I have a little tech game I am messing around with and I can't figure out the formula to position 1 object given another objects origin.
So I have a Spaceship and a Cannon. I have the game setup to use units, so 1 unit = 16 pixels (pixel art).
Basically my cannon should be placed 0.5625 units on the X and 0 on the Y relative to the origin of the Spaceship, which is located at 0, 0 (bottom left corner).
The cannon should is independent on the angle of the spaceship, it can aim in different directions rather than being fixed to aim the way of the spaceship.
I have it constantly following the cursor, which works fine. Now when I rotate the Spaceship, obviously the origin of the Spaceship is changing in world coordinates, so my formula to place the cannon is all messed up, like so:
protected Vector2 weaponMount = new Vector2();
weaponMount.set(getBody().getPosition().x + 0.5625f, getBody()
.getPosition().y);
Obviously if I position the ship at a 90° angle, X is going to be different and the cannon would be waaaayyy off the ship. Here is a screenshot example of what I mean:
What would be the formula for this? I have tried using cos/sin but that does not work.
Any ideas?
weaponMount.set(0.5625f,0).setAngle(SpaceshipAngle).add(getBody().getPosition());
Where SpaceshipAngle is the angle of your Spaceship.
The origin of the spaceship is the point, arround which the spaceship will rotate and scale (the Texture of it). The position instead is always the lower left corner of the Texture and does not depend on the rotation.
Your problem is, that your offset does not depent on the rotation of your spaceship.
To take care about this rotation you should store a Vector2 offset, which describes your weapons offset (in your case it is a Vector2(0.5625f, 0)).
Next store a float angle describing your spaceships rotation.
Then you can rotate the offset by using: offset.setAngle(rotation).
The last thing is to set the weapons position. The code for this did not change so much:
weaponMount.set(getBody().getPosition().x + offset.x, getBody()
.getPosition().y + offset.y);
Related
I am making a 3D game in which the player can rotate their view point via the mouse to look around the environment. I firstly just did x and y rotation via vertical and horizontal movement of the mouse and z via another control. But after playing the game I realised it did not rotate correctly. NOTE: I have a global variable matrix which represents the player's angle (3x1), at 0,0,0 it seems to work correctly as up or down is a direct x axis rotation and right or left is a direct y axis rotation, but if I move my camera diagonally for example then left doesn't directly correlate to a y axis rotation anymore.
Visually on a unit circle the players viewpoint wouldn't travel the full circumference anymore and would travel in a circle that is smaller that the circumference. This is the current code (x and yRateOfRot is the ratio of how far away from the centre the cursor is in each direction between -1 and 1):
private static void changeRotation(){
angle.set(Matrix.add(angle.matrix,new double[][]{
{ROTATION_SPEED * camera.xRateOfRot()},
{ROTATION_SPEED * camera.yRateOfRot()},
{ROTATION_SPEED * camera.zRateOfRot()}}));
}
I have looked at this source http://paulbourke.net/geometry/rotate/ and understand how to rotate via an arbitrary axis which I could do but I am not sure how to correlate this into getting a ratio to find out what the x,y and z change would be for looking in a specific direction i.e. at 0,0,0 the ratio of looking up would be x:1, y:0, z:0 but then at another angle the ratios would be different as looking up no longer means only an x rotation. Any information would be appreciated, thanks!
I'm writing a OpenGL application in which there is a rectangle placed on a 3D object. The 3D object can move around and rotate and the rectangle follows these movements.
What I would like to do is to point with the mouse towards the rectangle so that a dot would appear in that point on the rectangle, and I want the point to follow it as the 3D object that "holds" the rectangle moves around.
I know how to find the intersection on a plane, and I know how to find the world coordinates of the contact point. What I need is a way to convert the world coordinates to the 2D local coordinate system of the rectangle.
For example, suppose I have the plane positioned like this in the 3D world, with a given orientation (sorry, I can't really draw properly):
The black point in the center is the origin of the plane, while the blue point is the one I would like to find. The numbers near the points are their world coordinates; in this example the Z axis "comes out" of the screen.
I would like to map the coordinates of the blue point in the local coordinate system of the plane, like this:
I know that somehow this shouldn't be hard, but I can't find a way at all. Any hints would be appreciated!
You probably already use a transformation matrix to render the rectangle. If you have the 3D position of the point, just transform it with the inverse transformation matrix and you get a 3D position in the rectangle's space. If the local system is aligned with the rectangle, one of the coordinates should always be zero and you can drop it.
I found what I needed in this post here.
Basically the solution for me is to project the point onto the x and y axis of the local coordinate system of the rectangle.
