264 lines
6.7 KiB
Lua
264 lines
6.7 KiB
Lua
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------------------------------------------------
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--作者： xihan
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--日期： 2019-05-06
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--文件： Math.lua
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--模块： 无
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--描述： 数学
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------------------------------------------------
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---------------------[lua自带的]-----------------
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-- math.maxinteger 最大值 9223372036854775807
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-- math.mininteger 最小值 -9223372036854775808
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-- math.huge 无穷大 inf
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-- math.tointeger 转整数
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-- math.pi 圆周率 math.pi 3.1415926535898
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-- math.abs 取绝对值 math.abs(-2012) 2012
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-- math.ceil 向上取整 math.ceil(9.1) 10
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-- math.floor 向下取整 math.floor(9.9) 9
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-- math.max 取参数最大值 math.max(2,4,6,8) 8
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-- math.min 取参数最小值 math.min(2,4,6,8) 2
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-- math.sqrt 开平方 math.sqrt(65536) 256.0
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-- math.modf 取整数和小数部分 math.modf(20.12) 20 0.12
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-- math.randomseed 设随机数种子 math.randomseed(os.time())
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-- math.random 取随机数 math.random(5,90) 5~90
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-- math.rad 角度转弧度 math.rad(180) 3.1415926535898
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-- math.deg 弧度转角度 math.deg(math.pi) 180.0
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-- math.exp e的x次方 math.exp(4) 54.598150033144
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-- math.log 计算x的自然对数 math.log(54.598150033144) 4.0
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-- math.sin 正弦 math.sin(math.rad(30)) 0.5
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-- math.cos 余弦 math.cos(math.rad(60)) 0.5
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-- math.tan 正切 math.tan(math.rad(45)) 1.0
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-- math.asin 反正弦 math.deg(math.asin(0.5)) 30.0
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-- math.acos 反余弦 math.deg(math.acos(0.5)) 60.0
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-- math.atan 反正切 math.deg(math.atan(1)) 45.0
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-- math.type 获取类型是integer还是float
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-- math.fmod 取模 math.fmod(65535,2) 1
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------------------------------------------------
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local L_Floor = math.floor
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local L_Abs = math.abs
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--角度转弧度
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math.Deg2Rad = math.pi / 180
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--弧度转角度
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math.Rad2Deg = 180 / math.pi
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--机械极小值
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math.Epsilon = 1.401298e-45
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--value的p次幂
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function math.Pow(value, p)
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return value^p;
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end
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--大约（小数第一位四舍五入）
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function math.Round(num)
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return L_Floor(num + 0.5)
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end
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--函数返回一个数字的符号, 指示数字是正数,负数还是零
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function math.Sign(num)
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if num > 0 then
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num = 1
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elseif num < 0 then
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num = -1
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else
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num = 0
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end
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return num
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end
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--限制value的值在min和max之间, 如果value小于min,返回min，如果value大于于max,返回max
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function math.Clamp(num, min, max)
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if num < min then
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num = min
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elseif num > max then
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num = max
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end
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return num
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end
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local Clamp = math.Clamp
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--线性插值
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function math.Lerp(from, to, t)
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return from + (to - from) * Clamp(t, 0, 1)
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end
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--非限制线性插值
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function math.LerpUnclamped(a, b, t)
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return a + (b - a) * t;
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end
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--重复
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function math.Repeat(t, length)
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return t - (L_Floor(t / length) * length)
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end
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--插值角度
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function math.LerpAngle(a, b, t)
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local _num = math.Repeat(b - a, 360)
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if _num > 180 then
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_num = _num - 360
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end
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return a + _num * Clamp(t, 0, 1)
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end
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--移向
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function math.MoveTowards(current, target, maxDelta)
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if L_Abs(target - current) <= maxDelta then
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return target
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end
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return current + math.Sign(target - current) * maxDelta
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end
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--增量角
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function math.DeltaAngle(current, target)
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local _num = math.Repeat(target - current, 360)
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if _num > 180 then
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_num = _num - 360
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end
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return _num
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end
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--移动角
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function math.MoveTowardsAngle(current, target, maxDelta)
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target = current + math.DeltaAngle(current, target)
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return math.MoveTowards(current, target, maxDelta)
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end
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--近似
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function math.Approximately(a, b)
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return L_Abs(b - a) < math.max(1e-6 * math.max(L_Abs(a), L_Abs(b)), 1.121039e-44)
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end
