How to make a projectile align correctly with the entity that shot it

Question

I'm developing a 2D game. In the game, all entities can rotate 360 degrees. Each entity holds an angle value, and every frame it is drawn rotated around it's center by it's current angle value. For example:

An entity can 'shoot' another entity, a projectile. The Projectile is instantiated with a position and an angle. The position is calculated like so:

radius = entity.width / 2
angle = entity.angle
projectileX = entity.centerX + cos(angle) * radius
projectileY = entity.centerY + sin(angle) * radius

Example positions this calculation gives:

The angle the Projectile is instantiated with is the angle of the entity creating it. So if the entity's current angle value was 45, the angle of the new Projectile is going to be 45.

All of this creates a problem. I will demonstrate the steps leading to this problem:

1- An entity decides to shoot a Projectile. It's position is calculated like shown above.

2- A new Projectile is added to the game. It is instantiated with the position calculated in the previous step and with the angle of the entity instantiating it, for this example 45.

3- Every frame, each entity is drawn rotated around it's center by it's current angle value.

The angle of the new Projectile is 45, so it is drawn rotated around it's center by 45 degrees.

As you can see: after the rotation, the Projectile is no longer aligned correctly with the entity that created it. They are both rotated by the same angle, but the Projectile isn't 'pointing from the center' of the entity. It seems like it 'moved' a little to the side.

To clarify:

My question: how can I make the Projectile align correctly with the entity that created it? How can I make it still 'point from the middle' of the entity that created it, and not mess this up when rotating it around it's center?

Answer 1

Rather than rotating the projectile about its own centre, then translating it to the end of the cannon, you could translate it first and then rotate the projectile using the origin of the tank (the tank's centre, in this case) by the tank's rotation.

Here is how to rotate a point around another point in c++. (C# version)

Following that:

projectile.position = tank.position + cannonOffset;
projectile.position = rotatePoint(origin: tank.position,
                                  point: projectile.position,
                                  angle: tank.rotation);
projectile.rotation = tank.rotation;

Part of the reason for doing it this way is that you can make cannonOffset any relative position to the source entity. So if there is a gun on the front side (1,-1 instead of 2,0), this will still work.

Answer 2

I would instantiate the Projectile at the (x,y) location of the Entity and then move it in the direction of the Entity by radius distance. In code, that would go:

projectileX = entity.x + cos(entity.angle) * radius;
projectileY = entity.y + sin(entity.angle) * radius;

Then add your projectile to the game world and send it off!