Reconstruction of a 2D form from its projection in 1D

Question

I have a convex closed shape in 2 D space (on the xy plane). I don’t know how it looks. I rotate this shape approximately in the center of its bounding box 64 times by 5.625 degrees (360/64). For each rotation, I have the x-coordinates of the extreme points of the form. In other words, I know the left and right x extents of the shape for each rotation (assuming orthogonal projection). How to get 64 points on a figure that do not contradict x projections. Note that the 2D shape rotates, but the coordinate axes do not rotate with it. Therefore, if your object is a string, the x projection of each end, if it is constructed, will essentially be a sin / cos wave, depending on its initial orientation.

The higher the speed, if I have a solution, the closer I will get to my actual form.

In fact, I do not know the exact point at which I rotate the form, however, any solution that suggests that I know will still be useful, since I do not mind that the reconstruction is imperfect.

Answer 1

We used the direct adjustment method for recovery.

Projection is the shade of an object.

You start with a bounding two-dimensional window. For each projection, you cut out the left and right parts of the 2D shape that go beyond the projection. So, the main function calculates the intersection of two convex two-dimensional figures. You calculate these intersections for each projection.

P1, P2, P3, P4 :

, , :

4 . , . , .