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@loopspace loopspace/Tracks.lua
Created Dec 19, 2018

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Codea Tracks code
--[[
Track definitions.
--]]
function TrackPoints(a)
a = a or {}
local pts = a.points or {}
local t = a.start or 0
local r = a.step or .1
r = r*r
local s = a.delta or .1
local f = a.pathFunction or function(q) return q*vec3(1,0,0) end
local nf = a.normalFunction or function(q) return vec3(0,1,0) end
local b = a.finish or 1
local tpt = f(t)
table.insert(pts,{tpt,
tangent({delta = s, pathFunction = f, time = t}),
nf(t),t})
local dis
local p
while t < b do
dis = 0
while dis < r do
t = t + s
p = f(t)
dis = dis + p:distSqr(tpt)
tpt = p
end
if t > b then
t = b
p = f(b)
end
table.insert(pts,{p,
tangent({delta = s, pathFunction = f, time = t}),
nf(t),t})
tpt = p
end
return pts
end
function tangent(a)
local s = a.delta/2 or .1
local f = a.pathFunction or function(q) return q*vec3(1,0,0) end
local t = a.time or 0
local u = f(t-s)
local v = f(t+s)
return (v-u)/(2*s)
end
local Tracks = {}
function Tracks.torus(p,q)
local innerRa = 10
local innerRb = 10
local outerR = 30
local trackFunction = function(t)
local it = p*t*2*math.pi
local ot = q*t*2*math.pi
return vec3(
(outerR + innerRb*math.cos(it))*math.cos(ot),
innerRa*math.sin(it),
(outerR + innerRb*math.cos(it))*math.sin(ot)
)
end
local trackNormal = function(t)
local it = p*t*2*math.pi
local ot = q*t*2*math.pi
return vec3(
innerRa*math.cos(it)*math.cos(ot),
innerRb*math.sin(it),
innerRa*math.cos(it)*math.sin(ot)
)
end
local coreFunction = function(t)
local ot = q*t*2*math.pi
return vec3(
outerR*math.cos(ot),
0,
outerR*math.sin(ot)
)
end
local maxHeight = innerRa
local minHeight = -innerRa
return trackFunction, trackNormal, maxHeight, minHeight
end
function Tracks.mobius()
local r = 30
local trackFunction = function(t)
local a = 2*math.pi*t
return vec3(r*math.cos(a),0,r*math.sin(a))
end
local trackNormal = function(t)
local a = math.pi*t
return vec3(
math.sin(a)*math.cos(2*a),
math.cos(a),
math.sin(a)*math.sin(2*a))
end
return trackFunction,trackNormal,0.5,-0.5
end
function Tracks.loop(p,q,r,h)
local r = r or 30
local h = h or 10
local w = vec3(0,50,0)
local trackFunction = function(t)
local a = 2*math.pi*t
return vec3(
r*math.cos(a),
h*math.sin(p*a),
r*math.sin(q*a))
end
local trackNormal = function(t)
return w - trackFunction(t)
end
return trackFunction,trackNormal,h,-h
end
cmodule.export {
tangent = tangent,
Tracks = Tracks,
TrackPoints = TrackPoints
}
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