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--反插值
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function math.InverseLerp(from, to, value)
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if from < to then
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if value < from then
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return 0
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end
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if value > to then
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return 1
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end
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value = value - from
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value = value/(to - from)
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return value
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end
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if from <= to then
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return 0
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end
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if value < to then
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return 1
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end
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if value > from then
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return 0
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end
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return 1.0 - ((value - to) / (from - to))
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end
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--乒乓
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function math.PingPong(t, length)
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t = math.Repeat(t, length * 2)
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return length - L_Abs(t - length)
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end
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--是否是非数字值
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function math.IsNan(number)
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return not (number == number)
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end
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--伽玛函数
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function math.Gamma(value, absmax, gamma)
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local _flag = false
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if value < 0 then
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_flag = true
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end
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local _num = L_Abs(value)
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if _num > absmax then
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return (not _flag) and _num or -_num
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end
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local _num2 = (_num / absmax )^ gamma * absmax
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return (not _flag) and _num2 or -_num2
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end
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--平滑阻尼
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function math.SmoothDamp(current, target, currentVelocity, smoothTime, maxSpeed, deltaTime)
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maxSpeed = maxSpeed or math.huge
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deltaTime = deltaTime or Time.deltaTime
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smoothTime = math.max(0.0001, smoothTime)
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local _num = 2 / smoothTime
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local _num2 = _num * deltaTime
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local _num3 = 1 / (1 + _num2 + 0.48 * _num2 * _num2 + 0.235 * _num2 * _num2 * _num2)
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local _num4 = current - target
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local _num5 = target
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local max = maxSpeed * smoothTime
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_num4 = Clamp(_num4, -max, max)
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target = current - _num4
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local _num7 = (currentVelocity + (_num * _num4)) * deltaTime
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currentVelocity = (currentVelocity - _num * _num7) * _num3
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local _num8 = target + (_num4 + _num7) * _num3
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if (_num5 > current) == (_num8 > _num5) then
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_num8 = _num5
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currentVelocity = (_num8 - _num5) / deltaTime
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end
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return _num8,currentVelocity
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end
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--平滑阻尼角度
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function math.SmoothDampAngle(current, target, currentVelocity, smoothTime, maxSpeed, deltaTime)
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deltaTime = deltaTime or Time.deltaTime
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maxSpeed = maxSpeed or math.huge
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target = current + math.DeltaAngle(current, target)
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return math.SmoothDamp(current, target, currentVelocity, smoothTime, maxSpeed, deltaTime)
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end
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--平滑插值
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function math.SmoothStep(from, to, t)
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t = Clamp(t, 0, 1)
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t = -2 * t * t * t + 3 * t * t
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return to * t + from * (1 - t)
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end
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--水平角
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function math.HorizontalAngle(dir)
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return math.deg(math.atan(dir.x, dir.z))
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end
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--伽马转线性
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function math.GammaToLinearSpaceExact(value)
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if value <= 0.04045 then
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return value / 12.92;
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elseif value < 1.0 then
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return math.Pow((value + 0.055)/1.055, 2.4);
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else
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return math.Pow(value, 2.2);
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end
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end
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--线性转伽马
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function math.LinearToGammaSpaceExact(value)
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if value <= 0.0 then
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return 0.0;
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elseif value <= 0.0031308 then
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return 12.92 * value;
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elseif value < 1.0 then
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return 1.055 * math.Pow(value, 0.4166667) - 0.055;
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else
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return math.Pow(value, 0.45454545);
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end
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end
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--将数字转为整数或者小数。如72.0返回72； 72.5返回72.5 支持负数
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function math.FormatNumber(value)
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local t1, t2 = math.modf(value)
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if t2 == 0 then
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--小数部分如果等于0，则返回整数部分
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return t1
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else
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--小数部分如果大于0，则直接返回
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return value
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end
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end
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