3D box

gistfile1.txt

--# Main
displayMode(FULLSCREEN)
function setup()
    size,radius=200,10
    startPos=vec3(size/2,size/2,-size/2) --assumes centre of box is (0,0,0)
    CreateScene(size,radius,startPos)
    notStarted=true
end

function touched(t)
    if t.state==ENDED then
        local v=vec3(math.random()*6-3,math.random()*6-3,math.random()*6-3):normalize()*5
        PushBall(v)
        notStarted=false
    end
end

function CreateScene(size,radius,pos) --size is size of 3D box
    --make two boxes end to end using 5 lines
    boxSize=100 --size of virtual box
    local s=boxSize
    boxes={}
    boxes[1]=physics.body(EDGE,vec2(-s,-s/2),vec2(s,-s/2))
    boxes[2]=physics.body(EDGE,vec2(-s,s/2),vec2(s,s/2))
    boxes[3]=physics.body(EDGE,vec2(-s,-s/2),vec2(-s,s/2))
    boxes[4]=physics.body(EDGE,vec2(0,-s/2),vec2(0,s/2))
    boxes[5]=physics.body(EDGE,vec2(s,-s/2),vec2(s,s/2))
    for _,b in pairs(boxes) do 
        b.restitution=1 
        b.friction=0
    end
    circles={}
    for i=1,2 do
        local p=physics.body(CIRCLE,10)
        if i==1 then p.x,p.y=-s/2,0 else p.x,p.y=s/2,0 end
        p.restitution=1
        p.bullet=true
        circles[i]=p
    end
    physics.gravity(0,0) --turn off gravity
    physics.continuous=true
    scaling=boxSize/size
    --create visible box
    local img=readImage("SpaceCute:Background")--:copy(4,4,62,62)
    box=CreateBlock(size,size,size,color(255),vec3(0,0,0),img) 
    ball=CreateSphere(radius,readImage("Cargo Bot:Starry Background"),color(255))
end

function PushBall(v) 
    circles[1]:applyLinearImpulse(vec2(v.x,v.y)*scaling)
    circles[2]:applyLinearImpulse(vec2(v.x,v.z)*scaling)
end

function GetPos()
   return vec3(boxSize/2+circles[1].x,circles[1].y,circles[2].y)/scaling
end

function draw()
    background(220)
    perspective(90)
    local p=GetPos()
    camera(0,0,0,p.x,p.y,p.z)
    box:draw()
    pushMatrix()
    translate(p:unpack())
    ball:draw()
    popMatrix()
    ortho()
    viewMatrix(matrix())
    stroke(0)
    strokeWidth(1)
    local x,y=WIDTH-70,70
    local s=50
    local ss=s/scaling/size 
    line(x-s,y-s,x+s,y-s)
    line(x-s,y+s,x+s,y+s)
    line(x-s,y-s,x-s,y+s)
    line(x+s,y-s,x+s,y+s)
    fill(255,0,0,150)
    ellipse(x+p.x*ss,y+p.y*ss,radius*2*ss)
    text("XY",x-s+20,y+s-15)
    y=180
    line(x-s,y-s,x+s,y-s)
    line(x-s,y+s,x+s,y+s)
    line(x-s,y-s,x-s,y+s)
    line(x+s,y-s,x+s,y+s)
    ellipse(x+p.x*ss,y+p.z*ss,radius*2*ss)
    text("XZ",x-s+20,y+s-15)
    if notStarted then
        text(
        [[You are at the centre of a box with a red ball.
You can't see anything because the ball is around you
Touch the screen to push the ball in a random direction
and the camera will follow its movement.
Touch the screen to push it again.
        
The two boxes below show the two physics planes used
to handle collisions with the sides of the box
        ]]
        ,WIDTH/2,HEIGHT/2)
    end
end

