Implementation of spherical coordinates in C# (based on https://github.com/mrdoob/three.js/blob/master/src/math/Spherical.js)

Spherical.cs

using UnityEngine;

public struct Spherical {

	public float Radius;
	public float Phi;
	public float Theta;

	Spherical( float radius = 1f, float phi = 0f, float theta = 0f ) {
		Radius = radius;
		Phi = phi;
		Theta = theta;
	}

	public Spherical SetFromVector3( Vector3 vector ) {
		Radius = vector.magnitude;

		if ( Radius == 0f ) {

			Theta = 0f;
			Phi = 0f;

		} else {

			Theta = Mathf.Atan2( vector.x, vector.z );
			Phi = Mathf.Acos( Mathf.Clamp( vector.y / Radius, - 1, 1 ) );

		}

		return this;
	}

	public Vector3 SetVector3( ref Vector3 target ) {

		var sinPhiRadius = Mathf.Sin( Phi ) * Radius;

		target.x = sinPhiRadius * Mathf.Sin( Theta );
		target.y = Mathf.Cos( Phi ) * Radius;
		target.z = sinPhiRadius * Mathf.Cos( Theta );

		return target;
	}

	public static Spherical FromVector3( Vector3 vector ) {
		return new Spherical().SetFromVector3( vector );
	}
}

Obviously all credit goes to bhouston and WestLangley for writing the THREE.js implementation.