LÖVE: Line and Circle Collision

main.lua

circle = {x=400,y=300,r=100}
point = { x = 100, y = 100 }

col = false

function love.draw()
  if cols then
    love.graphics.print("Collision",0,0)
    love.graphics.setColor(255,0,0)
    for _,col in pairs(cols) do
      love.graphics.circle("line",col.x,col.y,5)
    end
  else
    love.graphics.setColor(255,255,255)
  end
  love.graphics.circle("line",circle.x,circle.y,circle.r)
  love.graphics.line(mx,my,point.x,point.y)
  love.graphics.line(circle.x,circle.y,point.x,point.y)
end

function love.update(dt)
  mx,my = love.mouse.getPosition()
  mx,my = mx,my
  cols = collision_line_and_circle(point,{x=mx,y=my},circle)
end

function love.mousepressed(x,y,button)
  if button == "l" then
    point.x = x
    point.y = y
  elseif button == "r" then
    circle.x = x
    circle.y = y
  elseif button == "wd" then
    circle.r = circle.r+10
  elseif button == "wu" then
    circle.r = circle.r-10
  end
end

function collision_line_and_circle(point1,point2,circle)
  local v1 = vector.new(point1,point2)
  local v2 = vector.new(point1,circle)
  local v1_mag = vector.mag(v1)
  local v2_mag = vector.mag(v2)
  local alpha = math.acos( vector.dot(v1,v2) / ( v1_mag * v2_mag ) )
  local dist_o = math.sin(alpha) * v2_mag
  if dist_o <= circle.r then
    local mag_a_r_left = dist_o / math.tan(alpha)
    local mag_a_r_right = circle.r * math.sin( math.acos( dist_o / circle.r ) )

    local mag_a_r_close = mag_a_r_left - mag_a_r_right
    local mag_a_r_far = mag_a_r_left + mag_a_r_right

    return {
      {
        x =  point1.x - v1.x / v1_mag * mag_a_r_close,
        y =  point1.y - v1.y / v1_mag * mag_a_r_close,
      },
      {
        x =  point1.x - v1.x / v1_mag * mag_a_r_far,
        y =  point1.y - v1.y / v1_mag * mag_a_r_far,
      },
    }

  end
end

function distance(point1,point2)
  return math.sqrt((point1.x - point2.x)^2 + (point1.y - point2.y)^2)
end

vector = {}

function vector.dot(vector1,vector2)
  return vector1.x*vector2.x + vector1.y*vector2.y
end

function vector.mag(vector)
  return math.sqrt(vector.x^2 + vector.y^2)
end

function vector.new(point1,point2)
  local v = {}
  v.x = point1.x - point2.x
  v.y = point1.y - point2.y
  return v
end