/*═══════════════════════════════════════════════════════════════════════╕
│ Liège Openscad Library |
│ Module de déformation et modification pour OpenSCAD │
╞══════════════════╤════════════════════════════════════╤════════════════╡
│ marc@vanlindt.be │ LGPL 2.1 marc@vanlindt.be 2022 │ v0.98 ---- wip |
╞══════════════════╧═══════════════════════╤════════════╧════════════════╛
│ Variables générales /
╘═══════════════════════════════════════*/
LogoFB= [[4.46567, 4.99666], [3.06433, 4.99666], [3.06433, 0], [0.987666, 0], [0.987666, 4.99666], [0, 4.99666], [0, 6.76134], [0.987666, 6.76134], [0.987666, 7.90467], [1.00769, 8.22956], [1.07504, 8.57716], [1.20063, 8.92712], [1.39537, 9.25909], [1.6702, 9.55271], [2.03602, 9.78764], [2.50376, 9.94352], [3.08433, 10], [4.62167, 9.99402], [4.62167, 8.28068], [3.505, 8.28068], [3.35933, 8.26038], [3.21662, 8.18648], [3.10811, 8.0397], [3.065, 7.80073], [3.065, 6.76073], [4.64833, 6.76073]];
LetterL=[[0,0],[0,70],[22,73],[19,21],[50,25],[48,-1],[0,0]];
//LetterO=[[0,35],[6.25,61.25],[25,70],[25,70],[43.75,61.25],[50,35],[43.75,8.75],[25,0],[6.25,8.75],[0,35]];
LetterO=[[0,0],[0,70],[50,70],[50,0],[0,0]];
blue = [0,0,1,1];
red = [1,0,0,1];
green = [0,1,0,1];
violet = [0.5,0,0.5,1];
yellow = [1,1,0,1];
cyan = [0,1,1,1];
black = [0,0,0,1];
white = [1,1,1,1];
oak = RVB(200,50,90,255);
orange = [1,0.5,0,1];
olive = [0.5,0.5,0,1];
sarcelle = [0,0.5,0.5,1];
marine = [0,0,0.5,1];
fuschia = [1,0,1,1];
glass = [1,0,1,0.2];
bleu = [0,0,1,1];
rouge = [1,0,0,1];
vert = [0,1,0,1];
jaune = [1,1,0,1];
noir = [0,0,0,1];
blanc = [1,1,1,1];
gris = [0.5,0.5,0.5,1];
gray = [0.5,0.5,0.5,1];
pink = RVB(255,107,219,255);
phi = 1.61803399;
aphi = phi-1;
biphi = phi+1;
angledor = 360/biphi;
py = sqrt(0.5);
bipy = sqrt(2);
pi = 3.141592654;
tau = pi*2;
/*═══════════╕
│ Exemples \
╘════════════*/
/* MOEBIUS / ELLIPSE
moebius(n=32,d=40,t=0.5)
ellipse([5,20],$fn=128);
moebius(n=32,d=40,t=0.5)
ellipse([20,5],$fn=128);
*/
/* CHULL
chull(m=true){
sphere(d=1,$fn=64);
translate([10,10,00]) sphere(d=1,$fn=16);
translate([20,0,00]) sphere(d=1,$fn=16);
translate([30,0,00]) sphere(d=1,$fn=16);
translate([30,-10,00]) sphere(d=1,$fn=16);
translate([0,-10,00]) sphere(d=1,$fn=16);
}
*/
/* PYTHATREE / BONE*/
//pythatree(d="z",h=50,maxit=6,r1=30,r2=30)
//bone(h=50,d1=20,d2=14.14214,c=40,$fn=64);
/*pythatree(d="z",h=10*biphi,maxit=8,a=90,r1=90,r2=90)
hull(){sphere(d=10,$fn=16);
translate([0,0,10*biphi])sphere(d=10*aphi,$fn=16);}
*/
//pythatree(d="y",h=10,sp=5,maxit=8)
//polygon(square([10,10],center=true));
/*pythatree(d="y",h=50,maxit=9,a=90,s=sqrt(0.5))
hull(){
circle(d=10,$fn=64);
translate([0,50])
circle(d=sqrt(0.5)*10,$fn=64);}
*/
/**/
/* ROTATE2
rotate2()
cube(center=true);
translate([0,2,0])
cube(center=true);
*/
/* RING
ring(d=10,n=11){
cylinder(d=1,h=5);
translate([0,0,5.6]) scale([1,1,2]) sphere(d=0.6,$fn=64);
}
*/
/* SKEW
skew(YX=1)
cube([2,2,2]);
*/
/* ROUNDSQUARE
roundsquare(s=[40,20],d=[5,10,5,15],$fn=64,center=true);
*/
/* NGON
ngon(d=20,fn=3,inside=true);
translate([0,0,-1]) #cylinder(d=20,$fn=64);
translate([25,0,0]) ngon(d=20,fn=3,inside=false);
translate([25,0,-1]) #cylinder(d=20,$fn=64);
translate([50,0,0])ngon(d=20,f=4,inside=true);
translate([50,0,-1])#cylinder(d=20,$fn=64);
translate([75,0,0])ngon(d=20,fn=4,inside=false);
translate([75,0,-1])#cylinder(d=20,$fn=64);
translate([100,0,0])ngon(d=20,fn=5,inside=true);
translate([100,0,-1])#cylinder(d=20,$fn=64);
translate([125,0,0])ngon(d=20,fn=5,inside=false);
translate([125,0,-1])#cylinder(d=20,$fn=64);
*/
/* OUTLINE*/
/*outline(w=1,t="in"){
ellipse([10,20],fn=64);ellipse([20,10],fn=64);}
translate([0,0,1]){#ellipse([10,20],fn=64);#ellipse([20,10],fn=64);}
*/
/*
outline(w=1,t="out"){
ellipse([10,20],fn=64);ellipse([20,10],fn=64);}
translate([0,0,1]){#ellipse([10,20],fn=64);#ellipse([20,10],fn=64);}
*/
/*outline(w=1,t="on"){
ellipse([10,20],fn=64);ellipse([20,10],fn=64);}
translate([0,0,1]){#ellipse([10,20],fn=64);#ellipse([20,10],fn=64);}
