Math = math

Math.E = 2.718281828459045 -- 自然数
Math.LN2 = 0.6931471805599453 -- 2的自然对数
Math.LN10 = 2.302585092994046 -- 10的自然对数
Math.LOG2E = 1.4426950408889634 -- log 2 为底的自然数
Math.LOG10E = 0.4342944819032518 -- log 10 为底的自然数
Math.PI = 3.141592653589793 -- π
Math.HALF_PI = 1.57079632679489661923 -- 1/2 π
Math.SQRT1_2 = 0.7071067811865476 -- 1/2的平方根
Math.SQRT2 = 1.4142135623730951 -- 2的平方根
-- p, q is on the same of line 1 
function Math.isSame(line1, p, q)
	local dx = line1.endPoint.x - line1.startPoint.x;
	local dy = line1.endPoint.y - line1.startPoint.y;
	
	local dx1 = p.x - line1.startPoint.x;
	local dy1 = p.y - line1.startPoint.y;
	local dx2 = q.x - line1.endPoint.x;
	local dy2 = q.y - line1.endPoint.y;
	
	
	return (dx*dy1-dy*dx1)*(dx*dy2-dy*dx2) > 0;
end

-- 2 line segments (s1, s2) are intersect? 
function Math.isIntersect(line1, line2)
	local b1 = Math.isSame(line1, line2.startPoint, line2.endPoint);
	local b2 = Math.isSame(line2, line1.startPoint, line1.endPoint);
	
	return not b1 and not b2;
end

function Math.round(num)
    return math.floor(num + 0.5)
end

function Math.angle2Radian(angle)
	return angle*math.pi/180
end

function Math.radian2Angle(radian)
	return radian/math.pi*180
end

-- 从球面坐标系(半径，经度，纬度)转换到笛卡尔坐标系(XYZ)
-- 半径，离原点的距离，一般是一个正数
-- 经度，0~2PI，0代表正前方，PI代表正后方
-- 纬度，HALF_PI代表水平位置，+PI代表底，0代表顶
function Math.SphericalToCartesian(sphericalPos)
	return {
		x = sphericalPos.x * math.cos(sphericalPos.y) * math.sin(sphericalPos.z);
		z = sphericalPos.x * math.sin(sphericalPos.y) * math.sin(sphericalPos.z);
		y = sphericalPos.x * math.cos(sphericalPos.z);
	}
end

-- 从笛卡尔坐标系(XYZ)转换到球面坐标系(半径，经度，纬度)
function Math.CartesianToSpherical(cartesianPos)
	local r = math.sqrt(cartesianPos.x * cartesianPos.x + cartesianPos.y * cartesianPos.y + cartesianPos.z * cartesianPos.z)
	local lon = math.atan2(cartesianPos.z, cartesianPos.x)
	local lat = math.acos(cartesianPos.y / r)
	return cc.vec3(r, lon, lat)
end