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Main Question or Discussion Point
Hi folks, I'm hoping for a little help with something which I'm sure should be pretty easy... but I dont have access to any kind of maths textbooks to look anything up, sadly, so I'm hoping you guys might help?
Let's consider a point P on the surface of a sphere, and define Vo as the unit vector from the origin of the sphere to this point. This vector also describes the normal to the plane which is tangential to the sphere at P.
Now let Va be a (unit) vector within this plane, i.e. Va is perpendicular to Vo, and the angle A describes the angle subtended by Va and the point within the plane which intersects the sphere's +Z axis.
Another way of looking at this would be: if Vz is the vector between P and the Z axis, within the plane normal to Vo, the angle A is between Va and Vz.
So now the question... if Vo and A are known... how do I get Va? (in terms of cartesian coords)
edit: made it a little clearer, I hope, and added a diagram drawn in MS Word which I hope should also help.
Let's consider a point P on the surface of a sphere, and define Vo as the unit vector from the origin of the sphere to this point. This vector also describes the normal to the plane which is tangential to the sphere at P.
Now let Va be a (unit) vector within this plane, i.e. Va is perpendicular to Vo, and the angle A describes the angle subtended by Va and the point within the plane which intersects the sphere's +Z axis.
Another way of looking at this would be: if Vz is the vector between P and the Z axis, within the plane normal to Vo, the angle A is between Va and Vz.
So now the question... if Vo and A are known... how do I get Va? (in terms of cartesian coords)
edit: made it a little clearer, I hope, and added a diagram drawn in MS Word which I hope should also help.
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