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143 lines
4.3 KiB
Lua
143 lines
4.3 KiB
Lua
--- Extended math functions
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--
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-- @module gear.mathx
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-- @copyright 2022 The 1414 Code Forge
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-- @author Lorenzo Cogotti
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local floor = math.floor
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local min, max = math.min, math.max
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local cos, pi = math.cos, math.pi
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local random = love and love.math.random or math.random
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local mathx = setmetatable({}, math)
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--- Clamp x within range [a,b] (where b >= a).
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--
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-- @number x value to clamp.
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-- @number a interval lower bound (inclusive).
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-- @number b interval upper bound (inclusive).
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-- @treturn number clamped value.
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function mathx.clamp(x, a, b) return min(max(x, a), b) end
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--- Sign function.
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--
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-- @number x value whose sign should be returned.
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-- @treturn number sign of x, -1 if negative, 1 if positive, 0 otherwise.
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function mathx.sign(x) return x > 0 and 1 or x < 0 and -1 or 0 end
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--- sign() variant returning 1 if x is non-negative.
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--
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-- @number x value whose sign should be returned.
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-- @treturn number sign of x, -1 if negative, 1 if non-negative.
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function mathx.sign2(x) return x >= 0 and 1 or -1 end
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--- Linear interpolation between a and b.
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--
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-- @number a first interpolation point.
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-- @number b second interpolation point.
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-- @number t the interpolation factor, a real number within [0,1].
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-- @treturn number the interpolated value.
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function mathx.lerp(a, b, t) return a*(1 - t) + b*t end
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--- Less accurate, but slightly faster, variant of lerp().
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function mathx.lerp2(a, b, t) return a + (b - a)*t end
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--- Cosine interpolation between a and b.
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--
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-- @number a first interpolation point.
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-- @number b second interpolation point.
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-- @number t the interpolation factor, a real number within [0,1].
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-- @treturn number interpolated value.
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function mathx.cerp(a, b, t)
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local tt = (1 - cos(t * pi)) * 0.5
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return a*(1 - tt) + b*tt
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end
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--- Cubic interpolation between a, b, c and d.
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--
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-- @number a first interpolation point.
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-- @number b second interpolation point.
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-- @number c third interpolation point.
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-- @number d fourth interpolation point.
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-- @number t the interpolation factor, a real number within [0,1].
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-- @treturn number the interpolated value.
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function mathx.cberp(a, b, c, d, t)
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local tt = t * t
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local a0 = d - c - a + b
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return a0*t*tt + (a - b - a0)*tt + (c - a)*t + b
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end
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--- Catmull-Rom spline interpolation between a, b, c and d.
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--
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-- @number a first interpolation point.
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-- @number b second interpolation point.
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-- @number c third interpolation point.
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-- @number d fourth interpolation point.
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-- @number t the interpolation factor, a real number within [0,1].
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-- @treturn number the interpolated value.
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function mathx.catmullrom(a, b, c, d, t)
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local tt = t * t
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local mha = -a * 0.5
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local hd = d * 0.5
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return (mha + 1.5*b - 1.5*c + hd)*t*tt + (a - 2.5*b + 2*c - hd)*tt + (mha + 0.5*c)*t + b
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end
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--- Hermite interpolation between a, b, c and d.
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--
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-- @number a first interpolation point.
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-- @number b second interpolation point.
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-- @number c third interpolation point.
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-- @number d fourth interpolation point.
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-- @number t the interpolation factor, a real number within [0,1].
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-- @number tension the tension factor, 1 is high, 0 normal (default), -1 is low.
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-- @number bias the bias factor, 0 is even (default), positive is towards the first segment, negative towards the other.
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-- @treturn number the interpolated value.
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function mathx.herp(a, b, c, d, t, tension, bias)
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tension = tension or 0
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bias = bias or 0
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local b0 = 1 + bias
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local b1 = 1 - bias
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local ht = (1 - tension) * 0.5
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local s0 = b0 * ht
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local s1 = b1 * ht
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local tt = t * t
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local ttt = tt * t
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local ttt2 = ttt * 2
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local tt3 = tt * 3
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local m0 = (b - a)*s0 + (c - b)*s1
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local m1 = (c - b)*s0 + (d - c)*s1
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local a0 = ttt2 - tt3 + 1
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local a1 = ttt - tt*2 + t
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local a2 = ttt - tt
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local a3 = tt3 - ttt2
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return a0*b + a1*m0 + a2*m1 + a3*c
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end
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--- Pseudo-random sign value.
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--
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-- @treturn number the pseudo-random sign value, either -1, 0, or 1.
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function mathx.rsign() return random(-1, 1) end
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--- rsign() variant returning -1 or 1.
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--
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-- @treturn number the pseudo-random sign value, either -1 or 1.
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function mathx.rsign2() return random(2) == 2 and 1 or -1 end
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--- Precise pseudo-random number within [min,max] (where max >= min).
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--
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-- @number min interval lower bound (inclusive).
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-- @number max interval upper bound (inclusive).
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-- @treturn number the pseudo-random real number within [a,b].
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function mathx.prandom(min, max)
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local t = random()
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return min * (1 - t) + max * t
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end
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return mathx
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