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  Where to learn 2D-vectors  (Read 1196 times)
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Offline Mattedatten

Senior Newbie





« Posted 2011-02-06 14:25:47 »

Hey all

I've been working on this small 2D-side scroller, after following MrJavaHelp's game tutorials on youtube.

I asked here and on another forum for how to solve my idea of a shot following the mouse-press.
I wanted to do this with angles, but I can't seem to get it right.

On the other forum where I asked, I got the answer to drop angles, and use vectors, and he linked me to R2-vectors on wikipedia, a short, non-informative text (in my view)

So, now I've been watching about 30min different youtube-videos explaining what a vector is, and I kind of get it now.

But I have no idea how to implement or use it in Java/programming.
..
So, where to find examples or tutorials or something that shows how and where to use vectors in Java-2D?
(Or, do anyone here have an personal example? Smiley )

Thanks if anyone has an answer
//M
Offline Kieran Newland

Senior Newbie





« Reply #1 - Posted 2011-02-06 15:05:34 »

I can't help you with vectors but I can with your angles problem.

The function, Math.atan2(y, x) can give you the angle of your mouse compared to the sprite. You could rotate your sprite to this angle or something similar to show that the angle is correct.

Im not sure if its the same with Java, but with flash, the angles are crooked. You need to -180 on the angle to get the real angle (its something like this anyway. Its easy enough to work out).

You should be able to get somewhere with that. I hope it works!

Kieran Newland
Offline krasse
« Reply #2 - Posted 2011-02-06 20:13:35 »

My 2D vector class:

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public class Vec2D {

   public double x;
   public double y;

   public static Vec2D ZERO = new Vec2D(0, 0);
   public static Vec2D X = new Vec2D(1, 0);
   public static Vec2D Y = new Vec2D(0, 1);

   @Override
   public String toString() {
      return "[" + x + ", " + y + "]";
   }

   public Vec2D() {
   }

   public Vec2D(Vec2D v) {
      set(v);
   }
   
   public Vec2D(double x, double y) {
      this.x = x;
      this.y = y;
   }

   public Vec2D(double... coords) {
      this.x = coords[0];
      this.y = coords[1];
   }

   public void rotate(Vec2D center, double angle) {
      double cx = center.x;
      double cy = center.y;

      double diffx = x - cx;
      double diffy = y - cy;
      x = cx + diffx * Math.cos(angle) - diffy * Math.sin(angle);
      y = cy + diffx * Math.sin(angle) + diffy * Math.cos(angle);
   }

   public Vec2D copy() {
      return new Vec2D(x, y);
   }

   // Returns a new Vec2D in the base b1 and b2 (which must be normalized
   // first)
   public static Vec2D getNewCoords(Vec2D v, Vec2D b1, Vec2D b2) {
      // Project v on both b1 and b2 to get the coordinates

      double c1 = v.dot(b1);
      double c2 = v.dot(b2);
      return new Vec2D(c1, c2);
   }

   public Vec2D crossWithZ() {
      return new Vec2D(-y, x);
   }

   // Projects this Vector to v
   public Vec2D projectCopy(Vec2D v) {
      double dot = dot(v);
      double vlength = v.length();
      return v.multCopy(dot / (vlength * vlength));
   }

   public double dot(Vec2D v) {
      return x * v.x + y * v.y;
   }

   public static Vec2D center(Vec2D v1, Vec2D v2) {
      return new Vec2D(0.5 * (v1.x + v2.x), 0.5 * (v1.y + v2.y));
   }

   public static Vec2D center(ArrayList<Vec2D> list) {
      Vec2D result = new Vec2D();
      if (list.size() > 0) {
         for (Vec2D v : list) {
            result.plus(v);
         }
         result.mult(1.0 / list.size());
      }
      return result;
   }

   public static Vec2D center(Vec2D v1, Vec2D v2, Vec2D v3) {
      return new Vec2D((v1.x + v2.x + v3.x) / 3.0, (v1.y + v2.y + v3.y) / 3.0);
   }


   public Vec2D rotateCopy(double angle) {
      Vec2D result = copy();
      result.rotate(angle);
      return result;
   }

   public Vec2D rotate(double angle) {
      double newX = x * Math.cos(angle) - y * Math.sin(angle);
      double newY = x * Math.sin(angle) + y * Math.cos(angle);
      x = newX;
      y = newY;
      return this;
   }

   public Vec2D multCopy(double val) {
      return new Vec2D(x * val, y * val);
   }

   public Vec2D mult(double val) {
      x *= val;
      y *= val;
      return this;
   }

   public Vec2D minusCopy(Vec2D v) {
      return new Vec2D(x - v.x, y - v.y);
   }

   public Vec2D plusCopy(Vec2D v) {
      return new Vec2D(x + v.x, y + v.y);
   }

   public Vec2D plus(double x, double y) {
      this.x += x;
      this.y += y;
      return this;
   }

   public Vec2D plusCopy(double x, double y) {
      return copy().plus(x, y);
   }

   public Vec2D perpendicularCopy() {
      return new Vec2D(y, -x);
   }

   public double angle(Vec2D v) {
      return Math.atan2(v.y, v.x) - Math.atan2(y, x);
      // return Math.atan2(diffy, diffx);
   }

