yzyCli/u3d/Lua/utils/GameMath.lua

GameMath = GameMath or {}
local GameMath = GameMath
local math = math
function GameMath.IsPointNear(p1x, p1y, p2x, p2y, near_val)
	near_val = near_val or 1.0

	local x_step = p1x - p2x
	local y_step = p1y - p2y
	local val = x_step*x_step + y_step*y_step
	return val <= near_val*near_val
end

--检查两个点是否在x或y方向上接近
--用来判断p2是否在距离p1
function GameMath.IsPointNearRect(p1x, p1y, p2x, p2y, near_val)
	if math.abs(p1x - p2x) > near_val then
		return false
	end
	if math.abs(p1y - p2y) > near_val then
		return false
	end
	return true
end

function GameMath.IsPointNearAbs(p1, p2, val)
	val = val or 1
	return (math.abs(p1.x - p2.x) <= val) and (math.abs(p1.y - p2.y) <= val)
end

function GameMath.Round(x)
	local val, pt = math.modf(x)
	if pt > 0.5 then
		val = val + 1
	end

	return val
end

--检测某点是否处于矩形内
function GameMath.IsInRect(px, py, rect_x, rect_y, rect_width, rect_height)
	if px < rect_x - rect_width / 2 or px >= rect_x + rect_width / 2
		or py < rect_y - rect_height / 2 or py >= rect_y + rect_height / 2 then
		return false
	end
	return true
end


--检测某点是否处于矩形内
function GameMath.HitRectTest(px, py, rect_x, rect_y, rect_width, rect_height)
	if px < rect_x or px >= rect_x + rect_width 
		or py < rect_y or py >= rect_y + rect_height then
		return false
	end
	return true
end

--检测某点o是否a,b,c,d四个点组成的菱形内
function GameMath.inDiamond(o, a, b, c, d)
	local l1 = co.Vector2(a.x - o.x,a.y - o.y)
	local l2 = co.Vector2(b.x - o.x,b.y - o.y)
	local l3 = co.Vector2(c.x - o.x,c.y - o.y)
	local l4 = co.Vector2(d.x - o.x,d.y - o.y)
	l1:normalise()
	l2:normalise()
	l3:normalise()
	l4:normalise()
	local total_degree = 0
	total_degree = total_degree + math.acos(l2:dotProduct(l1))
	total_degree = total_degree + math.acos(l3:dotProduct(l2))
	total_degree = total_degree + math.acos(l4:dotProduct(l3))
	total_degree = total_degree + math.acos(l1:dotProduct(l4))
	if math.abs(total_degree / 2 - math.pi) <= 0.001 then
		return true
	end
	return false
end

--[[
	求距离公式
	@param need_sqrt 是否需要开方运算（不开方可以减少不必要的运算）
	@x_mult,y_mult   距离倍率，小于1，两点距离扩大x_mult,y_mult倍 ，大于1，距离缩小x_mult,y_mult倍
]]--
function GameMath.GetDistance(p1x, p1y, p2x, p2y, need_sqrt,x_mult,y_mult)
	local x_step_mult = x_mult or 1
	local y_step_mult = y_mult or 1

	local x_step = p1x - p2x
	local y_step = p1y - p2y
	local val = x_step*x_step*x_step_mult + y_step*y_step*y_step_mult
	
	if need_sqrt then
		return math.pow(val,0.5)
	end
	
	return val
end

--[[
	求距离公式
	@param need_sqrt 是否需要开方运算（不开方可以减少不必要的运算）
	@x_mult,y_mult   距离倍率，小于1，两点距离扩大x_mult,y_mult倍 ，大于1，距离缩小x_mult,y_mult倍
]]--
function GameMath.GetDistance3D(p1x, p1y,p1z,p2x, p2y,p2z, need_sqrt,x_mult,y_mult)
	local x_step_mult = x_mult or 1
	local y_step_mult = y_mult or 1

	local x_step = p1x - p2x
	local y_step = p1y - p2y
	local val = x_step*x_step*x_step_mult + y_step*y_step*y_step_mult
	
	if need_sqrt then
		return math.pow(val,0.5)
	end
	
	return val
end

--[[
	求距离公式 椭圆
	@param need_sqrt 是否需要开方运算（不开方可以减少不必要的运算）
]]--
function GameMath.GetEllipseDistance(p1x, p1y, p2x, p2y, need_sqrt)

	local x_step = p1x - p2x
	local y_step = p1y - p2y
	local val = x_step*x_step + y_step*y_step * 4
	
	if need_sqrt then
		return math.pow(val,0.5)
	end
	
	return val
end


--把正圆的值转化成椭圆不同方向的值
function GameMath.ChangeEllipseValue(dir, value, ratio, type)
	if dir then
		ratio = ratio or 0.5
		local radian = 0
		if dir.x == 0 then
			if dir.y > 0 then
				radian = 90 / 180 * math.pi
			elseif dir.y == 0 then
				radian = 0
			elseif dir.y < 0 then
				radian = -270 / 180 * math.pi
			end
		else
			radian = math.atan(dir.y / dir.x) --先计算夹角
		end

		local func = nil
		if type == nil or type == 1 then --1为x方向较长  2 为y方向较长的椭圆
			func = math.cos
		else
			func = math.sin
		end

