ParaSurf Release v1.0.3 -Parametric Surfaces in Codea

1aTabOrder

ParaSurf Tab Order Version: 1.0.3
------------------------------
This file should not be included in the Codea project.
#Main
#ParaSurf

Main.lua

-- Display a few parametric surfaces 

VERSION = "1.0.3"
PROJECTNAME = "ParaSurf"

function setup()
    autoGist = AutoGist(PROJECTNAME,"Parametric Surfaces in Codea",VERSION,false)
    autoGist:backup(true)
    
    displayMode(FULLSCREEN)
    
    sphere = ParaSphere(1)
    sphere.color = color(253, 255, 0, 255)
    
    torus = ParaTorus(1)
    torus.color = color(242, 116, 27, 255)
    
    supersphere = ParaSuperellipsoid(1)
    supersphere.color = color(170, 220, 45, 255)
    
    supertorus = ParaSupertoroid(1)
    supertorus.color = color(60,150,240,255)
    
    supersphere2 = ParaSuperellipsoid(1)
    supersphere2.n1 = 1.7
    supersphere2.n2 = 1.7
    supersphere2.color = color(59, 240, 209, 255)
    
    trefoil = ParaTrefoil(1)
    trefoil.color = color(240,60,150,255)
    
    cyl1 = ParaCylinder(0.75)
    cyl1.color = color(39, 217, 155, 255)
    
    cyl2 = ParaSupercylinder(0.75)
    cyl2.color = color(119, 44, 158, 255)
    
    cyl3 = ParaSupercylinder(0.75)
    cyl3.n = 1.7
    cyl3.color = color(231, 25, 36, 255)
    
    grid = {
        { cyl3, supersphere2, trefoil },
        { cyl2, supersphere, supertorus },
        { cyl1, sphere, torus },
    }
    
    shadr = shader([[
attribute vec4 position;
attribute vec3 normal;
attribute vec3 color;

uniform mat4 modelViewProjection;

varying vec3 eyenormal;
varying vec3 diffuse;

void main(void)
{
    eyenormal = mat3(modelViewProjection) * normal;
    diffuse = color;
    gl_Position = modelViewProjection * position;
}
    ]], [[
uniform highp vec3 light;

varying mediump vec3 eyenormal;
varying lowp vec3 diffuse;

void main(void)
{
    highp vec3 N = normalize(eyenormal);
    highp vec3 L = normalize(light);
    highp vec3 E = vec3(0, 0, 1);
    highp vec3 H = normalize(L + E);
    
    highp float df = max(0.0, dot(N, L)) * 0.3;
    
    highp float sf = max(0.0, dot(N, H));
    sf = pow(sf, 250.0);
    if(abs(N.z) < 0.2) sf = sf + (1.0 - abs(N.z)*(1.0/0.2));
    sf = sf * 0.5;

    lowp vec3 color = vec3(1,1,1) * 0.7 * diffuse + df * diffuse + sf * vec3(1,1,1);

    gl_FragColor = vec4(min(1.0,color.x), min(1.0,color.y), min(1.0,color.z), 1.0);
}
    ]]
    )
    shadr.light = vec3(0,1500,1000)
    
    rx, ry = 0, 0
end

function draw()
    background(49, 49, 49, 255)
    
    pushMatrix()
    resetMatrix()
    perspective(90, WIDTH/HEIGHT)
    camera(0,0,-2, 0,0,0, 0,1,0)
    
    rotate(rx, 1, 0, 0)
    rotate(ry, 0, 1, 0)
    
    frame = (frame or 0) + 1
    
    for y = 1, #grid do
        for x = 1, #grid[y] do
            pushMatrix()
            translate(x-1-(#grid[y]-1)/2, y-1-(#grid-1)/2, 0)
            scale(0.75)
            rotate(frame, 0, 1, 0)
            
            local p = grid[y][x]
            local m = p:paramesh()
            m.shader = shadr
            m:draw()
            popMatrix()
        end
    end
    
    popMatrix()
end

function touched(touch)
    if tid then
        if touch.state == ENDED then
            tid = nil
            tweenid = tween(0.2, _G, {rx=0,ry=0})
        else
            ry = ry - (tx - touch.x)*0.1
            rx = rx - (ty - touch.y)*0.1
            tx = touch.x
            ty = touch.y
        end
    elseif touch.state == BEGAN then
        tid = touch.id
        tx = touch.x
        ty = touch.y
        if tweenid then 
            tween.stop(tweenid)
            tweenid = nil
        end
    end
end

ParaSurf.lua

-- Generate meshes for parametric surfaces
--
-- Parts adapted from code in
-- iPhone 3D Programming by Philip Rideout, O’Reilly, ISBN 978-0-596-80482-4.