*/
/**/
/* RANDOM
for(i=[1:10]){
echo(random(10,s=i));
}
*/
/* FIBONACCI
for(i=[1:15]){
echo(fibonacci(i));
}
*/
/* TEARDROP / RANDOM
for(i=[1:500]){
translate([random(500,i*10),random(500,i*50),random(500,i*60)])
color([0.6,0.6,0.9,0.5])teardrop(a=30+random(30,i));
}
*/
/* STAR
star(d1=10,d2=20,fn=9);
*/
/* TUBE - COUDE
tube(d1=10,d2=8,h=15,$fn=64);
translate([0,0,15])
coude(d1=10,d2=8,a=45,$fn=64);
translate([0,0,20])
rotate([0,045,0])
translate([0,0,5])
tube(d1=10,d2=8,h=5,$fn=64);
*/
/* ROUNDCUBE
roundcube(s=[50,100,150],b=[5,15,15,20],t=[25,35,40,5],$fn=64,center=true);
*/
/* PAIR
for(i=[0:20]){
echo(str(i,pair(i)==true?" est pair!":" est impair!"));
}
*/
/* GRID - CNC
grid(s=[100,100],x=5,y=10,w=2)
{
cnc(0.5,$fn=32){
ellipse([2,1],$fn=32);
ellipse([1,2],$fn=32);
}}
*/
/* PIEPART
piepart(d=10,p=20/100);
rotate([0,0,360*21/100])
piepart(d=10,p=78/100);
*/
/* PIE
pie(d=10,p=[1,2,1,2,1,2,3,2,1,3,2,1]);
*/
/* SUM
echo(sum([5,10,15,20]));
*/
/* MYANGLE/length*/
/* CORRECT / CHULL
rotate_extrude()
rotate_extrude_correct()
chull(){
circle(d=3);
translate([60,0])
circle(d=3);
translate([70,120])
circle(d=3);
}
*/
/* FRACTSHAPE
fractshape(d=40,fn=4,maxit=3);
translate([40,0,0]) fractshape(d=40,fn=5,it=3);
translate([80,0,0]) fractshape(d=40,fn=6,it=3);
*/
/* clean
test=[[0,0],[0,0],[10,10],[10,10],[20,20],[20,20],[30,30],[30,30],[40,40],[40,40],[50,50],[50,50]];
echo(clean(test));
*/
/* Kochflake
for(i=[0:3]){
translate([i*10,0,0])kochflake(d=10,maxit=i);}
*/
/* Chaincurve / TRACE
//points=[[0,0],[sin(30)*10,cos(30)*10],[10,0],[0,0]];
points=[[0,0],[0,10],[10,10],[20,0],[30,10],[40,20],[60,-20],[10,-10],[10,-5],[15,-5],[15,0],[0,0]];
color([0.4,1.0,0.4,1])
linear_extrude(1)
polygon(chaincurve(points,8));
color("red") linear_extrude(3)
trace(points,0.2);
color([0.5,0.5,1,1]) linear_extrude(3)
trace(chaincurve(points,8),0.1);
*/
/*
difference(){
rotate2() cube([10,10,10],center=true);
translate([0,0,10]) cube([20,20,20],center=true);}
/*
rotate2() cube([10,10,10],center=true);
*/
/*═══════════════════════════════╕
│ Modificateurs / déformations \
╘════════════════════════════════*/
module outline (w,t){
w=w==undef?1:w;
t=t==undef?"on":t;
difference()
{
offset(t=="out"?w:t=="in"?0:w/2)
children();
offset(t=="out"?0:t=="in"?-w:-w/2)
children();
}
}
module pythatree (a,h,sp,maxit,b,r1,r2,s,d){
a = a == undef ? 45 : a;
h = h == undef ? 1 : h;
sp = sp == undef ? 0 : sp;
maxit = maxit == undef ? 3 : maxit;
b = b == undef ? 1 : b;
r1 = r1 == undef ? 0 : r1;
r2 = r2 == undef ? 0 : r2;
s = s == undef ? py : s;
d = d == undef ? "y" : d;
children();
if(b<=maxit)
{
translate([d=="x"?h:d=="y"?sp:-sp, d=="x"?-sp:d=="y"?h:0, d=="x"?0:d=="y"?0:h])
rotate([d=="x"?0:d=="y"?r2:0, d=="x"?r2:d=="y"?0:-a, d=="x"?-a:d=="y"?-a:r2])
scale([s,s,s])
pythatree(a=a,h=h,sp=sp,maxit=maxit,b=b+1,r1=r1,r2=r2,s=s,d=d)
{
children();
};
translate([d=="x"?h:d=="y"?-sp:sp, d=="x"?sp:d=="y"?h:0, d=="x"?0:d=="y"?0:h])
rotate([d=="x"?0:d=="y"?r1:0, d=="x"?r1:d=="y"?0:a, d=="x"?a:d=="y"?a:r1])
scale([s,s,s])
pythatree(a=a,h=h,sp=sp,maxit=maxit,b=b+1,r1=r1,r2=r2,s=s,d=d)
{
children();
};
}
}
module chull (m){
union()
for(i=[0:$children-2]){
hull(){
children(m==true?0:i);
children(i+1);
}
}
}
module rotate2 (){
rotate([45,90-atan(sqrt(2)),0])
children();
}
module ring (d,n){
d=d==undef?10:d;
n=n==undef?5:n;
for(i=[0:n-1]){
rotate([0,0,360/n*i]){
translate([d/2,0,0])
children();
}
}
}
module fibo (s,n,r){
r=r==undef?true:r;
s=s==undef?1:s;
n=n==undef?128:n;
for(i=[1:n]){
rotate([0,0,angledor*i])
translate([s*i,0,0])
scale(r==true?s+pow(1.003,i):1)
children();
}
}
module skew (XY,XZ,YX,YZ,ZX,ZY){
matrice=[
[1,XY,XZ,0], //[redimX, skewXY, skewXZ,translateX]
[YX,1,YZ,0], //[SkewYX,RedimY,SkewYZ,translateY]
[ZX,ZY,1,0] //[SkewZX, SkewZY,redimZ,TranslateZ]
];
multmatrix(matrice){
children();
}
}
module cnc(d,show,fn){
show=show==undef?false:show;
d = d == undef ? 3:d;
fn = fn == undef ? 32:fn;
if(show==false){
offset(-d/2,$fn=fn)
offset(d/2,$fn=fn)
