// created by florian berger (flockaroo) - 2025
// License Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

// one-liner brick torus

Canvas.setpenopacity(.25);

const turtle = new Turtle();
const nth=21; //min=4,  max=100, step=.2
const nph=76.2; //min=4,  max=200, step=.2
const Th=1.03;  //min=0., max=3.2, step=.01
var pa,pp,ppp=pp=pa=[0,0,0];

function walk(i) {
    var i2=Math.floor(i/2);
    var x=i%2, s=i2%2-.5; if(s>0) x=1-x;
    ppp=pp; pp=pa;
    pa=rotX(Th,mix3(getTorusPoint(i2,      50,20,nph,nth),
                    getTorusPoint(i2+nth*x,50,20,nph,nth),.9),pa);
      
    turtle.goto(project(ppp));
    turtle.pendown();
    if( cross3(sub3(ppp,pa),sub3(ppp,pp))[2] * s < 0.0 ) turtle.penup();
    if(i<2) turtle.penup(); // only after ppp is filled

    return i < nph*nth*2*5+2;
}

function getTorusPoint(i,R,r,nph,nth)
{
    cst=CS(th=i/nth*Math.PI*2.0); csp=CS(th/nph);
    return[ (R+r*cst[0])*csp[0], (R+r*cst[0])*csp[1], r*cst[1] ];
}

function project(p) { p[2]+=180; return [p[0]/p[2]*180.,p[1]/p[2]*180.,p[2]]; }
function CS(x) { return [Math.cos(x),Math.sin(x)]; } 
function sub3(a,b) { return [a[0]-b[0],a[1]-b[1],a[2]-b[2]]; }
function mix3(a,b,f) { for(i=0;i<3;i++) a[i]=a[i]*(1.-f)+b[i]*f; return a; }
function cross3(a,b) { return [ a[1]*b[2]-b[1]*a[2], a[2]*b[0]-b[2]*a[0], a[0]*b[1]-b[0]*a[1] ]; }
function rotX(ph,v) { cs=CS(ph); return [ v[0],v[1]*cs[0]+v[2]*cs[1], v[2]*cs[0]-v[1]*cs[1] ]; }