Re: Rotated square in space


Luiz Borges wrote:
> Hi,
> I trying hard to figure that out, but no luck until now...
> I have the points of 4 corners of a square in a 2d perspective
> projection, this square have been rotated in all 3 axes on 3d space.
> With only the four 2d points of the corner can I discover the points of
> the square in the 3d space?
>
> Example:
> I have this projection:
> p1 0,5
> p2 5,0
> p3 15,5
> p4 10,15
>
> and now I want p1,p2,p3,p4 in 3d world coordinates.

I don't see that you can do this.

Call the viewpoint O. (Viewpoint lies somewhere off the projection
plane, i.e. the plane containing p1, p2, p3, p4). Draw lines Op1, Op2,
Op3, Op4, extended indefinitely. You are looking for four points A, B,
C, D, lying on those lines respectively, such that ABCD is a square. It
seems to me that if there is one such square then there must be
infinitely many, all parallel to each other.

.

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