├── README.md
└── Spring.lua


/README.md:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/Fraktality/Spring/d71c4f558c2de47e7e3418af26b9bcbf194fefc6/README.md


--------------------------------------------------------------------------------
/Spring.lua:
--------------------------------------------------------------------------------
  1 | -- Spring solver
  2 | -- Copyright 2023 Fractality
  3 | -- github.com/Fraktality/Spring
  4 | -- Distributed under the MIT license; see full notice at the end of this file.
  5 | 
  6 | local Spring = {} do
  7 | 	Spring.__index = Spring
  8 | 
  9 | 	local pi = math.pi
 10 | 	local exp = math.exp
 11 | 	local sin = math.sin
 12 | 	local cos = math.cos
 13 | 	local sqrt = math.sqrt
 14 | 
 15 | 	local EPS = 1e-4
 16 | 
 17 | 	function Spring.new(dampingRatio: number, frequency: number, position)
 18 | 		assert(type(dampingRatio) == "number", "Damping ratio must be a number")
 19 | 		assert(type(frequency) == "number", "Frequency must be a number")
 20 | 		assert(dampingRatio*frequency >= 0, "Spring does not converge")
 21 | 
 22 | 		return setmetatable({
 23 | 			d = dampingRatio,
 24 | 			f = frequency,
 25 | 			g = position,
 26 | 			p = position,
 27 | 			v = position*0, -- Match the original vector type
 28 | 		}, Spring)
 29 | 	end
 30 | 
 31 | 	function Spring:setGoal(newGoal)
 32 | 		self.g = newGoal
 33 | 	end
 34 | 
 35 | 	function Spring:getPosition()
 36 | 		return self.p
 37 | 	end
 38 | 
 39 | 	function Spring:getVelocity()
 40 | 		return self.v
 41 | 	end
 42 | 
 43 | 	function Spring:step(dt: number)
 44 | 		local d = self.d
 45 | 		local f = self.f*2*pi
 46 | 		local g = self.g
 47 | 		local p0 = self.p
 48 | 		local v0 = self.v
 49 | 
 50 | 		local offset = p0 - g
 51 | 		local decay = exp(-d*f*dt)
 52 | 
 53 | 		local p1, v1
 54 | 
 55 | 		if d == 1 then -- Critically damped
 56 | 			p1 = (offset*(1 + f*dt) + v0*dt)*decay + g
 57 | 			v1 = (v0*(1 - f*dt) - offset*(f*f*dt))*decay
 58 | 
 59 | 		elseif d < 1 then -- Underdamped
 60 | 			local c = sqrt(1 - d*d)
 61 | 
 62 | 			local i = cos(f*c*dt)
 63 | 			local j = sin(f*c*dt)
 64 | 
 65 | 			-- Damping ratios approaching 1 can cause division by small numbers.
 66 | 			-- To fix that, group terms around z=j/c and find an approximation for z.
 67 | 			-- Start with the definition of z:
 68 | 			--    z = sin(dt*f*c)/c
 69 | 			-- Substitute a=dt*f:
 70 | 			--    z = sin(a*c)/c
 71 | 			-- Take the Maclaurin expansion of z with respect to c:
 72 | 			--    z = a - (a^3*c^2)/6 + (a^5*c^4)/120 + O(c^6)
 73 | 			--    z ≈ a - (a^3*c^2)/6 + (a^5*c^4)/120
 74 | 			-- Rewrite in Horner form:
 75 | 			--    z ≈ a + ((a*a)*(c*c)*(c*c)/20 - c*c)*(a*a*a)/6
 76 | 
 77 | 			local z
 78 | 			if c > EPS then
 79 | 				z = j/c
 80 | 			else
 81 | 				local a = dt*f
 82 | 				z = a + ((a*a)*(c*c)*(c*c)/20 - c*c)*(a*a*a)/6
 83 | 			end
 84 | 
 85 | 			-- Frequencies approaching 0 present a similar problem.
 86 | 			-- We want an approximation for y as f approaches 0, where:
 87 | 			--    y = sin(dt*f*c)/(f*c)
 88 | 			-- Substitute b=dt*c:
 89 | 			--    y = sin(b*c)/b
 90 | 			-- Now reapply the process from z.
 91 | 
 92 | 			local y
 93 | 			if f*c > EPS then
 94 | 				y = j/(f*c)
 95 | 			else
 96 | 				local b = f*c
 97 | 				y = dt + ((dt*dt)*(b*b)*(b*b)/20 - b*b)*(dt*dt*dt)/6
 98 | 			end
 99 | 
100 | 			p1 = (offset*(i + d*z) + v0*y)*decay + g
101 | 			v1 = (v0*(i - z*d) - offset*(z*f))*decay
102 | 
103 | 		else -- Overdamped
104 | 			local c = sqrt(d*d - 1)
105 | 
106 | 			local r1 = -f*(d + c)
107 | 			local r2 = -f*(d - c)
108 | 
109 | 			local co2 = (v0 - offset*r1)/(2*f*c)
110 | 			local co1 = offset - co2
111 | 
112 | 			local e1 = co1*exp(r1*dt)
113 | 			local e2 = co2*exp(r2*dt)
114 | 
115 | 			p1 = e1 + e2 + g
116 | 			v1 = e1*r1 + e2*r2
117 | 		end
118 | 
119 | 		self.p = p1
120 | 		self.v = v1
121 | 
122 | 		return p1
123 | 	end
124 | end
125 | 
126 | -- Copyright 2023 Fractality
127 | --
128 | -- Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated
129 | -- documentation files (the "Software"), to deal in the Software without restriction, including without limitation the
130 | -- rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to
131 | -- permit persons to whom the Software is furnished to do so, subject to the following conditions:
132 | -- The above copyright notice and this permission notice shall be included in all copies or substantial portions of the
133 | -- Software.
134 | --
135 | -- THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
136 | -- WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
137 | -- COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
138 | -- OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
139 | 


--------------------------------------------------------------------------------