Re: Rotated square in space


Luiz Borges wrote:
> I think I found a way to solve my problems...
>
> 1) With the four projected corners, if I trace diagonals from them, the
> crossing of diagonals will be on the exact point in projection of where
> the center of the original square would lie.
> 2) Having the center C and the working with an edge at time (thus a
> triangle) with corners A and B, I can find any point I want on the line
> AB working with the angle ACB.
>
> Example: if i need the middle point of AB I will just bissect the angle
> ACB and pick the point where the bissection crosses AB. The same works
> for any other point in the border, if I need the point at 10% (I MUST
> work with percenteges) of side AB, I just pick 10% of the angle ACB
> from the line CA and make a line from C with that angle, the point
> where it intersects AB is my desired point.
>
> Can anybody correct me? I tried to be as clear as possible, but english
> isn't my first language.
> I will try to proof my results on paper before implement them, but I
> think this is one of the ways.
>
> Thanks,
> Luiz Borges

I'm a little confused about what you're doing here. You don't seem to
be anywhere finding the position in 3D-space of the four corners of the
square, which I thought was what you wanted?

When I read your first post I THOUGHT the problem was as follows (I
posted this text before actually, but it doesn't seem to have appeared
- at least not on Google - so here goes again.)

1. You have a projection plane, call it P, which for convenience I'll
designate as the xy-plane.

2. You have a single point somewhere in space, off the projection
plane, which I called the "viewpoint", O.

3. You have four points somewhere in space, A, B, C, D, forming a plane
square (if, indeed, there is any other type of square!)

4. You draw lines OA, OB, OC, OD, to intersect P at p1, p2, p3, p4
respectively.

5. Given the x- and y-coordinates of p1, p2, p3, p4, the problem is to
find, with some appropriate choice of O, the x-, y- and z-coordinates
of A, B, C, D.

Is that what you're trying to do?

Further question: is the line from O to the origin of the coordinate
system on P (relative to which p1 etc. are measured) intended to be
normal to P, or is that not a requirement?

.

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