z / cartCoords.x);
    if (cartCoords.x < 0)
        outPolar += Mathf.PI;
    outElevation = Mathf.Asin(cartCoords.y / outRadius);
}

Answer 2

• r: radial distance
• θ: inclination
• φ: azimuth

via Wikipedia

public Vector3 getCartesianFor(float radius, float inclination, float azimuth)
{
   return new Vector3(radius*Sin(inclination)*Cos(azimuth), radius*Sin(inclination)*Sin(azimuth), radius*Cos(inclination));
}

Answer 3

If by polar you mean the magnitude of the vector, and elevation is defined as the angle between vector and the xy plane (as the name implies), the function would be:

public Vector3 getCartesianFor(float elevation, float asimuth, float polar)
{
   return new Vector3(polar*Cos(elevation)*Cos(asimuth),
                      polar*Cos(elevation)*Sin(asimuth),
                      polar*Sin(inclination));
}

Note that this is very similar to MLM's answer, it all depends on how you define your elevation angle. I've also respected your function template signature, but I suggest a few changes:

• asimuth is a typo, the correct spelling would be azimuth
• polar usually refers to the 2D coordinate system (r, θ). The magnitude of the vector is commonly referred to as radius
• A more conventional order would have radius as the first parameter.