Finding a point in 3d space on a plane using 2d coordinates

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votes

visualization

I am searching the location of a point that lies on a plane. The relative location on the plane is given in u/v-Coordinates. The normal vector n is equal to the vector from (0,0,0) to the center of the plane (or any other distance ≠ 0, if more convenient)

The plane has no rotation around the n vector - u is always on the xy axis and v on the z (up) axis

I feel like there should be a simple formula for this, given Vector3 n along with the coordinates u and v, but i'm stuck here.

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math
Since the plane can rotate about n without changing the u,v coordinates of the point, there is not enough information to locate the point in space. – Beta
Right, that wouldn't work. The plane is always oriented like in the picture, with u on the horizontal plane and v on the vertical axis (edited in the question) – Ismir Egal
What are your inputs and expected outputs? What about edge cases where the normal vector itself lies in one or both of the planes that u and v are supposed to lie in? – kaya3
The inputs are u and v as double and n as as a vector3 (double). u and v lie in the plane constructed by the vector n and are thus always perpendicular towards it. – Ismir Egal

1 Answers

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You have the coordinates of the origin of the plane, namely (x, y, z)

Now we need the unit vectors u and v in global coordinates.

u is (y, -x, 0), normalized.

v is (-zx/r, -zy/r, r), normalized, where r=(x2+y2)1/2

Now you can add the location of the point in uv coordinates to the location of the plane origin in xyz coordinates.