I have a 3D math problem which I just can't seem to solve.
I have data of 3 points. The data is a (2D) coordinate on a plane, floating somewhere in 3D space. I also know the (2D) coordinate of the projection. That results in the following array of data:
[[[x1,y1], [px1,py1], [[x2,y2], [px2,py2], [[x3,y3], [px3,py3]]
Where the normal (x1 etc.) coordinates stand for the coordinates on the plane and the other (px1 etc.) for the projected coordinates.
What I would like to do is project a new 2D coordinate ([x4,y4]).
What I tried so far:
Ofcourse you need an eye for projection, so I set that to [xe,ye,-1]. The xe and ye are known. (It is photo referencing, so I just placed the eye in the center of the photograph.)
Beneath the eye I placed the projection surface (z=0). That gives the following projection coordinates:
[[[x1,y1], [px1,py1,0], [[x2,y2], [px2,py2,0], [[x3,y3], [px3,py3,0]]
I can't do the same for the coordinates on the plane, since I don't know anything about that plane.
I also figured that I could make a parameterized formula of the lines running from the eye through the projection coordinates. For line1 that would be:
line1x = xe+(px1-xe)*t1 line1y = ye+(py1-ye)*t1 line1z = -1+t1 // = -1+(0--1)*t1
I also know the distance between the points in 3D. That's the same as in 2D. That means the distance between point1 and point2 would be sqrt((x1-x2)^2+(y1-y2)^2).
I also know the distance between the lines (line1 and line2) at any time. That is sqrt((line1x-line2x)^2+(line1y-line2y)^2+(line1z-line2z)^2).
However, I don't really know how to go from here… Or even whether this is the right route to take.
I hope you understand what I want to be able to do, and that you can help me.
Thanks in advance!