// created by florian berger (flockaroo) - 2018
// License Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

// my 1st turtle...

// turtle torus

// You can find the Turtle API reference here: https://turtletoy.net/syntax
Canvas.setpenopacity(.25);

// Global code will be evaluated once.
const turtle = new Turtle();
const nth=16;
const nph=32;


// The walk function will be called until it returns false.
function walk(i) {
    p0=getTorusPoint(i,      50,20,nph,nth);
    p1=getTorusPoint(i+1,    50,20,nph,nth);
    p2=getTorusPoint(i+nth,  50,20,nph,nth);
    p3=getTorusPoint(i+1+nth,50,20,nph,nth);
    p0=rotX(1.,p0);
    p1=rotX(1.,p1);
    p2=rotX(1.,p2);
    p3=rotX(1.,p3);
    p0=project(p0);
    p1=project(p1);
    p2=project(p2);
    p3=project(p3);
    
    turtle.penup();
    turtle.goto(p1);
    turtle.pendown();
    turtle.goto(p0);
    turtle.goto(p2);
    // draw front faces 3 times - not very efficent (at least for the turtle)
    if(vec3_cross(vec3_sub(p1,p0),vec3_sub(p2,p0))[2]>0.0)
    {
        turtle.goto(p3);
        turtle.goto(p1);
        turtle.goto(p3);
        turtle.goto(p2);
        turtle.goto(p0);
        turtle.goto(p1);
    }
    return i < nph*nth;
}

function project(p)
{
    p[2]+=180;
    return [p[0]/p[2]*180.,p[1]/p[2]*180.,p[2]];
}

function getTorusPoint(i,R,r,nph,nth)
{
    th=i/nth*Math.PI*2.0;
    ph=th/nph;
    return[(R+r*mcos(th))*mcos(ph),(R+r*mcos(th))*msin(ph),r*msin(th)];
}

function mcos(x) {
    return Math.cos(x);
}

function msin(x) {
    return Math.sin(x);
}

function vec3_add(a,b) {
    return [a[0]+b[0],a[1]+b[1],a[2]+b[2]];
}

function vec3_sub(a,b) {
    return [a[0]-b[0],a[1]-b[1],a[2]-b[2]];
}

function vec3_cross(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) {
    return [ v[0],v[1]*mcos(ph)+v[2]*msin(ph), v[2]*mcos(ph)-v[1]*msin(ph) ];
}