   public static double angle(double x1, double y1, double x2, double y2) {
      return Math.atan2(y2, x2) - Math.atan2(y1, x1);
      // return Math.atan2(diffy, diffx);
   }

   public static double angle(double x, double y) {
      return Math.atan2(y, x);
   }

   public double angle() {
      return Math.atan2(y, x);
   }

   public double length() {
      return Math.sqrt(x * x + y * y);
   }

   public double sqLength() {
      return x * x + y * y;
   }

   public double getLength() {
      return Math.sqrt(x * x + y * y);
   }

   public double crossValue(Vec2D v) {
      return x * v.y - y * v.x;
   }

   public Vec2D normalizeCopy() {
      double l = Math.sqrt(x * x + y * y);
      return new Vec2D(x / l, y / l);
   }

   public Vec2D normalize() {
      double l = Math.sqrt(x * x + y * y);
      x /= l;
      y /= l;
      return this;
   }

   public static double distanceBetween(double x1, double y1, double x2,
         double y2) {
      double diffx = x1 - x2;
      double diffy = y1 - y2;
      return Math.sqrt(diffx * diffx + diffy * diffy);
   }

   public double distanceTo(Vec2D v) {
      double diffx = x - v.x;
      double diffy = y - v.y;
      return Math.sqrt(diffx * diffx + diffy * diffy);
   }

   public double distanceToSq(double tx, double ty) {
      double diffx = x - tx;
      double diffy = y - ty;
      return diffx * diffx + diffy * diffy;
   }


   public boolean within(int mx, int my, int width, double zoomx,
         double zoomy, double offsetx, double offsety) {
      int sx = (int) (zoomx * x - offsetx);
      int sy = (int) (zoomy * y - offsety);
      return (Math.abs(sx - mx) <= width && Math.abs(sy - my) <= width);
   }

   public Vec2D translate(double dx, double dy) {
      x += dx;
      y += dy;
      return this;
   }

   public Vec2D scale(double scalex, double scaley, double centerx,
         double centery) {
      double diffx = x - centerx;
      double diffy = y - centery;
      x = centerx + diffx * scalex;
      y = centery + diffy * scaley;
      return this;
   }

   public Vec2D scale(double scaleX, double scaleY) {
      return scale(scaleX, scaleY, 0.0, 0.0);
   }


   public Vec2D plus(Vec2D v) {
      x += v.x;
      y += v.y;
      return this;
   }

   public double distanceTo(double x, double y) {
      return distanceTo(new Vec2D(x, y));
   }

   public Vec2D negateCopy() {
      Vec2D result = copy();

      return result.negate();
   }

   public Vec2D negate() {
      x = -x;
      y = -y;
      return this;
   }

   public void set(Vec2D v) {
      this.x = v.x;
      this.y = v.y;
   }

   public void set(double x, double y) {
      this.x = x;
      this.y = y;
   }

   public Vec2D minus(Vec2D v) {
      x -= v.x;
      y -= v.y;
      return this;
   }



   public static double diffAngle(Vec2D v1, Vec2D v2) {
      Vec2D v1n = v1.normalizeCopy();
      Vec2D v2n = v2.normalizeCopy();

      double product = v1n.dot(v2n);

      double crossProductZ = v1n.crossValue(v2n);

      double result = Math.acos(product);

      if (crossProductZ > 0) {
         result *= -1;
      }
      return result;
   }



   public Vec2D rotateTowards(Vec2D v, double maxAngle) {
      double currentAngle = angle(v);
      // System.out.println(this + " " + currentAngle);
      if (currentAngle > maxAngle) {
         currentAngle = maxAngle;
      } else if (currentAngle < -maxAngle) {
         currentAngle = -maxAngle;
      }
      rotate(currentAngle);
      return this;
   }


}


If you want to create a vector between two points, such as the gun position and the mouse position, for animation, you can do like this:

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Vec2D gunPos = new Vec2D(gx, gy);
Vec2D mousePos = new Vec2D(mx, my);

Vec2D gunToMouseN = mousePos.minusCopy(gunPos).normalize();
// gunToMouseN is a vector of length 1

double bulletSpeed = ...;
Vec2D bulletVelocity = gunToMouseN.multCopy(bulletSpeed);

// Then, in animation where bulletPos is updated for each step
bulletPos.plus(bulletVelocity);


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Offline Mattedatten

Senior Newbie





« Reply #3 - Posted 2011-02-06 22:54:21 »

The function, Math.atan2(y, x) can give you the angle of your mouse compared to the sprite. You could rotate your sprite to this angle or something similar to show that the angle is correct.
That's what I'm trying to work with, but for some reason I can't seem to get the mathemathics right, hm, but I might have an idea to try out. (I guess what I can't see really is how to count the angle as 0,0 is top-right corner, not bottom-right. But as I said, I just got an idea what to try (if statements  Grin))



My 2D vector class:
[...]
If you want to create a vector between two points, such as the gun position and the mouse position, for animation, you can do like this:
[...]

Great, thanks .. but, I won't copy it, because that not learning  Roll Eyes
I will read the methodes that you'd use and rewrite them (Great that you have some comments in there)  Grin

Well, thanks again, both of you Smiley
Offline jezek2
« Reply #4 - Posted 2011-02-07 04:06:50 »

Check these nice articles:

Linear algebra for game developers ~ part 1
Linear algebra for game developers ~ part 2
Linear algebra for game developers ~ part 3
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