How to do a Ray/Direction 2D system?

Question

First of all, I'm sorry if my english isn't that great because I'm brazilian, so I'll try to describe my question decently.

Well, I'm developing a 2D tile-based game. Within the entities, I'm making a Projectile class. For now, the Projectile can move north/south/west/east, but I need to make it move to any direction. I've searched a bit but haven't found any good tutorials or examples about Ray 2D (only found about lighting ray-based).

For example:

x        
 \           x
  \         /
   \       /
    f     f

[x = projectile start position, f = projectile end position]

Supposing the projectile is consisted of X and Y (the width and height doesn't matter) and will move every tick, how can I achieve this?

Answer 1

I have no experience with lwjgl.

However, it looks like a question of math to me. So if you know the distance and angle of the 'trajectory' you can convert from polar coordinates (distance, angle) to cartesian coordinates (x, y).

The conversion is simple: x = distance * cos(angle) and y = distance * sin(angle). Then you simply need to add the x and y of the start coordinates.

I recommend to play around with examples of processing to get a feeling for a solution in lwjgl.

As a starter for processing you can use this snippet:

//start coordinates
float startx;
float starty;

//radius
float r;
//angle
float theta;


void setup() {
    size(640, 360);
    background(0);

   // Initialize all values
   startx = width/2;
   starty = height/2;
   r = random(startx);
   theta = -0.5;
}

void draw() {
    // Translate the origin point to the center of the screen
    translate(startx, starty);

   // Convert polar to cartesian
   float x = r * cos(theta);
   float y = r * sin(theta);

   // Draw the ellipse at the cartesian coordinate
   ellipseMode(CENTER);
   fill(200);
   ellipse(x, y, 12, 12);

   color c = #FFCC00;
   stroke(c);
   line(0,0,x,y);
}

Answer 2

Assuming you're asking how to move a point a fixed amount each frame, that is simple: The projectile already has an X and Y (its position), I suggest creating another X and Y for its direction/velocity then on each frame add the velocity to the position (Position += velocity). Because you are adding to the current position the direction/velocity is local to that object, for instance, if you wanted to right simply make the direction's/velocity's X positive.

I do not think using rays for simply moving is a very efficient method unless you are going to implement collisions with the tiles (if so the link will help with that) - you will need to store the direction anyway.

I suggest looking up about vectors (basically an X and Y as a class of useful functions). They are extremely useful for storing anything with coordinates such as positions and directions.
Here is a tutorial I followed when I wanted to learn about rays, its a great introduction into vectors and the general math side of programming.