children();
}
else
{
color("green")
linear_extrude(1)
children();
color("red")
linear_extrude(0.5)
difference()
{
offset(-d/2,$fn=fn)
offset(d/2,$fn=fn)
children();
children();
}
}
}
module moebius(d,t,fn){ // version 2.0
fn = fn == undef ? 128 :fn;
d = d == undef ? 30 :d;
t = t == undef ? 0.5 :t;
union(){
for(j=[0:$children-1])
{
for(i=[1:fn]){
hull(){
rotate([0,360/fn*i,0])
translate([d/2,0,0])
rotate([0,0,i*(360*t)/fn])
linear_extrude(0.1)
children(j);
rotate([0,360/fn*(i+1),0])
translate([d/2,0,0])
rotate([0,0,(i+1)*(360*t)/fn])
linear_extrude(0.1)
children(j);
}
}
}
}
}
module grid (dim,x,y){
dim=dim==undef?[100,100]:dim;
x=x==undef?10:x;
y=y==undef?10:y;
for(i=[1:x-1])
translate([i*dim[0]/x,0,0])
rotate([-90,0,0])
linear_extrude(dim[1])
children();
for(i=[1:y-1])
translate([0,i*dim[1]/y,0])
rotate([-90,0,-90])
linear_extrude(dim[0])
children();
}
module rotate_extrude_correct (){
difference(){
children();
translate([-100000,-50000])
square([100000,100000]);
}
}
/*═══════════════════╕
│ Nouvelles formes \
╞══════╤═══════════════╛
│ 2D │
╘═════*/
module teardrop (d,a,fn){
polygon(teardrop(d=d==undef?10:d,a=a==undef?30:a,fn=fn==undef?16:fn));
}
module star (d1,d2,fn){
polygon(star(d1=d1==undef?10:d1,d2=d2==undef?20:d2,fn=fn==undef?7:fn));
}
module ellipse (dim,fn){
polygon(ellipse(dim,fn));
}
module losange (dim){
polygon(losange(dim));
}
module roundsquare (table,d,fn){
polygon(roundsquare(s=table,d=d,fn=fn));
}
module kochflake (d,maxit){
polygon (
koch
(
ngon(d=d,fn=3),
maxit=maxit
)
);
}
module ngon (d,fn,inside){
polygon(ngon(d,fn,inside));
}
module piepart (d,a,p){
polygon(piepart(d=d,a=a,p=p));
}
module triangle (w,h){
polygon(triangle(w=w,h=h));
}
module fractshape (d,fn,inside,maxit){
polygon(fractshape(fn=fn,d=d,maxit=maxit,inside=inside));
}
module lghs (){
for(i=[-1:2:1])
{
rotate([0,0,i*45]){
translate([0,-50,0])
difference(){
cnc(10)
union(){
hull(){
circle(d=20);
translate([0,100,0])
circle(d=15);
}
translate([0,100,0])
circle(d=50);
}
hull(){
translate([0,150,0])
rotate([0,0,30])
circle(d=25,$fn=6);
translate([0,110,0])
rotate([0,0,30])
circle(d=25,$fn=6);
}
circle(d=10);
}
}
}
}
module trace(table,d,fn,dot,dotfn,tr,d2){
tr=tr==undef?true:tr;
fn=fn==undef?8:dot==true?4:fn;
dotfn=dotfn==undef?16:dotfn;
dot=dot==undef?true:dot;
d=d==undef?1:d;
d2=d2==undef?d*2:d2;
for(i=[0:len(table)-2]){
if(tr==true)
{
hull(){
translate(table[i])
circle(d=d,$fn=fn);
translate(table[i+1])
circle(d=d,$fn=fn);
}
}
if(dot==true){
translate(table[i]) circle(d=d2,$fn=dotfn);}
if(dot==true){
translate(table[i+1]) circle(d=d2,$fn=dotfn);}
}
}
module voronoi(dim, w, t, c, n,seed){
n=n==undef?100:n;
dim=dim==undef?[1000,500]:dim;
table=pointgrid([dim[0],dim[1]],n=n,seed=seed);
c=c==undef?0:c;
t=table[0][0]+table[0][1];
w=w==undef?1:w;
seed=seed==undef?1/fn*n*c/w:seed;
outline(w=w*2,t="in") square(dim);
difference(){
square(dim);
cnc(-c/2)
for (p=table){
intersection_for(p2=table){
if (p!=p2){
translate((p+p2)/2 -normal(p2-p)*w){
rotate([0,0,-myangle(p,p2)])
translate([-t,-t])
square([2*t, t]);
}}}}}}
/*════════╕
│ 2D/3D │
╘════════*/
/*═════╕
│ 3D │
╘═════*/
module tube (d1,d2,h,center){
d1=d1==undef?10:d1;
d2=d2==undef?8:d2;
h=h==undef?30:h;
center=center==undef?false:center;
translate([0,0,center==true?-h/2:0])
difference(){
cylinder(d=d1,h=h);
translate([0,0,-1])
cylinder(d=d2,h=h+2);
}
}
module coude (d1,d2,a){
d1=d1==undef?10:d1;
d2=d2==undef?8:d2;
a=a==undef?90:a<=-90?-90:a>=90?90:a;
difference(){
union(){
cylinder(d=d1,h=d1/2);
translate([0,0,d1/2])
sphere(d=d1);
translate([0,0,d1/2])
rotate([0,a,0])
cylinder(d=d1,h=d1/2);
}
union(){
translate([0,0,-1])
cylinder(d=d2,h=d1/2+1);
translate([0,0,d1/2])
sphere(d=d2);
translate([0,0,d1/2])
rotate([0,a,0])
cylinder(d=d2,h=d1/2+1);
}
}
}
module roundcube (s,b,t,center,q){
s=s==undef?[50,40,30]:s;
b=b==undef?[5,5,5,5]:b;
t=t==undef?[20,20,20,20]:t;
q=q==undef?16:q;
center=center==undef?false:center;
translate([center==true?-s[0]/2:0,center==true?-s[1]/2:0,center==true?-s[2]/2:0])
