math = math == nil and {} or math;

math.pi = math.pi == nil and 3.14159265358979 or math.pi;

---clamp
---@param v number @number
---@param Min number @min
---@param Max number @max
---@return number    @clamp v between Min and Max
function math.clamp(v, Min, Max)
	local min = math.min(Min, Max)
	local max = math.max(Min, Max)
	if v < min then return min end
	if v > max then return max end
	return v
end

--- 随机bool变量
function math.randBool() return math.pop() > 0.5; end

---clamp
---@param a number          @First number to compare
---@param b number          @Second number to compare
---@param Tolerance number  @Maximum allowed difference for considering them as 'nearly equal'
---@return boolean          @true if a and b are nearly equal
function math.isNearlyEqual(a, b, Tolerance)
	if Tolerance == nil then Tolerance = 0.01 end
	return math.abs(a - b) <= Tolerance;
end

--- 一个存放随机数的列表
math.RandomList = {};

function math.init(InCount)
	for i = 1, InCount do table.insert(math.RandomList, math.random()); end
end

function math.pop()
	local val = math.RandomList[1]
	if val == nil then
		math.init(100);
		return math.pop();
	end
	table.remove(math.RandomList, 1);
	return val;
end

--- 在给定圆内随机生成一个给定半径的圆，返回圆的中心点
---@param Center FVector 给定圆
---@param Radius float 给定圆的半径
---@param MinRadius float 目标生成圆的半径圆的半径
function math.randomCircleInCircle(Center, Radius, MinRadius)
	local TargetRadius = Radius - MinRadius;
	if TargetRadius < 0 then return nil; end
	if TargetRadius == 0 then return Center; end
	
	local X = Center.X + (math.randBool() and 1 or -1) * math.pop() * TargetRadius;
	local Y = Center.Y + (math.randBool() and 1 or -1) * math.pop() * TargetRadius;
	
    local ResCenter = {};
	local ANum = math.sqrt((X - Center.X) ^ 2 + (Y - Center.Y) ^ 2)
	if ANum > TargetRadius then
		ResCenter = { X = Center.X - TargetRadius + ANum, Y = Center.Y - TargetRadius + ANum, Z = Center.Z, };
	end
    ResCenter = {X = X, Y = Y, Z = Center.Z, };
    -- 检查一下距离
    local Dis = math.sqrt((ResCenter.X - Center.X) ^ 2 + (ResCenter.Y - Center.Y) ^ 2 + (Center.Z and (ResCenter.Z - Center.Z) ^ 2 or 0))
    if Dis > TargetRadius then return math.randomCircleInCircle(Center, Radius, MinRadius); end
    return ResCenter;
end

---@param c FVector
---@param R float
---@param r float
function math.randCircle(c, R, r)
    local x = math.pop() * 2 * (R - r) + (c.X - (R - r));
    local a = math.pop() * math.pi;
    local p = math.getCirclePoint(c, math.abs(x), {X = x, Y = c.Y, }, a);
    return { X = p.X, Y = p.Y, Z = c.Z, };
end

--- 获取圆上一点与圆心连接的线形成 θ 角度的另一个点（逆时针）
---@param o FVector2D 圆点所在坐标
---@param r float 圆的半径
---@param p FVector2D 圆上的一点
---@param t float 跟 @p 到 @o 形成夹角为 t 的线，弧度值
function math.getCirclePoint(o, r, p, t)
    local angle = math.atan((p.Y - o.Y) / (p.X - o.X)) + t
    return { X = o.X + r * math.cos(angle), Y = o.Y + r * math.sin(angle), };
end