		--椭圆处理
		return value * ratio + math.abs(func(radian)) * value * (1 - ratio)
	else
		return value
	end
end
--[[
	取最近的点
	@param point_list 坐标数组
	@param px 参照点x坐标
	@param py 参照点y坐标
	@param get_point_func 从数组中的一个对象取出坐标，return x,y
]]--
function GameMath.GetNearestPoint(point_list,px,py,get_point_func)

	local result
	local prev_distance = -1
	
	for _, point in pairs(point_list) do
		local curr_distance
		if get_point_handler == nil then 			
			curr_distance = GameMath.GetDistance(px, py, point.x, point.y)
		else
			curr_distance = GameMath.GetDistance(px, py, get_point_func(point))			
		end

		if prev_distance == -1 or prev_distance > curr_distance then
			result = point
			prev_distance = curr_distance
		end
	end 

	return result
end


--判断点和直线的距离
function GameMath.DistancePointToLine(dir, pos, need_sqrt)	
	local x0, y0 = pos.x, pos.y	--目标点相对于直线起点的相对坐标
	local A, B = dir.y, -dir.x 	--直线方程的系数
	local d1 = (A*x0 + B*y0)     	
	local d = (d1*d1) / (A*A + B*B)		--目标点和直线的距离的平方
	
	if need_sqrt then
		d = math.pow(d, 0.5)
	end
	return d
end


--二维角度值转成二维标准向量
function GameMath.AngleToDirection(angle)
	local radian = angle / 180 * math.pi
	local dir = co.TableXY(math.cos(radian), math.sin(radian))
	co.NormaliseXYTable(dir)
	return dir
end

function GameMath.Smooth(from, to, vel, smoothTime, timeDelta)
    local omega = 2.0 / smoothTime
    local x = omega * timeDelta
    local exp = 1.0 / (1.0 + x + 0.48*x*x + 0.235*x*x*x)
    local change = from - to
    local temp = (vel + change * omega) * timeDelta
    local new_vel = (vel - temp * omega) * exp
    vel = new_vel
    return to + (change + temp) * exp, vel
end


function GameMath.Lerp(from,to,t) 
	if t > 1 then
		t = 1
	elseif t < 0 then
		t = 0
	end
	local delta = to - from
	return from + delta * t
end


function GameMath.EaseOutQuad(from,to,value)
	to = to - from
	return -to * value * (value - 2) + from
end

function GameMath.EaseInQuad(from,to,value)
	to = to - from
	return to * value * value + from
end

function GameMath.EaseInOutQuad(from,to,value)
	value = value /0.5
	to = to - from
	if (value < 1) then return to * 0.5 * value * value + from end
	value = value - 1
	return - to * 0.5 * (value * (value - 2) - 1) + from
end

function GameMath.EaseInOutQuart(from,to,value)
	value = value /0.5
	to = to - from
	if (value < 1) then return to * 0.5 * value  * value * value + from end
	value = value - 1
	return - to * 0.5 * (value * value * (value - 2) - 1) + from
end



function GameMath.EaseInOutCubic(from,to,value)
	value = value /0.5
	to = to - from
	if value < 1 then
		return to * 0.5 * value * value * value + from
	end

	value = value - 2
	return to * 0.5 * (value * value * value + 2) + from

end

--获取中心点为x, y, 半径为dist的圆上的一个点
function GameMath.GetPosByCeterPoint(x, y, dist)
	local angle = math.random(0, 360)
	local dir = GameMath.AngleToDirection(angle)
	local end_pos = co.TableXY((x + dir.x * dist), (y + dir.y * dist))
	return end_pos
end

--[[
/**
 *计算两点p1,p2连线上位置为pp的垂线上的某点，该点与连线的距离为l
 * @param p1 起点
 * @param p2 终点
 * @param pp 0到1，表示p1到p2连线上的位置
 * @param l  所求点与p1,p2连线的距离，可有正负
 */	]]	
function GameMath.GetVerticlePoint(p1, p2, pp, l)
	local offset_x = p2.x-p1.x == 0 and 1 or p2.x-p1.x
	local dir = co.Vector2((p1.y-p2.y)/offset_x, 1)
	dir:normalise()
	local p3 = p1 * (1-pp) + p2 * pp
	p3 = p3 + dir * l
	return p3
end

function GameMath.Bezier(list, t)

