// created by florian berger (flockaroo) - 2018 // License Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. // derived from "medusas hairdo" https://www.shaderoo.org/?shader=IkKuv9 // using reinder's occlusion magic from "Cubic space division #2" Canvas.setpenopacity(1.); // Global code will be evaluated once. const turtle = new Turtle(); const polygonList = []; const quads = []; const PI2 = Math.PI*2.0; function mcos(x) { return Math.cos(x); } function msin(x) { return Math.sin(x); } function cos2(x) { return [Math.cos(x[0]),Math.cos(x[1])]; } function sin2(x) { return [Math.sin(x[0]),Math.sin(x[1])]; } function SC(x) { return [Math.sin(x),Math.cos(x)]; } function add2(a,b) { return [a[0]+b[0],a[1]+b[1]]; } function add3(a,b) { return [a[0]+b[0],a[1]+b[1],a[2]+b[2]]; } function sub3(a,b) { return [a[0]-b[0],a[1]-b[1],a[2]-b[2]]; } function dot3(a,b) { return a[0]*b[0]+a[1]*b[1]+a[2]*b[2]; } function scale2(a,b) { return [a[0]*b,a[1]*b]; } function scale3(a,b) { return [a[0]*b,a[1]*b,a[2]*b]; } function scale4(a,b) { return [a[0]*b,a[1]*b,a[2]*b,a[3]*b]; } function mul4(a,b) { return [a[0]*b[0],a[1]*b[1],a[2]*b[2],a[3]*b[3]]; } function mymix(a,b,f) { return a*(1.0-f)+b*f; } function mymix22(a,b,f) { return [a[0]*(1.0-f[0])+b[0]*f[0],a[1]*(1.0-f[1])+b[1]*f[1]]; } function mix3(a,b,f) { return add3(scale3(a,(1.0-f)),scale3(b,f)); } function length2(a) { return Math.sqrt(a[0]*a[0]+a[1]*a[1]); } function length3(a) { return Math.sqrt(a[0]*a[0]+a[1]*a[1]+a[2]*a[2]); } function normalize3(a) { return scale3(a,1.0/length3(a)); } function 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] ]; } const G=(.5+Math.sqrt(5./4.)); //const PI2=(3.141592653*2.); const PI=3.141592653; function fract(a) {return a-Math.floor(a);} function floor2(a) { return [Math.floor(a[0]),Math.floor(a[1])];} function fract2(a) { return [fract(a[0]),fract(a[1])];} // noise funcs by Morgan McGuire https://www.shadertoy.com/view/4dS3Wd function hash(n) { return fract(Math.sin(n) * 1.0e4); } function hash2(p) { return fract(1.0e4 * Math.sin(17.0 * p[0] + p[1] * 0.1) * (0.1 + Math.abs(Math.sin(p[1] * 13.0 + p[0])))); } function noise(x) { var i = Math.floor(x); var f = fract(x); var u = f * f * (3.0 - 2.0 * f); return mymix(hash(i), hash(i + 1.0), u); } function noise2(x) { var i = floor2(x); var f = fract2(x); var r1=mymix(hash2(add2(i,[0,0])), hash2(add2(i,[1,0])), f[0]); var r2=mymix(hash2(add2(i,[0,1])), hash2(add2(i,[1,1])), f[0]); return mymix(r1, r2, f[1]); } function getRand01Sph(pos) { var res = [1024,1024]; //var texc=((pos.xy*123.+pos.z)*res+.5)/res; var texc=[ pos[0]*123.+pos[2]+.5/res[0], pos[1]*123.+pos[2]+.5/res[1] ]; var n=1.0-noise2(scale2(texc,256.)); return [0,0,0,0]; return [n,n,n,n]; } //const vec4 p0 = vec4( 1, G, -G ,0 )/length(vec2(1,G)); const pI = scale4([ 1, G, -G ,0 ],1.0/length2([1,G])); /*vec3 icosaPosRaw[12] = vec3[] ( -p0.xwz, p0.xwy, -p0.xwy, p0.xwz, p0.wyx, -p0.wzx, p0.wzx, -p0.wyx, p0.yxw, p0.zxw, -p0.zxw, -p0.yxw );*/ const icosaPosRaw = [ [-pI[0],-pI[3],-pI[2]/*.xwz*/], [ pI[0], pI[3], pI[1]/*.xwy*/], [-pI[0],-pI[3],-pI[1]/*.xwy*/], [ pI[0], pI[3], pI[2]/*.xwz*/], [ pI[3], pI[1], pI[0]/*.wyx*/], [-pI[3],-pI[2],-pI[0]/*.wzx*/], [ pI[3], pI[2], pI[0]/*.wzx*/], [-pI[3],-pI[1],-pI[0]/*.wyx*/], [ pI[1], pI[0], pI[3]/*.yxw*/], [ pI[2], pI[0], pI[3]/*.zxw*/], [-pI[2],-pI[0],-pI[3]/*.zxw*/], [-pI[1],-pI[0],-pI[3]/*.yxw*/] ]; const posIdx = [ 0, 6, 1, 0, 11, 6, 1, 4, 0, 1, 8, 4, 1, 10, 8, 2, 5, 3, 2, 9, 5, 2, 11, 9, 3, 7, 2, 3, 10, 7, 4, 8, 5, 4, 9, 0, 5, 8, 3, 5, 9, 4, 6, 10, 1, 6, 11, 7, 7, 10, 6, 7, 11, 2, 8, 10, 3, 9, 11, 0 ]; // get icosahedron triangle function getIcosaTri(idx) { var i1 = posIdx[(idx%20)*3+0]; var i2 = posIdx[(idx%20)*3+1]; var i3 = posIdx[(idx%20)*3+2]; var p1=icosaPosRaw[i1]; var p2=icosaPosRaw[i2]; var p3=icosaPosRaw[i3]; return [p1,p2,p3]; } // subdivide 1 triangle into 4 triangles and give back closest triangle function getTriSubDiv(idx, p1, p2, p3) { var p4 = normalize3(add3(p1,p2)); var p5 = normalize3(add3(p2,p3)); var p6 = normalize3(add3(p3,p1)); if (idx==0) { p1=p1; p2=p4; p3=p6; } else if(idx==1) { p1=p6; p2=p5; p3=p3; } else if(idx==2) { p1=p6; p2=p4; p3=p5; } else if(idx==3) { p1=p4; p2=p2; p3=p5; } return [p1, p2, p3]; } var triStripIndex = [0,1,2,1,3,2]; function mixSq3(a,b,f) { return mymix3(a,b,Math.cos(f*PI)*.5+.5); } function geomTangentCurve(pos1, pos2, tan1, tan2, r1, r2, rSegNum, tSegNum, vIdx) { var l = length3(sub3(pos1,pos2)); l*=.4; var i=Math.floor(vIdx/3/2)%tSegNum; //{ // converted some loops into proper vertex index values var fact, fact2; fact=Math.max(0.,(i)/(tSegNum)); // force >=0 because of sqrt below fact=-Math.cos(fact*PI)*.5+.5; // more homogeneous steps var p1=mix3(add3(pos1,scale3(tan1,l*Math.sqrt(fact ))),sub3(pos2,scale3(tan2,l*Math.sqrt(1.-fact ))),fact ); fact2=Math.max(0.,(i+1)/(tSegNum)); // force >=0 because of sqrt below fact2=-Math.cos(fact2*PI)*.5+.5; // more homogeneous steps var p2=mix3(add3(pos1,scale3(tan1,l*Math.sqrt(fact2))),sub3(pos2,scale3(tan2,l*Math.sqrt(1.-fact2))),fact2); var ta = mix3(tan1,tan2,fact); var tn = mix3(tan1,tan2,fact2); var dph=PI*2./(rSegNum); //vec3 b1=normalize(vec3(ta.x,-ta.y,0)); var b1=normalize3(cross(ta,p1)); var b2=normalize3(cross(ta,b1)); //vec3 b3=normalize(vec3(tn.x,-tn.y,0)); var b3=normalize3(cross(tn,p2)); var b4=normalize3(cross(tn,b3)); var r_1 = mymix(r1,r2,fact); var r_2 = mymix(r1,r2,fact2); var j=Math.floor(vIdx/3/2/tSegNum)%rSegNum; //{ var ph = (j)*dph; var ph2 = ph+dph; var v1 = add3(p1,scale3(add3(scale3(b1,mcos(ph )),scale3(b2,msin(ph ))),r_1)); var v2 = add3(p1,scale3(add3(scale3(b1,mcos(ph2)),scale3(b2,msin(ph2))),r_1)); var v3 = add3(p2,scale3(add3(scale3(b3,mcos(ph )),scale3(b4,msin(ph ))),r_2)); var v4 = add3(p2,scale3(add3(scale3(b3,mcos(ph2)),scale3(b4,msin(ph2))),r_2)); var v = [v1,v2,v3,v4]; var pos = v[triStripIndex[vIdx%6]]; var normal = normalize3(cross(sub3(v[1],v[0]),sub3(v[2],v[0]))); //} //} return [pos,normal] } function calcAngle(v1, v2) { return Math.acos(dot3(v1,v2)/length3(v1)/length3(v2)); } // distance to 2 torus segments in a triangle // each torus segment spans from the middle of one side to the middle of another side function geomTruchet(p1, p2, p3, dz, rSegNum, tSegNum, trNum, radius, idx ) { if (radius<0.0) radius=.45*dz; var d = 10000.0; var rnd =getRand01Sph(add3(add3(p1,p2),p3))[0]; var rnd2=getRand01Sph(add3(add3(p1,p2),p3))[1]; // random rotation of torus-start-edges if (rnd>.75) { var d=p1; p1=p2; p2=d; } else if (rnd>.50) { var d=p1; p1=p3; p3=d; } else if (rnd>.25) { var d=p2; p2=p3; p3=d; } var p4 = scale3(p1,(1.