💾 Archived View for callistix.srht.site › projects › vshmup › pages › 003_mathconsiderations.gmi captured on 2024-06-16 at 12:16:00. Gemini links have been rewritten to link to archived content

View Raw

More Information

⬅️ Previous capture (2024-03-21)

-=-=-=-=-=-=-

3. Math considerations

Math road to nowhere

I was trying to figure out the maths behind keeping track of speed and direction of a shot fired in an arbitrary direction. The shot would be fired by an enemy into the direction of the center of the player ship. I though I might go about it like this:

If we think of the line between enemy and player as the long side of a triangle, and the x and y distances as the short sides, we could try to apply trigonometry to find the angle the shot was fired at.

The math would look like this:

γ = asin( (sin(β) / b) * y_dist )

The only unknown here is `b`, which is the long side of the triangle aka the distance between enemy and player. But we can calculate it like this:

b = sqrt(x_dist^2 + y_dist^2 - 2 * x_dist * y_dist * cos(β))

Combining the two formulas we get:

γ = asin( (sin(β) / (sqrt(x_dist^2 + y_dist^2 - 2 * x_dist * y_dist * cos(β)))) * y_dist)

That unfortunately looks computationally expensive, let's see if we can simplify it now that we know that `β = PI/2` (or 90 degrees):

b = sqrt(x_dist^2 + y_dist^2 - 2 * x_dist * y_dist * cos(pi/2))
γ = asin(y_dist / b)

And combined:

γ = asin(y_dist / (sqrt(x_dist^2 + y_dist^2 - 2 * x_dist * y_dist * cos(pi/2))))

That is still way to computationally expensive and overkill for our purpose, let's think about something way simpler.

Simpler approach

Thinking about this a little more I could probably just do this:

This should result in the same movement, but with almost no effort. Some pseudo code:

speed = 0.05

bullet_x = enemy.x
bullet_y = enemy.y

dist_x = enemy.x - player.x
dist_y = enemy.y - player.y

while true do
  bullet.x = bullet.x + dist_x * speed
  bullet.y = bullet.y + dist_y * speed
end

That should work in theory, will test this soon.

⬅ 2. The initial status of the game

⬆ A vertical shoot'em'up game in Lua with LÖVE

🏠 callistix Gemini capsule

Created: 25/Jan/2024

Modified: 5/Feb/2024