ParaSurf = class()

function ParaSurf:init()
    self.divx = 32
    self.divy = 32
    self.maxx = 100
    self.maxy = 100
end

function ParaSurf:sgn(x)
    if x < 0 then return -1
    elseif x > 0 then return 1
    end
    return 0
end

function ParaSurf:eval(x, y, wrap)
    if wrap then
        if x < 0 then x = x + self.maxx end
        if y < 0 then y = y + self.maxy end
        if x > self.maxx then x = x - self.maxx end
        if y > self.maxy then y = y - self.maxy end
    end
    return self:calculate(x,y)
end

function ParaSurf:calculate(x, y)
    return vec3(x,y,0)
end

function ParaSurf:normal(x, y)
    local v, v1, v2
    local s = 0.001
    if x + s >= self.maxx then x = x - s end
    if y + s >= self.maxy then y = y - s end
    if x <= s then x = x + s end
    if y <= s then y = y + s end
    v = self:eval(x, y, true)
    v1 = self:eval(x+s, y, true)-v
    v2 = self:eval(x, y+s, true)-v
    return v1:cross(v2):normalize()
end

function ParaSurf:paramesh(rebuild)
    local m
    if rebuild or not self.mesh then m = mesh()
    else return self.mesh end
    local v = {}
    local n = {}
    for y = 0, self.divy-2 do
        for x = 0, self.divx-2 do
            x1 = ((x+self.divx)%(self.divx) * self.maxx)/(self.divx-1)
            y1 = ((y+self.divy)%(self.divy) * self.maxy)/(self.divy-1)
            x2 = ((x+1)%(self.divx) * self.maxx)/(self.divx-1)
            y2 = ((y+self.divy)%(self.divy) * self.maxy)/(self.divy-1)
            x3 = ((x+1)%(self.divx) * self.maxx)/(self.divx-1)
            y3 = ((y+1)%(self.divy) * self.maxy)/(self.divy-1)
            x4 = ((x+self.divx)%(self.divx) * self.maxx)/(self.divx-1)
            y4 = ((y+1)%(self.divy) * self.maxy)/(self.divy-1)
            v1 = self:eval(x1, y1, x, y)
            v2 = self:eval(x2, y2, x, y)
            v3 = self:eval(x3, y3, x, y)
            v4 = self:eval(x4, y4, x, y)
            table.insert(v, v1)
            table.insert(v, v2)
            table.insert(v, v3)
            table.insert(v, v1)
            table.insert(v, v3)
            table.insert(v, v4)
            n1 = self:normal(x1, y1, x, y)
            n2 = self:normal(x2, y2, x, y)
            n3 = self:normal(x3, y3, x, y)
            n4 = self:normal(x4, y4, x, y)
            table.insert(n, n1)
            table.insert(n, n2)
            table.insert(n, n3)
            table.insert(n, n1)
            table.insert(n, n3)
            table.insert(n, n4)
        end
    end
    m.vertices = v
    m.normals = n
    m:setColors(self.color or color(200))
    self.mesh = m
    return m
end

ParaSphere = class(ParaSurf)

function ParaSphere:init(radius)
    ParaSurf.init(self)
    self.maxx = math.pi
    self.maxy = math.pi*2
    self.radius = (radius or 1)/2
end

function ParaSphere:calculate(u, v)
    local x = self.radius * math.sin(u) * math.cos(v)
    local y = self.radius * math.cos(u)
    local z = self.radius * -math.sin(u) * math.sin(v)
    return vec3(x,y,z)
end

ParaSuperellipsoid = class(ParaSphere)

function ParaSuperellipsoid:init(radius)
    ParaSphere.init(self, radius)
    self.n1 = 0.5
    self.n2 = 0.5
end

function ParaSuperellipsoid:calculate(u, v)
    local x = self.radius * math.pow(math.abs(math.sin(u)),self.n1) * math.pow(math.abs(math.cos(v)),self.n2) * self:sgn(math.sin(u)) * self:sgn(math.cos(v))
    local y = self.radius * math.pow(math.abs(math.cos(u)),self.n1) * self:sgn(math.cos(u))
    local z = self.radius * -math.pow(math.abs(math.sin(u)),self.n1) * math.pow(math.abs(math.sin(v)),self.n2) * self:sgn(math.sin(u)) * self:sgn(math.sin(v))
    return vec3(x,y,z)
end