hull(){
translate([b[0]/2,b[0]/2,b[0]/2]) sphere(d=b[0],$fn=q);
translate([s[0]-b[1]/2,b[1]/2,b[1]/2]) sphere(d=b[1],$fn=q);
translate([s[0]-b[2]/2,s[1]-b[2]/2,b[2]/2]) sphere(d=b[2],$fn=q);
translate([b[3]/2,s[1]-b[3]/2,b[3]/2]) sphere(d=b[3],$fn=q);
translate([t[0]/2,t[0]/2,s[2]-t[0]/2]) sphere(d=t[0],$fn=q);
translate([s[0]-t[1]/2,t[1]/2,s[2]-t[1]/2]) sphere(d=t[1],$fn=q);
translate([s[0]-t[2]/2,s[1]-t[2]/2,s[2]-t[2]/2]) sphere(d=t[2],$fn=q);
translate([t[3]/2,s[1]-t[3]/2,s[2]-t[3]/2]) sphere(d=t[3],$fn=q);
}
}
module bone (h,d1,d2,c,q){
h = h == undef ? 50 : h;
d1 = d1 == undef ? 20 : d1;
d2 = d2 == undef ? 14.14214 : d2;
c = c == undef ? 40 : c;
q = q == undef ? 128 : q;
rotate_extrude(){
rotate_extrude_correct(){
cnc((c)*1,fn=q)
{
translate([0,h,0]) circle(d=d2,$fn=q);
translate([0,0])
circle(d=d1,$fn=q);
}
}
}
}
module rock(d,c,seed){
c=c==undef?3:c;
seed=seed==undef?1:seed;
intersection_for(i=[0:c]){
a=[random(360,s=i*seed),random(360,s=i*seed*2),random(360,s=i*seed*3)];
rotate(a)
cube([d,d,d*10],center=true);
}
}
module pie (d,p,pct,i=1,a=0){
pct=topct(p);
echo(pct);
rotate([0,0,a*360])
linear_extrude(i)
piepart(d=d,p=p[i-1]/sum(p)+0.01);
if(i<len(p)){
pie(d=d,p=p,i=i+1,a=a+pct[i-1]);
}
}
/*══════════════════════╕
│ Nouvelles fonctions \
╞═══════════════════╤════╛
│ Sur nombres (a) │
╘══════════════════*/
function random (n,s,pos) = rands(pos==undef?0:pos==true?0:-n,n,1,s==undef?n:s)[0];
function fibonacci (n,a=0,b=1,c=1) = c<n+1?fibonacci(a=b,b=a+b,c=c+1,n=n):a;
function hypo (a,b) = sqrt((a*a)+(b*b));
function real (a,b,c) = ((a*a)+(b*b))+c;
function imaginary (a,b,c) = (2*a*b)+c;
function pair (a) = a%2==0?true:false;
function normal (a) = a/(sqrt(a[0]*a[0]+a[1]*a[1]));
/*═════════════════════════╕
│ Sur tables [a,b,c, ...] │
╘═════════════════════════*/
function sum (a,b=0,c=0,n) = b<(n==undef?len(a):n)?sum(a=a,b=b+1,c=c+a[b],n=n):c;
function topct (a) = a/sum(a);
function moyenne (a,b=0,c=0) = b<len(a)?sum(a=a,b=b+1,c=c+a[b])/len(a):c;
function invert (a) = let(b=[for(i=[0:len(a)-1]) a[(len(a)-1)-i]])b;
function sort (a,invert=false) = len(a) == 0 ? [] : let (
b=floor(len(a)/2),
c=[for(i=a) if (i<a[b]) i],
d=[for(i=a) if (i>a[b]) i],
e=[for(i=a) if (i==a[b]) i]
)
invert==false?concat(sort(c),e,sort(d)):invert(concat(sort(c),e,sort(d)));
/*════════════════════════════╕
│ Sur vecteurs [[a,b],[c,d]] │
╘════════════════════════════*/
function length (a,b) = sqrt(((b[0]-a[0])*(b[0]-a[0]))+((b[1]-a[1])*(b[1]-a[1])));
function divide (a,b,c) = [a[0]+(b[0]-a[0])*c, a[1]+(b[1]-a[1])*c];
function myangle (a,b) = atan2(b[0]-a[0],b[1]-a[1]);
function join (a,c=0,t=[]) = let (u=concat(t,a[c]))c==len(a)?t:join(a=a,c=c+1,t=u);
// NIGHTLY BUILDS ONLY
function join2(aa) = [for(i=[0:len(aa)-1] ) each aa[i]];
function clean(a) = [for(i=[0:len(a)-1]) each (a[i]==a[i+1]?"":a[i][0]==undef?"":[a[i]])];
function koch (a,angle,maxit,it) = let(
a=a[0]==a[len(a)-1]?a:concat(a,[a[0]]),
b = [ for ( i = [ 0 : len(a)-2 ] ) [
a[i],
divide(a[i],a[i+1],1/3),
divide(a[i],a[i+1],1/3) + [
sin(myangle(a[i],a[i+1])-(angle==undef?60:angle<=60?60:angle>=180?180:angle))*length(a[i], a[i+1])/3,
cos(myangle(a[i],a[i+1])-(angle==undef?60:angle<=60?60:angle>=180?180:angle))*length(a[i],a[i+1])/3],
divide(a[i],a[i+1],2/3)+[sin(-90+myangle(a[i],a[i+1])-((90+(90-(angle<=60?60:angle>=180?180:angle)))))*length(a[i],a[i+1])/3,cos(-90+myangle(a[i],a[i+1])-(90+(90-(angle<=60?60:angle>=180?180:angle))))*length(a[i],a[i+1])/3],
divide(a[i],a[i+1],2/3),
a[i+1]
]],
maxit=maxit==undef?0:maxit,
it=it==undef?0:it
)
it==maxit?clean(join2(b)):koch(a=clean(join2(b)),angle=angle,maxit=maxit,it=it+1);
function fract(a,angle,in,maxit,it,close)= let(
close=close==undef?true:close,
a=close==true?a[0]==a[len(a)-1]?a:concat(a,[a[0]]):a,
maxit=maxit==undef?3:maxit==0?1:maxit,
it=it==undef?0:it,
inside=in==undef?1:in==true?1:-1,
angle=angle==undef?60:angle,
b = [ for ( i = [ 0 : len(a)-2 ] ) [
a[i],
divide(a[i],a[i+1],angle/180),
