Fortune's Algorithm

• This code has some double precision issues.
• Only 150 lines.
• This code uses splay tree. Worst time complexty is O(n log n).
• Calculating the Voronoi Diagram with 1 million(1,000,000) random points in 2 seconds (single core, Intel(R) Core(TM) i9-9900K CPU @ 3.60GHz).
• Code

https://jacquesh.github.io/post/fortunes-algorithm/

sh build.sh

./A input.txt

n : # of points

(n)
(x1) (y1)
(x2) (y2)
...
(xn) (yn)

• point must be distinct.
• n != 0

Reading main.cpp rendering part can be helpful to know about function format.

• std::vector<pdd> input
  • Inputs. Order can (and will) be changed, so user should pay attention about this.
  • Additionally, input will sorted by (y, x) order.
• std::vector<pdd> vertex
  • Vertex is locations of Voronoi Diagram's intersection points. It can contain same points, and the degree of each point is 3.
  • This code doesn't compress same points. If you want, then you should implement it.
• std::vector<pii> edge
  • for(pii c : edge), Voronoi Diagram contains line from vertex[c.first] to vertex[c.second].
  • Voronoi can contain rays or straight line. In this case, rays are depicted as {-1, (point index)} or {(point index), -1}, and straight line are depicted as {-1, -1}. A direction of each line can calculate using area array.
• std::vector<pii> area
  • Let (a, b) := i-th element of array area, and (u, v) := i-th element of array edge.
  • Then, Point input[a] is located CCW of an u->v line (or ray, or straight line), and point input[b] is located CW of an u->v line.
  • u->v line is a subset of perpendicular bisector of line segment from input[a] to input[b].
  • Straight line {a, b}, {-1, -1} through midpoint of input[a] and input[b].

• Mouse whill operates to change scale.
• Mouse drag operates to move screen.

Feel free to ask questions.

And sorry for my poor English.