ParaTorus = class(ParaSurf)

function ParaTorus:init(radius)
    ParaSurf.init(self)
    self.maxx = math.pi * 2
    self.maxy = math.pi * 2
    self.radius = radius/2-radius/6
    self.rinner = radius/6
end

function ParaTorus:calculate(u, v)
    local x = (self.radius + self.rinner*math.cos(v)) * math.cos(u)
    local y = (self.radius + self.rinner*math.cos(v)) * math.sin(u)
    local z = self.rinner * math.sin(v)
    return vec3(x,y,z)
end

ParaSupertoroid = class(ParaTorus)

function ParaSupertoroid:init(radius)
    ParaTorus.init(self, radius)
    self.n1 = 0.5
    self.n2 = 0.5
end

function ParaSupertoroid:calculate(u, v)
    local x = (self.radius + self.rinner*math.pow(math.abs(math.cos(v)),self.n1) * self:sgn(math.cos(v))) * math.pow(math.abs(math.cos(u)),self.n2) * self:sgn(math.cos(u))
    local y = (self.radius + self.rinner*math.pow(math.abs(math.cos(v)),self.n1) * self:sgn(math.cos(v))) * math.pow(math.abs(math.sin(u)),self.n2) * self:sgn(math.sin(u))
    local z = self.rinner * math.pow(math.abs(math.sin(v)),self.n1) * self:sgn(math.sin(v))
    return vec3(x,y,z)
end

ParaTrefoil = class(ParaSurf)

function ParaTrefoil:init(radius)
    ParaSurf.init(self)
    self.divx = self.divx * 2
    self.divy = self.divy / 2
    self.maxx = math.pi*2
    self.maxy = math.pi*2
    self.radius = (radius or 1)/2
end

function ParaTrefoil:calculate(dx, dy)
    local a, b, c, d = 0.5, 0.3, 0.5, 0.25
    local u = (math.pi*2 - dx) * 2
    local v = dy
    local r = a + b * math.cos(1.5 * u)
    local x = r * math.cos(u)
    local y = r * math.sin(u)
    local z = c * math.sin(1.5 * u)
    local dv = vec3(
        -1.5 * b * math.sin(1.5 * u) * math.cos(u) - (a + b * math.cos(1.5 * u)) * math.sin(u),
        -1.5 * b * math.sin(1.5 * u) * math.sin(u) + (a + b * math.cos(1.5 * u)) * math.cos(u),
         1.5 * c * math.cos(1.5 * u))
    local q = dv:normalize()
    local qvn = vec3(q.y, -q.x, 0):normalize()
    local ww = q:cross(qvn)
    local range = vec3(
        x + d * (qvn.x * math.cos(v) + ww.x * math.sin(v)),
        y + d * (qvn.y * math.cos(v) + ww.y * math.sin(v)),
        z + d * ww.z * math.sin(v))
    return range * self.radius
end

ParaCylinder = class(ParaSurf)

function ParaCylinder:init(radius)
    ParaSurf.init(self)
    self.maxx = math.pi
    self.divx = 4
    self.maxy = math.pi*2
    self.radius = (radius or 1)/2
end

function ParaCylinder:normal(u, v, uu, vv)
    if uu == 1 then
        local n = self:calculate(u,v,uu,vv)
        n.y = 0
        return n:normalize()
    end
    return ParaSurf.normal(self, u, v)
end

function ParaCylinder:calculate(u, v)
    local x = self.radius * math.sin(u) * math.cos(v)
    local y = (self.radius * math.cos(u) < 0) and -self.radius or self.radius
    local z = self.radius * -math.sin(u) * math.sin(v)
    return vec3(x,y,z)
end

ParaSupercylinder = class(ParaCylinder)

function ParaSupercylinder:init(radius)
    ParaCylinder.init(self, radius)
    self.n = 0.2
end

function ParaSupercylinder:calculate(u, v)
    local x = self.radius * math.pow(math.abs(math.sin(u)),self.n) * math.pow(math.abs(math.cos(v)),self.n) * self:sgn(math.sin(u)) * self:sgn(math.cos(v))
    local y = (self.radius * math.cos(u) < 0) and -self.radius or self.radius
    local z = self.radius * -math.pow(math.abs(math.sin(u)),self.n) * math.pow(math.abs(math.sin(v)),self.n) * self:sgn(math.sin(u)) * self:sgn(math.sin(v))
    return vec3(x,y,z)
end