divide(a[i],a[i+1],angle/180) +
[
sin(myangle(a[i],a[i+1]) + angle*inside) * (length(a[i],a[i+1])/3) ,
cos(myangle(a[i],a[i+1]) + angle*inside) * (length(a[i],a[i+1])/3)
],
divide(a[i],a[i+1],1-(angle/180)),
a[i+1]]
]
)
it+1==maxit?clean(join2(b)):fract(a=clean(join2(b)),angle=angle,in=in,maxit=maxit,it=it+1,close=close);
/*
function fract (a,angle,in,maxit,it) = let(
a=a[0]==a[len(a)-1]?a:concat(a,[a[0]]),
maxit=maxit==undef?3:maxit==0?1:maxit,
it=it==undef?0:it,
angle=angle==undef?60:angle,
b = [ for ( i = [ 0 : len(a)-2 ] ) [
a[i],
divide(a[i],a[i+1],angle/180),
divide(a[i],a[i+1],1/2) +
[
sin(myangle(a[i],a[i+1]) + (in==false?-90:90)) * (length(a[i],a[i+1])/3) ,
cos(myangle(a[i],a[i+1]) + (in==false?-90:90)) * (length(a[i],a[i+1])/3)
],
divide(a[i],a[i+1],1-(angle/180)),
a[i+1]]
]
)
it+1==maxit?clean(join2(b)):fract(a=clean(join2(b)),angle=angle,in=in,maxit=maxit,it=it+1);
*/
function curve(table,fn) = let(
fn = fn == undef ? 8 : fn,
c = [ for ( i = [0:(fn)] ) each [divide(table[0],table[1],1/(fn)*i)]],
d = [ for ( i = [0:(fn)] ) each [divide(table[1],table[2],1/(fn)*i)]],
e = [ for ( i = [0:(fn)] ) each [divide(c[i],d[i],1/(fn)*i)]])
e;
function doublevector(table,f,it=0) = let(
f=f==undef?0:f,
aa = [for (i=[0:len(table)-1]) each [table[i],divide(table[i],table[i+1],0.5)]]
)
it==f?clean(aa):doublevector(clean(aa),f=f,it=it+1);
function ngon(d,fn,inside) = let (
d=d==undef?10:inside==undef?d:inside==true?d:d*((d/2)/(cos(360/fn/2)*d/2)),
fn=fn==undef?4:fn,
aa=[for(i=[0:fn])[sin(360/fn*i)*d/2,cos(360/fn*i)*d/2]]
)
aa;
function square(d,center)=let(
center=center==undef?false:center,
d=d==undef?[10,10]:d,
c1 = center == true ? [-d[0]/2,-d[1]/2] : [ 0, 0],
c2 = center == true ? [-d[0]/2, d[1]/2] : [ 0, d[1]],
c3 = center == true ? [ d[0]/2, d[1]/2] : [ d[0], d[1]],
c4 = center == true ? [ d[0]/2,-d[1]/2] : [ d[0], 0],
aa=[c1,c2,c3,c4,c1]
)
aa;
function ellipse(s,fn) = let (
fn=fn==undef?16:fn,
s=s==undef?[10,10*aphi]:s,
aa=[for(i =[0:fn] ) [sin(360/fn*i)*s[0]/2,cos(360/fn*i)*s[1]/2]]
)
aa;
function losange(s) = let (
s=s==undef?[10,10*aphi]:s,
aa=[for(i =[0:4] ) [sin(360/fn*i)*s[0]/2,cos(360/fn*i)*s[1]/2]]
)
aa;
function circle(d,r,fn) = let (
fn=fn==undef?16:fn,
r=r==undef?d==undef?5:d/2:r,
aa=ngon(d=r*2,fn=fn)
)
aa;
function star(d1,d2,fn) = let (
d1=d1==undef?10:d1/2,
d2=d2==undef?5:d2/2,
fn=fn==undef?7:fn,
aa=[for(i=[0:2*(fn)])[sin(360/(2*fn)*i)*(pair(i)==true?d1:d2),cos(360/(2*fn)*i)*(pair(i)==true?d1:d2)]]
)
aa;
function roundsquare(s,d,fn) = let (
fn = fn == undef ? 8:fn,
s = s == undef ? [15,20] : s,
d = d == undef ? [3,6,3,6] : len(d) == 1 ? [d[0]/2,d[0]/2,d[0]/2,d[0]/2]:len(d)==2?[d[0]/2,d[1]/2,d[1]/2,d[1]/2]:len(d)==3?[d[0]/2,d[1]/2,d[2]/2,d[2]/2]:d[0]==undef?[d/2,d/2,d/2,d/2]:d/2,
p1 = [0,0],
p2 = [0,d[0]],
p3 = [0,s[1]-d[1]],
p4 = [0,s[1]],
p5 = [d[1],s[1]],
p6 = [s[0]-d[2],s[1]],
p7 = [s[0],s[1]],
p8 = [s[0],s[1]-d[2]],
p9= [s[0],d[3]],
p10= [s[0],0],
p11= [s[0]-d[3],0],
p12= [d[0],0],
c1=curve([p3,p4,p5],fn=fn),
c2=curve([p6,p7,p8],fn=fn),
c3=curve([p9,p10,p11],fn=fn),
c4=curve([p12,p1,p2],fn=fn),
aa=clean(join2([c1,c2,c3,c4,[p3]]))
)
aa;
function piepart(d,a,p) = let (
d=d==undef?10:d/2,
a=a==undef?p==undef?90:p>=1?360*1/p:360*p:a,
aa=concat([[0,0]],[for(i=[0:a])[-sin(-90+i)*d,cos(-90+i)*d]])
)
aa;
function triangle(w,h)= let (
h=h==undef?cos(30)*w:h,
aa=[[-w/2,0],[0,h],[w/2,0],[-w/2,0]]
)
aa;
function fractshape(d,fn,inside,maxit)= let(
d=d==undef?10:d/2,
fn=fn==undef?5:fn,
maxit=maxit==undef?3:maxit,
inside=inside==undef?true:inside,
angle=fn==3?60:fn==4?89:360/fn,
points=fract(ngon(d=d*2,fn=fn),maxit=maxit,angle=angle,in=inside)
)
points;
function teardrop(d,a,fn)=let (
d=d==undef?10:d,
a=a==undef?30:a,
h=d*tan(90-a),
fn=fn==undef?16:fn,
courbe= [for(i=[0:fn]) [sin(90-a+(360-(90-a)*2)/fn*i)*d/2,cos(90-a+(360-(90-a)*2)/fn*i)*d/2]],
aa=concat(courbe,[[0,(cos(90-a)*d/2)+h*sin(90-a)/2]],[[sin(90-a)*d/2,cos(90-a)*d/2]])
)
aa;
function fractalize(table,force,maxit,seed)= let (
