Skip to content

Commit

Permalink
Added new description.
Browse files Browse the repository at this point in the history
  • Loading branch information
Yatoom committed Apr 8, 2021
1 parent b6c9a0c commit c9e92f9
Showing 1 changed file with 14 additions and 4 deletions.
18 changes: 14 additions & 4 deletions docs/index.rst
Original file line number Diff line number Diff line change
Expand Up @@ -9,10 +9,20 @@ Foronoi
Foronoi is a Python implementation of the Fortune's algorithm based on the description of "Computational Geometry:
Algorithms and Applications" by de Berg et al.

This algorithm is a sweep line algorithm that scans top down over the
cell points and traces out the lines via breakpoints in between parabola's (arcs). Once a new point is inserted, a check
is done to see if it will converge with the lines on the left or right. If that's the case, it will insert a so-called
circle-event which causes a new vertex (i.e. a cross-way between edges) to be created in the middle of the circle.
This algorithm is a sweep line algorithm that scans top down over the cell points. Every time a new cell point is
scanned, a corresponding parabola (arc) is added. The intersections of this arc with other arcs are so-called
"breakpoints". These breakpoints trace out the borders between two cell points. At the same time when an arc is added,
a check is done to see if this arc will converge with the two arcs on the left or the arcs on the right. If that’s the
case, it will insert a so-called circle-event which causes a new vertex (i.e. a cross-way between edges) to be created
in the middle of the circle.

If you would like to play around with a simple example to get a better understanding, I recommend visiting
|desmos|.

.. |desmos| raw:: html

<a href="https://www.desmos.com/calculator/ejatebvup4" target="_blank">this toy example</a>


The algorithm keeps track of the status (everything above the line is handled) in a so-called status-structure. This
status-structure is a balanced binary search tree that keeps track of the positions of the arcs (in its leaf nodes) and
Expand Down

0 comments on commit c9e92f9

Please sign in to comment.