The Sierpinski Triangle is a famous fractal named after the mathematician who discovered it. It is made up of nested triangles that get smaller and smaller. If you were to zoom in, you would see the same image (though it may be translated) and you could zoom forever and never find the end. So, how do you create the Sierpinski Triangle in AS3? First you have to know how to do recursion. Recursion is...

In the first post on A*, we explored the theory behind A*. Then we took A-star and put it into code. Now we will look at different heuristics for A* and how they affect the path. The Manhattan Method This is the heuristic function we used in our implementation of A*. The Manhattan method will get you to the end cell in the least steps, but it doesn't always guarantee the shortest path. It will usually give the...

The Separation of Axis Theorem(SAT) is a technique to test whether two convex polygons are colliding. The SAT theorem: "given two convex shapes, there exists a line onto which their projections will be separate if and only if they are not intersecting." The line where the shapes have disjoint projections is called the separating axis. A separating line is the line that can be drawn between the two shapes,...

In yesterday's post on the basics of A star, we explored the theory behind A*. Today we will take that theory and put it into code. Because A-star uses a grid made up of cells, we need some classes to store that data. First the cell class: [as3] package com.rocketmandevelopment.grid.cells { import flash.display.Graphics; public class Cell { public var f:Number = 0; public var g:Number = 0; public var...

Ray casting is a technique usually used in 3D worlds (often for rendering). Ray casting is exactly what it implies a ray is cast from a start point until it hits something (or a max length, so the computer doesn't die). Ray casting in 2D is great for collision detections, especially fast-moving objects (bullets). In this post, we will learn the basics of ray casting in 2D, then we will apply it to bullets in a...

A* (A-star) is an algorithm used for pathfinding. Pathfinding is where a computer computes the shortest (or best) path from a start point to an end point through a grid or nodes. We will be using a grid to find a path. The green cell is the start point and the red cell is the end point. The computer must find the shortest route from start to finish without going through the walls. We are using a grid because...

A* (A-star) is an algorithm used for pathfinding. Pathfinding is where a computer computes the shortest (or best) path from a start point to an end point through a grid or nodes. We will be using a grid to find a path. The green cell is the start point and the red cell is the end point. The computer must find the shortest route from start to finish without going through the walls. We are using a grid because...