--# Utility

function CreateBlock(w,h,d,col,pos,tex) --width,height,depth,colour,position,texture
    local x,X,y,Y,z,Z=pos.x-w/2,pos.x+w/2,pos.y-h/2,pos.y+h/2,pos.z-d/2,pos.z+d/2
    local v={vec3(x,y,Z),vec3(X,y,Z),vec3(X,Y,Z),vec3(x,Y,Z),vec3(x,y,z),vec3(X,y,z),vec3(X,Y,z),vec3(x,Y,z)}
    local vert={v[1],v[2],v[3],v[1],v[3],v[4],v[2],v[6],v[7],v[2],v[7],v[3],v[6],v[5],v[8],v[6],v[8],v[7],
                v[5],v[1],v[4],v[5],v[4],v[8],v[4],v[3],v[7],v[4],v[7],v[8],v[5],v[6],v[2],v[5],v[2],v[1]}
    local texCoords
    if tex then    
        local t={vec2(0,0),vec2(1,0),vec2(0,1),vec2(1,1)}            
        texCoords={t[1],t[2],t[4],t[1],t[4],t[3],t[1],t[2],t[4],t[1],t[4],t[3],t[1],t[2],t[4],t[1],t[4],t[3],
                   t[1],t[2],t[4],t[1],t[4],t[3],t[1],t[2],t[4],t[1],t[4],t[3],t[1],t[2],t[4],t[1],t[4],t[3]}
    end
    local n={vec3(0,0,1),vec3(1,0,0),vec3(0,0,-1),vec3(-1,0,0),vec3(1,0,0),vec3(-1,0,0)}
    local norm={}
    for i=1,6 do for j=1,6 do norm[#norm+1]=n[i] end end
    local ms = mesh()
    ms.vertices = vert
    ms.normals=norm
    if tex then ms.texture,ms.texCoords = tex,texCoords end
    ms:setColors(col or color(255))
    return ms
end  

function CreateSphere(r,tex,col,nx,ny)
    local vertices,tc = Sphere_OptimMesh(nx or 40,ny or 20)
    vertices = Sphere_WarpVertices(vertices)
    for i=1,#vertices do vertices[i]=vertices[i]*r end
    local ms = mesh()
    ms.vertices=vertices
    if tex then ms.texture,ms.texCoords=tex,tc end
    ms:setColors(col or color(255))
    return ms
end

function Sphere_OptimMesh(nx,ny)
    local v,t={},{}
    local k,s,x,y,x1,x2,i1,i2,sx,sy=0,1,0,0,{},{},0,0,nx/ny,1/ny
    local c = vec3(1,0.5,0)
    local m1,m2
    for y=0,ny-1 do
        local nx1 = math.floor( nx * math.abs(math.cos(( y*sy-0.5)*2 * math.pi/2)) )
        if nx1<6 then nx1=6 end
        local nx2 = math.floor( nx * math.abs(math.cos(((y+1)*sy-0.5)*2 * math.pi/2)) ) 
        if nx2<6 then nx2=6 end
        x1,x2 = {},{}
        for i1 = 1,nx1 do x1[i1] = (i1-1)/(nx1-1)*sx end  x1[nx1+1] = x1[nx1]
        for i2 = 1,nx2 do x2[i2] = (i2-1)/(nx2-1)*sx end  x2[nx2+1] = x2[nx2]
        local i1,i2,n,nMax,continue=1,1,0,0,true
        nMax = nx*2+1
        while continue do
            m1,m2=(x1[i1]+x1[i1+1])/2,(x2[i2]+x2[i2+1])/2
            if m1<=m2 then 
                v[k+1],v[k+2],v[k+3]=vec3(x1[i1],sy*y,1)-c,vec3(x1[i1+1],sy*y,1)-c,vec3(x2[i2],sy*(y+1),1)-c
                t[k+1],t[k+2],t[k+3]=vec2(-x1[i1]/2,sy*y) ,vec2(-x1[i1+1]/2,sy*y),vec2(-x2[i2]/2,sy*(y+1))
                if i1<nx1 then i1 = i1 +1 end
            else
                v[k+1],v[k+2],v[k+3]=vec3(x1[i1],sy*y,1)-c,vec3(x2[i2],sy*(y+1),1)-c,vec3(x2[i2+1],sy*(y+1),1)-c
                t[k+1],t[k+2],t[k+3]=vec2(-x1[i1]/2,sy*y),vec2(-x2[i2]/2,sy*(y+1)),vec2(-x2[i2+1]/2,sy*(y+1))
                if i2<nx2 then i2 = i2 +1 end
            end        
            if i1==nx1 and i2==nx2 then continue=false end
            k,n=k+3,n+1
            if n>nMax then continue=false  end
        end
    end   
    return v,t
end

function Sphere_WarpVertices(verts)
    local m = matrix(0,0,0,0, 0,0,0,0, 1,0,0,0, 0,0,0,0)
    local vx,vy,vz,vm        
    for i,v in ipairs(verts) do
        vx,vy = v[1], v[2]
        vm = m:rotate(180*vy,1,0,0):rotate(180*vx,0,1,0)
        vx,vy,vz = vm[1],vm[5],vm[9]
        verts[i] = vec3(vx,vy,vz)
    end    
    return verts
end