force=force==undef?1:force,
maxit=maxit==undef?3:maxit,
seed=seed==undef?1:seed,
aa=
[
for(i=[0:len(table)-2], ab = doublevector([[table[i][0],table[i][1]],[table[i+1][0],table[i+1][1]]],maxit=maxit))
for(j=ab[0]) each clean([[ab][0],[ab][1]]+[[(random(pos=false,n=force,s=sin(seed)*sin(ab[0])+sin(ab[1]))),(random(pos=false,n=force,s=cos(seed)*cos(ab[0])-sin(ab[1])))],[(random(n=force,s=tan(seed)+sin(ab[0])+2*cos(ab[1]))),(random(n=force,s=cos(seed)+cos(ab[0])-3*cos(ab[1])))]])
]
)
clean(aa);
function pointgrid(dim,n,seed) =[for(i=[0:n-1])[random(n=dim[0],s=sin(i/n/(seed==undef?1:seed))),random(n=dim[1],s=cos(i*2/n/(seed==undef?1:seed)))]];
function rescale(a,s) = [for (i=a) i*s];
function retranslate(a,t) = [for (i=a) i+t];
function 2Drot(object,angle) = [for(i=[0:len(object)-1]) [sin(myangle([0,0],object[i])+angle)*length([0,0],object[i]),cos(myangle([0,0],object[i])+angle)*length([0,0],object[i])]];
function to3D(a,b,h,bottom,top) = let (
bottom=bottom==undef?true:bottom,
top=top==undef?true:top,
aa=[ for(i=[0:len(a)]) each[[a[i][0],a[i][1],0],[b[i][0],b[i][1],h]] ],
bb=[ for(i=[0:1:len(aa)]) each [[i,i+1,i+2],[i+1,i+3,i+2]] ],
cc=bottom==true?[ for(i=[0:2:len(aa)]) each [i] ]:[],
// dd=top==true?[ for(i=[0:2:len(aa)]) each [len(aa)-1-i] ]:[],
dd=top==true?[ for(i=[0:2:len(aa)]) each [len(aa)-1-i] ]:[],
ee=concat(bb,[cc],[dd])
)
[clean(aa),clean(ee)];
function simple3D(a,b,h,bottom,top,angle,correct) = let (
angle=angle==undef?0:angle,
correct=correct==undef?0:correct,
bottom=true,
top=true,
c=2Drot(interpolate(a,b,maxstep=1,step=0,correct=correct,q=1),angle),
d=2Drot(interpolate(a,b,maxstep=1,step=1,correct=correct,q=1),angle),
aa=[ for(i=[0:len(c)]) each[[c[i][0],c[i][1],0],[d[i][0],d[i][1],h]] ],
bb=[ for(i=[0:1:len(aa)]) each [[i,i+1,i+2],[i+1,i+3,i+2]] ],
cc=bottom==true?[ for(i=[0:2:len(aa)]) each [i] ]:[],
dd=top==true?[ for(i=[0:2:len(aa)]) each [len(aa)-1-i] ]:[],
ee=concat(bb,[cc],[dd])
)
[clean(aa),clean(ee)];
function vectranslate(a,n,it)=let(
n=n==undef?0:n,
it=it==undef?0:it,
aa=n==0?a:[for(i=[0:len(a)-1]) i==0?a[len(a)-2]:a[i-1]]
)
it==n+len(a)-2?aa:vectranslate(a=aa,n=n,it=it+1);
module 2Dto3D(a,b,h,segment,correct,quality,rotation){
angle=rotation==undef?0:rotation/segment;
quality=quality==undef?1:quality;
he=h==undef?64:h;
mm=segment==undef?16:segment;
aabc=a==undef?ngon(d=50,fn=3):a;
adef=b==undef?chaincurve(koch(ngon(d=50,fn=3),maxit=1),fn=4):b;
correct=correct==undef?0:correct;
union(){
for(i=[0:mm-1]){
my3Dobject=to3D(
2Drot(interpolate(aabc,adef,maxstep=mm,step=i,correct=correct,q=quality),i*angle),
2Drot(interpolate(aabc,adef,maxstep=mm,step=i+1,correct=correct,q=quality),(i+1)*angle),
h=he/mm,
top=i==mm-1?true:true,
bottom=i==0?true:true);
translate([0,0,i*he/mm])
color([1/mm*i,1-(1/mm*i),1,1])
union()
{
polyhedron(my3Dobject[0],my3Dobject[1]);
polyhedron(my3Dobject[0],my3Dobject[1]);
}
}
}
}
function interpolate(a,b,step,maxstep,correct,q)= let(
pp=ppcm(len(a)-1,len(b)-1,q)-[1,1],
correct=correct==undef?0:correct,
abc=vectranslate(multiplyfaces(a,pp[0]),n=correct==undef?0:correct),
def=multiplyfaces(b,pp[1]),
aa=[for(i=[0:len(def)]) each [divide(abc[i],def[i],step/(maxstep))]])
clean(aa);
function ppcm(a,b,q)=let(
aa=[for(i=[0:max(a,b)]) each [i*a*(q==undef?1:q)]],
bb=[for(i=[0:max(a,b)]) each [i*b*(q==undef?1:q)]],
cc=[for(i=[0:max(a,b)]) each [for(j=[1:100]) each aa[i]==bb[j]?bb[j]:""]])
[cc[0]/a,cc[0]/b];
function multiplyfaces(object,n)=let(
n=n==undef?1:n==0?0:n,
aa=n==0?object:[for(i=[0:len(object)-2]) each
addpoints(object[i],object[i+1],n)
])
concat(clean(aa),[object[0]]);
function addpoints(c1,c2,n)=[for(i=[0:n]) each [divide(c1,c2,i/(n+1))]];
function chaincurve(table,fn,closed,detail) = let (
detail=detail==undef?1:detail==0?1:detail*sign(detail)*2+1,
closed=closed==undef?true:closed,
// table=table[0]==table[len(table)-1]?table:concat([for(i=[0:len(table)]) table[i]],table[len(table)-1]),
//totaltab=table,
totaltab=concat(table,[table[0]],closed==true?[table[1]]:"",closed==true?[table[2]]:""),
