Codea Tracks code

Tracks.lua

--[[
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
   }