Shoot from same point of a rotating image - lua

Question

I am trying to make a basic prototype for a top down shooter in LOVE but I am having some issues getting the bullet to shoot from the same point of the image when it is rotated. This is the code I have so far which works fine as the bullet shoots from the center of the image but I want it to shoot from the right hand side of the sprite where the gun is:
function love.load()
love.graphics.setBackgroundColor(54, 172, 248)
player = love.graphics.newImage('/assets/images/player.png')
playerX = 300
playerY = 300
playerSpeed = 200
bullets = { }
bulletSpeed = 250
cursor = love.mouse.newCursor('assets/images/crosshair.png', 24, 24);
love.mouse.setCursor(cursor);
end
function love.update(dt)
-- Get mouse position to rotate player
local mouseX, mouseY = love.mouse.getPosition()
playerRotation = math.atan2(mouseY - playerY, mouseX - playerX);
-- Keyboard input to move the player
if love.keyboard.isDown('s') then
playerY = playerY + playerSpeed * dt
elseif love.keyboard.isDown('w') then
playerY = playerY - playerSpeed * dt
end
if love.keyboard.isDown('a') then
playerX = playerX - playerSpeed * dt
elseif love.keyboard.isDown('d') then
playerX = playerX + playerSpeed * dt
end
-- update all bullets position
for i, v in ipairs(bullets) do
v.x = v.x + (v.dx * dt)
v.y = v.y + (v.dy * dt)
end
end
function love.draw(dt)
-- Draw player
love.graphics.draw(player, playerX, playerY, playerRotation, 0.5, 0.5, player:getWidth() / 2, player:getHeight() / 2);
-- Draw all bullets
love.graphics.setColor(128, 128, 128)
for i, v in ipairs(bullets) do
love.graphics.circle("fill", v.x, v.y, 3);
end
end
function love.mousepressed(x, y, button)
if button == 1 then
local startX = playerX;
local startY = playerY;
local mouseX = x
local mouseY = y
local angle = math.atan2((mouseY - startY), (mouseX - startX))
local bulletDx = bulletSpeed * math.cos(angle)
local bulletDy = bulletSpeed * math.sin(angle)
table.insert(bullets, {x = startX , y = startY, dx = bulletDx, dy = bulletDy})
end
end
How do I draw it from the same point of the sprite as it is rotated?

Answer 1

If I got you correctly you have an image representing your player. (playerX, playerY) is the position of your player where the center of your image is.
Atm you start your bullets at the image center.
So the starting point of your bullets is invariant to player rotation.
If you move the gun away from the player center it rotates around that point where the radius is the distance of the gun position to the player position.
For distance 1 you can refer to the unit circle
So simply multiply that with your radius so:
local gunXRotated = playerX + r * math.cos(t)
local gunYRotated = playerY + r * math.sin(t)
where t is your rotation angle and r is the Euclidean distance between player center and gun muzzle.
Then simply use the new gun coordinates as the origin of your bullets.