如何从角度和距离计算点？

Question

I searched and implemented things from this forum, it doesn't come out right. What I'm trying to achieve is to calculate a spawnPoint for player bullets relative to his position and rotation .

The spawnPoint should be and his X + his width (the player is set to point to the right by default) and y + height/2 (to spawn from his center on the Y axis).

This is what I got from this forum:

this.bulletSpawn.x = (float)(this.position.x + this.width/2 + this.width * Math.cos(rotation));
this.bulletSpawn.y = (float)(this.position.y + this.height/2 + this.height/2 * Math.sin(rotation));

The rotation is in Radians. The this is the Player class.

Images showing what I expect to happen:

• Original Position
• Expected Behaviour

The red dot is the spawnPoint I'm trying to calculate knowing the player position and rotation . The player Sprite is what rotates, and it rotates related to his center x and y, which is done with a lib, i do not have these variables. The entire arrow would be the player , the arrow direction is where the player is pointing at, and the red dot would be the bulletSpawn point (or the expected one)

Using the code I posted, the bullets seem to be spawning from somewhere else. Even at the beggining they have an offset and when I rotate the player the spawnPoint seems to be relative to a different origin than what I'm expecting.

This is the bullet position code:

position.x = holder.bulletSpawn.x - (float)(this.width/2 * holder.rotation);
position.y = holder.bulletSpawn.y - (float)(this.height/2 * holder.rotation);

This is inside the Bullet class. The position variable is a Vector2 of bullet , and holder is the player instance. This code is merely to give an offset for the bullet to spawn at the center of its own size

I added some fixes related to the comments, but the bullets still have a tiny offset that looks wrong at certain angles. Basically the distance i want to get is the width of the player, and his center y which is height/2.

Answer 1

Let's initial position is X0, Y0 , rotation is about center point CX, CY , and rotation angle is Theta . So new position after rotation is:

 NX = CX + (X0-CX) * Cos(Theta) - (Y0-CY) * Sin(Theta)
 NY = CY + (X0-CX) * Sin(Theta) + (Y0-CY) * Cos(Theta)

This equations describe affine transformation of rotation of arbitrary point about center point, and affine matrix is combination of translation, rotation, and back translation matrices.

About center CX, CY - you wrote

it rotates related to his x and y origin at his bottom left

About initial point coordinate - for bullet it seems to be

X + Width, Y + Height/2

Answer 2

Swift extension:

extension CGSize {
    static func offsetFrom(angle:CGFloat, distance:CGFloat) -> CGSize {
        let rad = angle * CGFloat.pi / 180
        return CGSize(width: sin(rad) * distance, height: cos(rad) * distance)
    }
}