tab = multiplyfaces(totaltab,detail),
d = [for (i=[(closed==true?4:2):2:len(tab)-(closed==false?4:2)]) each curve([tab[(i)-1],tab[i],tab[i+1]],fn)],
b =table[0],
c = table[len(table)-1],
a = d
)
clean(a);
function RVB(a,b,c,d)= let( a=a==undef?0.5:1/255*a,
b=b==undef?0.5:1/255*b,
c=c==undef?0.5:1/255*c,
d=d==undef?1:1/255*d,
aa=[a,b,c,d]
)aa;
function mirror(a,x,y)=let(
xx=x==undef?1:x==true?-1:1,
yy=y==undef?1:y==true?-1:1,
aa=[
for(i=[0:len(a)-1])
each
[
[a[i][0]*xx,a[i][1]*yy]
]
]
)aa;
function center(a,center)=let(
LMax=sort([for(i=[0:len(a)-1])a[i][0]])[0],
LMin=sort([for(i=[0:len(a)-1])a[i][0]],invert=true)[0],
HMax=sort([for(i=[0:len(a)-1])a[i][1]])[0],
HMin=sort([for(i=[0:len(a)-1])a[i][1]],invert=true)[0],
LargMax=LMax*sign(LMax),
LargMin=LMin*sign(LMin),
HautMax=HMax*sign(HMax),
HautMin=HMin*sign(HMin),
Largeur=LargMax<=LargMin?LargMin-LargMax:LargMax-LargMin,
Hauteur=HautMax<=HautMin?HautMin-HautMax:HautMax-HautMin,
aa=retranslate(a,[-LMax-(center==false?0:Largeur/2),-HMax-(center==false?0:Hauteur/2)])
)aa;
function offset(a,d,i)= let
(
invert=i==undef?false:true,
aa=mesangles(a),
mesangles=orientangles(aa),
bb=[
for(i=[0:len(a)-2]) each [[a[i][0]+sin(90-mesangles[i])*d,a[i][1]+cos(90-mesangles[i])*d]]
]
)
concat(bb,[bb[0]]);
function mesangles(a,invert)=let
(
invert=invert==undef?false:true,
aa=[
for(i=[0:len(a)-2])
let(
a1=(invert==false?90:-90)-myangle(a[i],a[i==len(a)-2?0:i+1]),
a2=(invert==false?90:-90)-myangle(a[i],a[i==0?len(a)-2:i-1]),
aa1=(invert==false?90:-90)-myangle(a[i],a[i==len(a)-2?0:i+1]),
aa2=(invert==false?90:-90)-myangle(a[i],a[i==0?len(a)-2:i-1]),
a3=(a1+a2)/2+180,
aaa=aa[i-1]
)
a3
]
)
aa;
function orientangles(a,i)=
let
(
i=i==undef?0:i,
aa=[
for(j=[0:len(a)-1])
each (a[j]-a[j-1])>=90?a[j]-180:(a[j]-a[j-1])<=-90?a[j]+180:a[j]]
)
i==len(a)-1?aa:orientangles(a=aa,i=i+1);
function coeffdirect(a)=let //coefficient directeur
(
aa=(a[1][1]-a[0][1])/(a[1][0]-a[0][0])
)
aa;
/*
Dans un plan cartésien, on peut trouver les coordonnées du point d’intersection de deux courbes (comme par exemple deux droites) en résolvant le système d’équations.
Soit les droites dont les équations sont y = x – 4 et y = –2x + 5, alors : x – 4 = –2x + 5. On représente ces droites dans un plan cartésien.
Donc : 3x = 9 et x = 3
Puis : y = –1
Les coordonnées du point d’intersection de ces droites sont (3, –1).
*/
module 2D(a){
polygon(a);
}
module 3D(a){
if(a[1]!=undef)
{
polyhedron(a[0],a[1]);
}
}
function cube(d,center)=let
(
d=d==undef?[10,10,10]:d,
center=center==undef?false:center,
mys=square([d[0],d[1]],center=center),
aa=to3D(mys,mys,h=d[2])
)
center==false?aa:translate3D(aa,[0,0,-d[2]/2]);
function cylinder(d,d1,d2,h,fn,center)=let
(
d1=d==undef?d1==undef?10:d1:d,
d2=d==undef?d2==undef?10:d2:d,
h=h==undef?40:h,
fn=fn==undef?16:fn,
center=center==undef?false:center,
myg1=ngon(d=d1,fn=fn),
myg2=ngon(d=d2,fn=fn),
aa=to3D(myg1,myg2,h=h)
)
center==false?aa:translate3D(aa,[0,0,-h/2]);
function translate3D(a,b)=[[for(i=[0:len(a[0])-1]) a[0][i]+b],a[1]];
function rescale3D(a,s)= [[for(i=[0:len(a[0])-1]) a[0][i]*s],a[1]];
function gradient(a,b,c) = let
(
c=c==undef?1:c,
aR=a[0], aV=a[1], aB=a[2], aA=a[3],
bR=b[0], bV=b[1], bB=b[2], bA=b[3],
mR=(aR-bR)/c, mV=(aV-bV)/c, mB=(aB-bB)/c, mA=(aA-bA)/c,
aa=[for(i=[0:c-1]) [a[0]-mR*i,a[1]-mV*i,a[2]-mB*i,a[3]-mA*i]]
)
aa;
module menger(d,maxit,it){
let(it=it==undef?0:it)
if(it==maxit){
square([d,d]);
}
else{
union(){
menger(d=d/3+0.001,maxit=maxit,it=it+1);
translate([d/3,0])
menger(d=d/3+0.001,maxit=maxit,it=it+1);
translate([d/3*2,0])
menger(d=d/3+0.001,maxit=maxit,it=it+1);
translate([0,d/3])
menger(d=d/3+0.001,maxit=maxit,it=it+1);
translate([d/3*2,d/3])
menger(d=d/3+0.001,maxit=maxit,it=it+1);
translate([0,d/3*2])
menger(d=d/3+0.001,maxit=maxit,it=it+1);
translate([d/3,d/3*2])
menger(d=d/3+0.001,maxit=maxit,it=it+1);
translate([d/3*2,d/3*2])
menger(d=d/3+0.001,maxit=maxit,it=it+1);
}}}
module menger3d(it,d,maxit){
