Interactive Polygon Background

Thor

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If you can find and existing 3D convex hull algorithm implementation, what you can do is take a set of 2D points (x,y) each, project them onto a paraboloid (x,y,x*x+y*y), put this through the convex hull algorithm to get a set of triangles.

Then you reject the upper part of the hull by throwing away triangles whose z component of its normal is positive. The remaing triangle set is the Delaunay triangulation of the original points.

Then render as you wish (looks like the examples compute the average pixel colours of the triangle and render the triangle as a constant colour being that average. The points seem to be a random sampling inside the image. For some of them it looks as though an outline polygon may have been computed from the image or the edges of the image were sampled (easier) to include points on the boundary of the images (eg the fruit).
 
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This reminds me, and sorry to hijack the thread for a bit but back at varsity I saw my a screensaver on my lecturers PC.
The screensaver creates a picture from other pictures while it zooms out from the initial picture.

Can any of you point me in the direction of such an app?
 
I think a background like this is annoying. Just a newer version of all the spinning gifs & animations from the 90's
 
Merely an attempt at humour. That was a excellent technical breakdown.

Thanks. Well, I hope it helps - it touches on topics that are presented usually at the start of 1st year maths or in admaths (paraboloids and normals), but are pretty straightforward. I should have added that by moving the points chosen in some fashion, the triangles would have the effect of moving with them.
 
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