local point1 = {
	['x'] = -1,
	['y'] = 0,
}

local point2= {
	['x'] = -1,
	['y'] = 1,
}

-- 獲取斜截式直線（垂直x的直線不適用斜截式，因為斜率無限大）
local GetKB = function(p1, p2)
	if p1.x == p2.x then return end
	local k, b
	k = (p2.y - p1.y)/(p2.x - p1.x)
	b = p1.y - (p1.x * (p2.y - p1.y) / (p2.x - p1.x))
	if p1.y == p2.y then k = 0 end
	return k, b
end

-- 獲取以P1為圓心，r為半徑的圓與p1 ,p2組成直線的交點
local GetPoints = function(p1, p2, r)
	if p1.x == p2.x and p1.y == p2.y then return end --傳入兩個相同的點求不了
	local x1, y1, x2, y2
	local m, n = p1.x, p1.y -- 圓心座標m, n
	if p1.x ~= p2.x then
		local k, b = GetKB(p1, p2)
		local A, B, C -- 轉換一元二次方程Ax^2 + Bx + C = 0
		A = 1 + k * k
		B = 2 * k * (b - n) - 2 * m
		C = m * m + (b - n) * (b - n) - r * r
		x1 = (-B + math.sqrt(math.pow(B, 2) - 4 * A * C)) / (2 * A)
		y1 = k * x1 + b
		x2 = (-B - math.sqrt(math.pow(B, 2) - 4 * A * C)) / (2 * A)
		y2 = k * x2 + b
	else
		x1 = m
		x2 = m
		y1 = n + r
		y2 = n - r
	end
	local point1 , point2 = {}, {}
	point1.x, point1.y= x1, y1
	point2.x, point2.y= x2, y2
	print("x1:", x1)
	print("y1:", y1)
	print("x2:", x2)
	print("y2:", y2)
	return point1, point2
end

GetPoints(point1, point2, 1)