-dz)); var p5 = scale3(p2,(1.-dz)); var p6 = scale3(p3,(1.-dz)); // FIXME: why is this necessary - very seldom actually!? var xchg=false; if(dot3(cross(sub3(p2,p1),sub3(p3,p1)),p1)>0.0) { var dummy; dummy=p2; p2=p3; p3=dummy; dummy=p5; p5=p6; p6=dummy; xchg=true; } var lp1 = length3(p1); var lp4 = length3(p4); var r,r1,r2,fact,ang,fullAng; var n = normalize3(cross(sub3(p2,p1),sub3(p3,p1))); // torus segments: // actually i have to fade from one torus into another // because not all triangles are equilateral var m; // std::vector <vec3> p; var v1,v2,v3,v4,v5,v6; var tubeNum=rSegNum*tSegNum*2*3; var i=Math.floor(idx/(tubeNum))%trNum; { if(i==0) { v1=p1; v2=p2; v3=p3; v4=p4; v5=p5; v6=p6; } if(i==1) { v1=p2; v2=p3; v3=p1; v4=p5; v5=p6; v6=p4; } if(i==2) { v1=p3; v2=p1; v3=p2; v4=p6; v5=p4; v6=p5; } //if(dot(cross(v2-v1,v3-v1),v1)>0.0) { vec3 dummy=v2; v2=v3; v3=dummy; } //if(dot(cross(v5-v4,v6-v4),v4)>0.0) { vec3 dummy=v5; v5=v6; v6=dummy; } fullAng = calcAngle(sub3(v3,v1),sub3(v2,v1)); //ang = calcAngle(pos2-v1,v2-v1); var dang=fullAng/(tSegNum); //if (fullAng<.001) break; //float r1, r2; //r1=length(v2-v1)*.5f; r1=length(v3-v1)*.5f; var pos1, pos2, pos3; pos1 = scale3(normalize3(add3(v2,v1)),lp1); pos2 = scale3(normalize3(add3(v6,v4)),lp4); //pos3 = scale3(normalize3(add3(v2,v3)),lp4); // FIXME: why is this necessary - very seldom actually!? - see above if(xchg) { pos1 = scale3(normalize3(add3(v5,v4)),lp1); pos2 = scale3(normalize3(add3(v3,v1)),lp4); } if(rnd2>.25) { if(i==0) { pos1 = scale3(normalize3(add3(v5,v4)),lp4); pos2 = scale3(normalize3(add3(v6,v4)),lp4); } if(i==1) { pos1 = scale3(normalize3(add3(v2,v1)),lp1); pos2 = scale3(normalize3(add3(v3,v1)),lp1); } } var tan1 = normalize3(cross(sub3(v2,v1),v1)); var tan2 = normalize3(cross(sub3(v3,v1),v1)); var pn = geomTangentCurve(pos1,pos2,tan1,tan2,radius,radius,rSegNum,tSegNum, idx%tubeNum); return pn; } } // final shape function geom_medusa(rNum, tNum, subdiv, idx) { var p1,p2,p3; var icosaFaceNum = 20; var subDivNum = 4; var trNum = 3; // tubes per truchet segemnt var truchetNum=rNum*tNum*2*3*trNum; // 2 triangles * 3 vertices * trNum tubes //for(int i1=0;i1<icosaFaceNum;i1++) var idiv=truchetNum; for(var i=0;i<subdiv;i++) idiv*=subDivNum; var pi = getIcosaTri(Math.floor(idx/idiv)); var p_subDivNum_i = 1; for(var i=0;i<subdiv;i++) { idiv=Math.floor(idiv/subDivNum); var isub = Math.floor(idx/idiv)%subDivNum; pi = getTriSubDiv(isub,pi[0],pi[1],pi[2]); p_subDivNum_i*=subDivNum; } var pn = geomTruchet(pi[0],pi[1],pi[2],0.12/(1+subdiv),rNum,tNum,trNum,-1.,idx%truchetNum); return pn; } function medusaTri(idx) { var pos = [0,0,0]; var normal = [0,0,0]; var