it=it==undef?1:it;
if (it==maxit){
cube([d,d,d],center=true);
}
if (it<=maxit){
union(){
for (i=[-1:1]){
translate([d/3,d/3,d/3*i]) rotate([0,90,0]) menger3d(it=it+1,d=d*1/3,maxit=maxit);
translate([-d/3,d/3,d/3*i]) rotate([0,90,0]) menger3d(it=it+1,d=d*1/3,maxit=maxit);
}
translate([0,d/3,d/3]) rotate([0,90,0]) menger3d(it=it+1,d=d*1/3,maxit=maxit);
translate([0,d/3,-d/3]) rotate([0,90,0]) menger3d(it=it+1,d=d*1/3,maxit=maxit);
for (i=[-1:1]){
translate([d/3,-d/3,d/3*i]) rotate([0,90,0]) menger3d(it=it+1,d=d*1/3,maxit=maxit);
translate([-d/3,-d/3,d/3*i]) rotate([0,90,0]) menger3d(it=it+1,d=d*1/3,maxit=maxit);
}
translate([0,-d/3,d/3]) rotate([0,90,0]) menger3d(it=it+1,d=d*1/3,maxit=maxit);
translate([0,-d/3,-d/3]) rotate([0,90,0]) menger3d(it=it+1,d=d*1/3,maxit=maxit);
translate([d/3,0,d/3]) rotate([0,90,0]) menger3d(it=it+1,d=d*1/3,maxit=maxit);
translate([d/3,0,-d/3]) rotate([0,90,0]) menger3d(it=it+1,d=d*1/3,maxit=maxit);
translate([-d/3,0,d/3]) rotate([0,90,0]) menger3d(it=it+1,d=d*1/3,maxit=maxit);
translate([-d/3,0,-d/3]) rotate([0,90,0]) menger3d(it=it+1,d=d*1/3,maxit=maxit);
}}}
module jcube(it,d,maxit){
it=it==undef?1:it;
union()
{
if(it==maxit)
{
cube([d,d,d],center=true);
}
if(it<=maxit)
{
translate([d/2,d/2,d/2])
translate([-d/2*(sqrt(2)-1),-d/2*(sqrt(2)-1),-d/2*(sqrt(2)-1)])
jcube(it=it+1,maxit=maxit,d=d*(sqrt(2)-1));
translate([-d/2,d/2,d/2])
translate([d/2*(sqrt(2)-1),-d/2*(sqrt(2)-1),-d/2*(sqrt(2)-1)])
jcube(it=it+1,maxit=maxit,d=d*(sqrt(2)-1));
translate([d/2,-d/2,d/2])
translate([-d/2*(sqrt(2)-1),d/2*(sqrt(2)-1),-d/2*(sqrt(2)-1)])
jcube(it=it+1,maxit=maxit,d=d*(sqrt(2)-1));
translate([-d/2,-d/2,d/2])
translate([d/2*(sqrt(2)-1),d/2*(sqrt(2)-1),-d/2*(sqrt(2)-1)])
jcube(it=it+1,maxit=maxit,d=d*(sqrt(2)-1));
translate([d/2,d/2,-d/2])
translate([-d/2*(sqrt(2)-1),-d/2*(sqrt(2)-1),d/2*(sqrt(2)-1)])
jcube(it=it+1,maxit=maxit,d=d*(sqrt(2)-1));
translate([-d/2,d/2,-d/2])
translate([d/2*(sqrt(2)-1),-d/2*(sqrt(2)-1),d/2*(sqrt(2)-1)])
jcube(it=it+1,maxit=maxit,d=d*(sqrt(2)-1));
translate([d/2,-d/2,-d/2])
translate([-d/2*(sqrt(2)-1),d/2*(sqrt(2)-1),d/2*(sqrt(2)-1)])
jcube(it=it+1,maxit=maxit,d=d*(sqrt(2)-1));
translate([-d/2,-d/2,-d/2])
translate([d/2*(sqrt(2)-1),d/2*(sqrt(2)-1),d/2*(sqrt(2)-1)])
jcube(it=it+1,maxit=maxit,d=d*(sqrt(2)-1));
translate([-d/2,-d/2,0])
translate([d/2*(1-(2*(sqrt(2)-1))),d/2*(1-(2*(sqrt(2)-1))),0])
jcube(it=it+1,maxit=maxit,d=d*(1-(2*(sqrt(2)-1))));
translate([-d/2,d/2,0])
translate([d/2*(1-(2*(sqrt(2)-1))),-d/2*(1-(2*(sqrt(2)-1))),0])
jcube(it=it+1,maxit=maxit,d=d*(1-(2*(sqrt(2)-1))));
translate([d/2,-d/2,0])
translate([-d/2*(1-(2*(sqrt(2)-1))),d/2*(1-(2*(sqrt(2)-1))),0])
jcube(it=it+1,maxit=maxit,d=d*(1-(2*(sqrt(2)-1))));
translate([d/2,d/2,0])
translate([-d/2*(1-(2*(sqrt(2)-1))),-d/2*(1-(2*(sqrt(2)-1))),0])
jcube(it=it+1,maxit=maxit,d=d*(1-(2*(sqrt(2)-1))));
translate([-d/2,0,-d/2])
translate([d/2*(1-(2*(sqrt(2)-1))),0,d/2*(1-(2*(sqrt(2)-1)))])
jcube(it=it+1,maxit=maxit,d=d*(1-(2*(sqrt(2)-1))));
translate([-d/2,0,d/2])
translate([d/2*(1-(2*(sqrt(2)-1))),0,-d/2*(1-(2*(sqrt(2)-1)))])
jcube(it=it+1,maxit=maxit,d=d*(1-(2*(sqrt(2)-1))));
translate([d/2,0,-d/2])
translate([-d/2*(1-(2*(sqrt(2)-1))),0,d/2*(1-(2*(sqrt(2)-1)))])
jcube(it=it+1,maxit=maxit,d=d*(1-(2*(sqrt(2)-1))));
translate([d/2,0,d/2])
translate([-d/2*(1-(2*(sqrt(2)-1))),0,-d/2*(1-(2*(sqrt(2)-1)))])
jcube(it=it+1,maxit=maxit,d=d*(1-(2*(sqrt(2)-1))));
translate([0,-d/2,-d/2])
translate([0,d/2*(1-(2*(sqrt(2)-1))),d/2*(1-(2*(sqrt(2)-1)))])
jcube(it=it+1,maxit=maxit,d=d*(1-(2*(sqrt(2)-1))));
translate([0,-d/2,d/2])
translate([0,d/2*(1-(2*(sqrt(2)-1))),-d/2*(1-(2*(sqrt(2)-1)))])
jcube(it=it+1,maxit=maxit,d=d*(1-(2*(sqrt(2)-1))));
translate([0,d/2,-d/2])
translate([0,-d/2*(1-(2*(sqrt(2)-1))),d/2*(1-(2*(sqrt(2)-1)))])
jcube(it=it+1,maxit=maxit,d=d*(1-(2*(sqrt(2)-1))));
translate([0,d/2,d/2])
translate([0,-d/2*(1-(2*(sqrt(2)-1))),-d/2*(1-(2*(sqrt(2)-1)))])
jcube(it=it+1,maxit=maxit,d=d*(1-(2*(sqrt(2)-1))));
}}}