Raycasting explained

Raycasting can be an extremely useful tool in computer games. There is a lot of confusion on what raycasting really is and how it can be used. I’ll try to explain some it in simple terms and give some simple examples.

Raycasting - as the name suggests involves a ray – but what exactly is a ray?

A ray is part of a line which is finite in one direction, but infinite in the other. It can be defined by two points, the initial point, A, and one other, B.

Source: Wikipedia

In Farseer Physics Engine we define a ray as two vectors; start and end. We can for obvious reasons not have an infinite length ray, we have to have some kind of boundary where the ray stops. This means that rays essentially become lines and then we simply use those lines to test for collisions with other stuff like other lines, AABB or geometries.

Collision testing

There are 4 test cases that can be performed:

  1. Point
  2. Line
  3. AABB
  4. Geometry

The great thing about all those (except number 1) is that they can be reduced to simple line vs. line tests. An AABB is made up of 4 lines and a geometry is made of N (where N > 2) lines. With this in mind we just have to know how to test two lines against each other.

This is done simply by using a linear equation from basic algebra:

d24ebc87176b242c935535a363c5fc10

Using this equation we can create a line. m is the amount that the y-value grows or shrinks with each time x increases by 1. b is point on which the line crosses the y-axis. With this knowledge we can draw a line like this:

OneLine

It has the equation: y = 2*x+1

Now that we know how to create a line, we need a second one to test against:

TwoLines

This line has the equation y = –1*x+1. From what we gathered earlier, b was the point where the line crosses the y-axis. Since both linear equations has a b value of 1, they must be intersecting each other there at (0, 1).

To check for intersections, we take the two equations and simply does an equality check between them and input the result (the value of x) into one of our equations:

image

So our intersection point is at (0,1). Exactly how this is done in code is a little more complicated. In Farseer Physics Engine we implemented line intersection like described here: Intersection Point Of Two Lines

Usage

Now we know that raycasting operates on lines, but how can this be applied to games? Here is a list of a few examples:

  • Collision detection
  • Distance calculation
  • Jumping
  • Lasers
  • Field of view
  • Lightning
  • Suspension
  • Many more…

You can use rays for collision detection and check the distance between the two objects. You can also use it for smooth jumping on to platforms and even car suspension. Another common usage is finding the field of view. The only limit is your imagination.

Ray casts are cheap, but they should not be used for everything. Some physics engines incorporate rays into their broad phase collider to speed up permanent rays. This will soon be implemented into Farseer Physics Engine too.

Comments

Post a Comment

Popular posts from this blog

.NET Compression Libraries Benchmark

Image
I often find myself needing a compression library in a software development project, and after a few tests with disappointing results I usually fall back to spawning 7Zip as an external process. This time however, the application specification prohibits any data written to disk, which 7Zip needs to do in order to work correctly. I needed to do everything in memory, and so I had to test some of the C# libraries available for compression as well as the different compression algorithms. Here is a full list of the tested libraries: .NET DeflateStream ICSharpCode SharpZip Zlib.NET DotNetZip Managed LZMA LZMA SDK QuickLZ    Compression 101 Before I get to the results of the benchmark, I think it is important to understand the different archive formats and compression algorithms in order to compare the results with other benchmarks/and or tests. Lets get to it! A compression algorithm can be compared to a small machine that takes in some data, do some math on it and...
Read more

Reducing the size of self-contained .NET Core applications

Just for note keeping, I've written down some methods of reducing the size of a .NET Core application. I thought others could use it as well, so here you go. Original Size First off, let's see how much disk space a self-contained 'hello world' application takes up. > dotnet new console > dotnet publish -r win-x86 -c release Size: 53.9 MB -  yuck! Trimming Microsoft has built a tool that finds unused assemblies and removes them from the distribution package. This is much needed since the 'netcoreapp2.0' profile is basically .NET Framework all over again, and it contains a truckload of assemblies our little 'hello world' application don't use. > dotnet new console > dotnet add package Microsoft.Packaging.Tools.Trimming -v 1.1.0-preview1-25818-01 > dotnet publish -r win-x86 -c release /p:TrimUnusedDependencies=true Size: 15.8 MB Much better! Although, we have only removed unused assemblies - what about unused...
Read more

Convex polygon based collision detection

Image
A lot of people have asked me: Why use a convex polygon only engine like Box2D? In this post I will provide some info on why convex polygons is the optimal polygon type to use. What does convex mean? Convex polygons needs to satisfy the following requirements: All internal angles must be below 180 degrees Every line segment between two vertices can be contained fully inside or at the edge the polygon A non-convex polygon is called a concave polygon and it must have an internal angle measuring greater than 180 degrees. As you might have thought about yourself; concave polygons can be quite handy. Convex-only engines can’t represent a simple player polygon like Pac-Man . Why use convex-only? There are really only one big juicy reason: performance Physics engines are able to take quite a few shortcuts and use cheap algorithms to determine the closest vertex, shortest distance and a lot more. An algorithm like Separating Axis Theorem and the Gilbert – Johnson –...
Read more