In pseudo code it's like this:
// I compute the direction that go from the origin of the rectangle to its x axis, in world coordinates, and take the norm; same thing for the y axis
var xDir = Norm(mRectangle.LocalToWorld([1, 0, 0]) - mRectangle.LocalToWorld([0, 0, 0]));
var yDir = Norm(mRectangle.LocalToWorld([0, 1, 0]) - mRectangle.LocalToWorld([0, 0, 0]));
// I compute the dot product
mLocalPosition.x = Dot(xDir, (contactPoint - mRectangle.LocalToWorld([0, 0, 0])));
mLocalPosition.y = Dot(yDir, (contactPoint - mRectangle.LocalToWorld([0, 0, 0])));
// I can now set the position of the point converting the local coordinates found to world coordinates
mPoint.SetPosition(mRectangle.LocalToWorld([mLocalPosition.x, mLocalPosition.y, 0]));
While working on Projectiles I thought that it would be a good idea to rotate the sprite as well, to make it look nicer.
I am currently using a 1-Dimensional Array, and the sprite's width and height can and will vary, so it makes it a bit more difficult for me to figure out on how to do this correctly.
I will be honest and straight out say it: I have absolutely no idea on how to do this. There have been a few searches that I have done to try to find some stuff, and there were some things out there, but the best I found was this:
DreamInCode ~ Rotating a 1-dimensional Array of Pixels
This method works fine, but only for square Sprites. I would also like to apply this for non-square (rectangular) Sprites. How could I set it up so that rectangular sprites can be rotated?
Currently, I'm attempting to make a laser, and it would look much better if it didn't only go along a vertical or horizontal axis.
You need to recalculate the coordinate points of your image (take a look here). You've to do a matrix product of every point of your sprite (x, y) for the rotation matrix, to get the new point in the space x' and y'.
You can assume that the bottom left (or the bottom up, depends on your system coordinate orientation) of your sprite is at (x,y) = (0,0)
And you should recalculate the color too (because if you have a pure red pixel surrounded by blue pixel at (x,y)=(10,5) when you rotate it can move for example to (x, y)=(8.33, 7.1) that it's not a real pixel position because pixel haven't float coordinate. So the pixel at real position (x, y)=(8, 7) will be not anymore pure red, but a red with a small percentage of blue)... but one thing for time.
It's easier than you think: you only have to copy the original rectangular sprites centered into bigger square ones with transparent background. .png files have that option and I think you may use them.
i have a fixed rectangle. When ball hits a vertex of a triangle, i calculate tangent at point of contact(rectangle vertex). Then i rotate Velocity vector to coincide with the tangent, flip the y value of velocity and rotate it back. Here is my code for top-left corner:
double c1x=rec.x-ball.getX();
double c1y=rec.y-ball.getY();
if(c1*c1+c2*c2<ball.getRadius()*ball.getRadius())
{
double angle=Math.atan2(-c1x,c1y); //angle made by tangent
Vector2D v=ball.velocity.rotate(angle); //rotate velocity vector by 'angle'
if(v.y<0.0f) //ball is already moving away from corner
return;
v.setY(-v.y); //flip y
ball.velocity=v.rotate(-angle); //rotate back
return;
}
But this code doesnot works. When ball strikes the corner it gets stuck, moves along the top edge and then falls off, not bouncing back. Am i doing it correct?
Making some guesses about your conventions, I suggest this:
double angle=Math.atan2(-c1x,-c1y);
If that doesn't work, we can do some experiments to figure out what's actually going on.
EDIT:
All right, we must build up from simpler solutions. Try these experiments:
1) Set velocity to (0,1) and verify that the ball moves straight up after the collision.
2) Set velocity to (-1,1) and verify that the ball moves up and leftward.
If those work as expected, then pick a trajectory that you would expect to behave in a normal way, such as approaching from above and to the left, then rebounding almost straight up but slightly leftward, then run it through your code but print out all the values in the collision and tell us what they are. That's at least c1x, c1y, angle, and the values of velocity initially and after each rotation.You'll probably notice where things go screwy, and if you don't we will.
I've implemented a kind of Pong where the paddles (Rectangle2D) can rotate.
To obtain more accuracy, many things are managed by Graphics2D.
The rotation too is managed by the methods rotate(...) of the previous told class.
To reach a realistic bounce, I need to know where the ball hits the paddle (only the side, not the particular point).
I've tried to define (and rotate) two Rectangle2D that represent the back and the front side of the paddle and then recognize the bounce in one of these two by the method hit(Rectangle2D r, Shape s, boolean onStroke), but it doesn't work properly.
Here is the java class Graphics2D:
http://docs.oracle.com/javase/7/docs/api/java/awt/Graphics2D.html
Have you any idea?
Assuming you have one rectangle for your paddle and know the center of rectangle and circle and the rotation of your rectangle.
Assuming a rotation of zero means, your rectangle is aligned horizontally (width > height).
Calculate the difference vector (center of circle) - (center of rectangle)
Get the angle of that vector and subtract the rotation of your rectangle (angle of vector is Math.atan2(y, x))
The resulting value a tells you the relative direction of your circle
Make sure a lies between 0 and 2*pi
q = Math.atan2(height of rectangle, width of rectangle)
If a is between q and pi-q, your circle has hit on the front long (upper) side.
If a is lower than q or bigger than 2*pi-q it's on the right side.
If a is between pi-q and pi+q it's on the left side.
If a is between pi+q and 2pi-q it's hit the bottom of your rectangle