A New Wrinkle with Voronoi

[bplus]

Shading gives us a lovely psuedo-3D effect!

Code: QB64: [Select]

1. _Title "Shading Voronoi Demo" 'b+ 2019-12-11  shading 2021-05-10
2. Const xymax = 700, nPoints = 50
3. Type pType
4.     x As Single
5.     y As Single
6.     c As _Unsigned Long
7. End Type
8. Screen _NewImage(xymax, xymax, 32)
9. _ScreenMove 300, 20
10. Randomize Timer
11. Dim pts(1 To nPoints) As pType
12. For i = 1 To nPoints
13.     pts(i).x = xymax * Rnd
14.     pts(i).y = xymax * Rnd
15.     pts(i).c = _RGB32(155 * Rnd + 100, -(Rnd < .5) * 255 * Rnd, -(Rnd < .5) * 255 * Rnd)
16. Next
17. For i = 1 To nPoints
18.     Circle (pts(i).x, pts(i).y), 5, pts(i).c
19. Next
20. _Delay .5
21. For y = 0 To xymax
22.     For x = 0 To xymax
23.         minD = 49000
24.         For p = 1 To nPoints
25.             d = ((pts(p).x - x) ^ 2 + (pts(p).y - y) ^ 2) ^ .5
26.             If d < minD Then minD = d: saveP = p
27.         Next
28.         PSet (x, y), Ink~&(pts(saveP).c, &HFF000000, minD / 85)
29.     Next
30. Next
31. Sleep
32.  
33. Sub cAnalysis (c As _Unsigned Long, outRed, outGrn, outBlu, outAlp)
34.     outRed = _Red32(c): outGrn = _Green32(c): outBlu = _Blue32(c): outAlp = _Alpha32(c)
35. End Sub
36.  
37. Function Ink~& (c1 As _Unsigned Long, c2 As _Unsigned Long, fr##)
38.     Dim R1, G1, B1, A1, R2, G2, B2, A2
39.     cAnalysis c1, R1, G1, B1, A1
40.     cAnalysis c2, R2, G2, B2, A2
41.     Ink~& = _RGB32(R1 + (R2 - R1) * fr##, G1 + (G2 - G1) * fr##, B1 + (B2 - B1) * fr##, A1 + (A2 - A1) * fr##)
42. End Function
43.  
44.  

 

[bplus]

So what happens if we go the other way?

Same code except here:

Code: QB64: [Select]

1. PSet (x, y), Ink~&(pts(saveP).c, &HFF000000, minD / 85)
2.  

Make this:

Code: QB64: [Select]

1. PSet (x, y), Ink~&(pts(saveP).c, &HFFFFFFFF, minD / 85)
2.  

 

[bplus]

Here's one for johnno56 in the key of blue

 

[bplus]

Someone at Syntax Bomb alerted me to this method for Voronoi
https://en.wikipedia.org/wiki/Fortune%27s_algorithm

Looks interesting! Who can code it first?

[johnno56]

The small animation reminded me of the creation of soap bubbles...

[bplus]

Yeah, I am wondering if Andy Amaya's method is using any of this or is it an entirely different 3rd approach.

The Wiki is way over my head with formula jargon but (ironically) there is a link to something more readable from AMS.
 https://www.ams.org/publicoutreach/feature-column/fcarc-voronoi

[johnno56]

The Wiki is "over your head" but the AMS is more readable? Aw man. The AMS example may as well have been written in Romulan... Says a lot about my ability to understand 'jargon'... *sigh*

[jack]

I found a C++ implementation of the Fortune's Algorithm  https://www.cs.hmc.edu/~mbrubeck/voronoi.html
but an easier explanation of the algorithm is found here https://jacquesheunis.com/post/fortunes-algorithm/

[bplus]

Thanks Jack, I saw the C++ code before Yikes! the other looks readable and may help supplement with AMS paper.

At moment I am dogging 2 ball collisions with vectors.