Fortune's algorithm
So, imagine you have a bunch of points on a piece of paper, like toys scattered around your room. Now imagine you want to draw a nice curve that goes through all these points, like a string connecting all the toys.
Fortune's algorithm is like a magic way to draw that curve without lifting your pencil off the paper. It's like drawing with a string that can stretch and bend as needed to go through all the points efficiently.
To do this, the algorithm splits the paper into separate areas based on the points' position. Then it uses a tree structure (kind of like the branches of a tree) to keep track of which parts of the curve have been drawn and where there are still gaps. It also uses some special calculations to avoid crossing over itself or going through any of the points.
Then, as the algorithm progresses, it adds new points and curves to the tree, connecting them together like puzzle pieces. Eventually, all the points are connected by the curve without any gaps or overlaps.
So why is this useful? Well, it's used in a lot of computer programs that rely on maps or geography. For example, it can be used to find the shortest path between two points on a map or to create a smooth border around a set of land masses. It's also used in some 3D printing and engineering applications to create precise shapes and structures.
Fortune's algorithm is like a magic way to draw that curve without lifting your pencil off the paper. It's like drawing with a string that can stretch and bend as needed to go through all the points efficiently.
To do this, the algorithm splits the paper into separate areas based on the points' position. Then it uses a tree structure (kind of like the branches of a tree) to keep track of which parts of the curve have been drawn and where there are still gaps. It also uses some special calculations to avoid crossing over itself or going through any of the points.
Then, as the algorithm progresses, it adds new points and curves to the tree, connecting them together like puzzle pieces. Eventually, all the points are connected by the curve without any gaps or overlaps.
So why is this useful? Well, it's used in a lot of computer programs that rely on maps or geography. For example, it can be used to find the shortest path between two points on a map or to create a smooth border around a set of land masses. It's also used in some 3D printing and engineering applications to create precise shapes and structures.