Implementing Vector Maths

Newbie & Debugging Questions
#1

Hello, I recently started learning Vector maths and I’m find it really interesting. But I’m struggling trying to implement them into game programming (2D), specifically Vectors that require a direction and a speed, and how I would translate it into a game. For example, say I wanted to add something like wind or velocity, I would need the speed and the direction it is going, of course speed isn’t an issue but what about the direction of the vector, how would I specify something like that within a game?

Sorry If what I’m asking is a bit vague, I’m looking for more for guidance than a page of code (though an example is always nice).
Thanks!

#2 

directionVector.normalize().multiply(speed)

Gives you a Cartesian vector.
Where directionVector is the direction you want it to go (in x, y).

If you want a polar vector converting to Cartesian, there’s some different maths for that.

#3

All a “Vector” essentially is is collection of two values: direction and speed.

Direction and Speed, viewed through another lens is just an X and Y value (coordinates). In other words, a vector is practically the same as a Point.

Now, depending on what you’re doing (physics, programming, maths, whatever) you may want to interpret the values in different ways (direction, speed, length, position etc).

Direction can be viewed as just another way of saying how the position (x and y values) should change in relation to each other (not how much they should change, speed says that).

All you need to do is know how to convert a Directional value which is usually defined by an “angle” in degrees or radians. How you do that is a simple dip into the basics of trigonometry. Java like any programming I’ve ever familiarized myself with have already code made to deal with most basic Maths thingies such as basic trigonometry. (In Java the ‘Math’ class)

For example, taking a vector with Direction 45 (north-east, 0 degrees pointing conventionally directly to the right) and Speed 100 we can with simple cosine and sine get that the resulting x and y coordinated would be just about x=71, y=71. If we change the Direction to 90 degrees we’d get x = 0 and y = 100.

You might wonder how a simple point can be viewed as a Vector? Quite simple really, the start of the vector is at position (0,0) and the end at the point (x,y). With that information you can get the length (speed), direction, whatever you need.

#4

As a non-mathy person, I found this to be extremely helpful.

http://blog.wolfire.com/2009/07/linear-algebra-for-game-developers-part-1/

It also has nice pictures, so easily distracted persons like myself don’t get lost.

#5

Nice blog post, explains it a lot better than me.

#6

Thanks a lot guys, particularly jonjava, that explanation really helped, and that blog post looks awesome as well.