Re: Rotated square in space


<matt271829-news@xxxxxxxxxxx> wrote in message
news:1118057127.671791.195540@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
>
> 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.
>

Agreed.

Consider the simplest case - the projection onto the 2D plane is itself a
square.

Now is this the shadow of a square the same size just above the 2D surface,
or of a tiny square right next to the projection point?



.

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