	local point_list = DeepCopy(list)
	local function lerp_xyz(from,to,t)
		local x = GameMath.Lerp(from.x,to.x,t)
		local y = GameMath.Lerp(from.y,to.y,t)
		local z = GameMath.Lerp(from.z,to.z,t)
		from.x = x
		from.y = y
		from.z = z
		return from
	end

	local function calc_fun()
		local lenth = #point_list
		for i = 1, lenth-1 do
			point_list[i] = lerp_xyz(point_list[i], point_list[i+1], t)
		end
		point_list[lenth] = nil
	end
	while #point_list > 2 do
		calc_fun()
	end
	return GameMath.LerpXYZ(point_list[1], point_list[2], t)
end
function GameMath.LerpXYZ(from,to,t)

	local x = GameMath.Lerp(from.x,to.x,t)
	local y = GameMath.Lerp(from.y,to.y,t)
	local z = GameMath.Lerp(from.z,to.z,t)

	return co.TableXYZ(x,y,z)
end
function GameMath.GetDistanceXYZ(p1x,p1y,p1z,p2x,p2y,p2z)
	local x_step = p1x - p2x
	local y_step = p1y - p2y
	local z_step = p1z - p2z
	local val = x_step*x_step + y_step*y_step + z_step*z_step
	
	return math.pow(val,0.5)
end

function GameMath.IsPointInDiamondRect(point,A,B,C,D)
	local a = (B.x - A.x) * (point.y - A.y) - (B.y - A.y) * (point.x - A.x)
	local b = (C.x - B.x) * (point.y - B.y) - (C.y - B.y) * (point.x - B.x)
	local c = (D.x - C.x) * (point.y - C.y) - (D.y - C.y) * (point.x - C.x)
	local d = (A.x - D.x) * (point.y - D.y) - (A.y - D.y) * (point.x - D.x)

	if (a > 0 and b > 0 and c > 0 and d > 0) or (a < 0 and b < 0 and c < 0 and d < 0) then
		return true
	end

	return false
end
-- 判断点是否在多边形
function GameMath.IsPointInPolygonRect(checkPoint,polygonPoints)
	local inside = false
	local pointCount = #polygonPoints
	local p1,p2 
	local i,j = 1,pointCount
	for i = 1,pointCount do 
		p1 = polygonPoints[i]
		p2 = polygonPoints[j]
		if checkPoint.y < p2.y then
			if p1.y <= checkPoint.y then
				if ((checkPoint.y - p1.y) * (p2.x - p1.x) > (checkPoint.x - p1.x) * (p2.y - p1.y)) then
					inside = not inside
				end
			end
		elseif checkPoint.y < p1.y then
			if ((checkPoint.y - p1.y) * (p2.x - p1.x) < (checkPoint.x - p1.x) * (p2.y - p1.y)) then
				inside = not inside
			end
		end
		j = i
	end
	return inside
end
--判断直线 AB 是否与线段CD 相交
function GameMath.LineIntersectSide(A,B,C,D)
	local fC = (C.y - A.y) * (A.x - B.x) - (C.x - A.x) * (A.y - B.y)
	local fD = (D.y - A.y) * (A.x - B.x) - (D.x - A.x) * (A.y - B.y)

	if fC * fD > 0 then
		return false
	end

	return true
end

local GameMath_LineIntersectSide = GameMath.LineIntersectSide

function GameMath.SideIntersectSide(A,B,C,D)
	if not GameMath_LineIntersectSide(A,B,C,D) then
		return false
	end
	if not GameMath_LineIntersectSide(C,D,A,B) then
		return false
	end
	return true 
end

function GameMath.PreciseDecimal(num, n)

	n = n or 0
	local nDecimal = 1/(10 ^ n)
	local nLeft = num % nDecimal
	local ret_val = num - nLeft

	if nLeft*(10^n) >= 0.5 then
		ret_val = ret_val + nDecimal
	end

	return ret_val
end

--两个向量之间的线性插值
function GameMath.GetVecLerp( v1, v2, alpha )
	local result = {}
	result.x = v1.x*(1 - alpha) + v2.x*alpha
	result.y = v1.y*(1 - alpha) + v2.y*alpha
	return result
end

function GameMath.PointRotate( p1, p2 )
	local result = {}
	result.x = p1.x*p2.x - p1.y*p2.y
	result.y = p1.x*p2.y + p1.y*p2.x
    return result
end

--vec向量以pivot为中心旋转angle角
function GameMath.RotateByAngle( vec, pivot, angle )
	local Rad2Deg = 57.29578
	angle = angle/Rad2Deg
	local vec_angle = {x=math.cos(angle), y=math.sin(angle)}
	local result = {}
	result.x = vec.x - pivot.x 
	result.y = vec.y - pivot.y
	result = GameMath.PointRotate(result, vec_angle)
	result.x = result.x + pivot.x
	result.y = result.y + pivot.y
	return result
end