pn; pn=geom_medusa(8,6,0,idx); //pn=geomTangentCurve([-2,0,0], [0,0,2], [1,0,0], [0,0,-1], .1, .1, 10, 10, idx); pos=pn[0]; //pn = getIcosaTri(Math.floor(idx/3)); //pos=pn[idx%3]; return pos; } function rotX(ph,v) { return [ v[0],v[1]*mcos(ph)+v[2]*msin(ph), v[2]*mcos(ph)-v[1]*msin(ph) ]; } function rotY(ph,v) { return [ v[0]*mcos(ph)+v[2]*msin(ph), v[1], v[2]*mcos(ph)-v[0]*msin(ph) ]; } function project(p) { p[2]+=180; return [p[0]/p[2]*180.,p[1]/p[2]*180.,p[2]]; } function insertQuad(p0,p1,p2,p3) { var z = p0[2]+p1[2]+p2[2]+p3[2]; var idx=0; for(idx=0;idx<quads.length && quads[idx+8]<z;idx+=9); // hmm, why is the one below not working... !? //for(var i=0;i<quads.length;i+=9) { // if(quads[i+8]>z) { idx=i; break; } //} quads.splice(idx, 0, p0[0], p0[1], p1[0], p1[1], p2[0], p2[1], p3[0], p3[1], z); } function walk(i) { var num = 8*6*3*20; if(i==0){ for(let j=0;j<num;j++) { var p0=medusaTri(j*6); var p1=medusaTri(j*6+1); var p2=medusaTri(j*6+2); var p3=medusaTri(j*6+4); p0=scale3(p0,70.0); p1=scale3(p1,70.0); p2=scale3(p2,70.0); p3=scale3(p3,70.0); p0=rotX(1.4,p0); p1=rotX(1.4,p1); p2=rotX(1.4,p2); p3=rotX(1.4,p3); p0=rotY(.1,p0); p1=rotY(.1,p1); p2=rotY(.1,p2); p3=rotY(.1,p3); p0=project(p0); p1=project(p1); p2=project(p2); p3=project(p3); if(cross(sub3(p1,p0),sub3(p2,p0))[2]<0.0) { insertQuad(p0,p2,p3,p1); } } } var p0=[quads[i*9+0],quads[i*9+1]]; var p1=[quads[i*9+2],quads[i*9+3]]; var p2=[quads[i*9+4],quads[i*9+5]]; var p3=[quads[i*9+6],quads[i*9+7]]; const p = new Polygon(); p.cp.push([p0[0], p0[1]]); p.cp.push([p1[0], p1[1]]); p.cp.push([p2[0], p2[1]]); p.cp.push([p3[0], p3[1]]); p.addOutline(0); drawPolygon(turtle, p); /*turtle.penup(); turtle.goto(p0); turtle.pendown(); turtle.goto(p1); turtle.goto(p2); turtle.goto(p0);*/ /*turtle.goto(p3); turtle.goto(p2);*/ return i <= num/1.8; } //////////////////////////// // reinder's occlusion code parts from "Cubic space division #2" //////////////////////////// function drawPolygon(turtle, p) { let vis = true; for (let j=0; j<polygonList.length; j++) { if(!p.boolean(polygonList[j])) { vis = false; break; } } if (vis) { p.draw(turtle, 0); polygonList.push(p); } } // polygon functions function LineSegment(p1, p2) { this.p1 = p1; this.p2 = p2; } function Polygon() { this.cp = []; // clip path: array of [x,y] pairs this.dp = []; // 2d line to draw: array of linesegments } Polygon.prototype.addOutline = function(s=0) { for (let i=s, l=this.cp.length; i<l; i++) { this.dp.push(new LineSegment(this.cp[i], this.cp[(i+1)%l])); } } Polygon.prototype.createPoly = function(x,y,c,r,a) { this.cp = []; for (let i=0; i<c; i++) { this.cp.push( [x + Math.sin(i*Math.PI*2/c+a) * r, y + Math.cos(i*Math.PI*2/c+a) * r] ); } } Polygon.prototype.draw = function(t, inp=0) { if (this.dp.length ==0) { return; } for (let i=0, l=this.dp.length; i<l; i++) { const d = this.dp[i]; if (!vec2_equal(d.p1, t.pos())) { t.penup(); t.goto([d.p1[0]+inp*(Math.random()-.5), d.p1[1]+inp*(Math.random()-.5)]); t.pendown(); } t.goto([d.p2[0]+inp*(Math.random()-.5), d.p2[1]+inp*(Math.random()-.5)]); } } Polygon.prototype.inside = function(p) { // find number of i ntersection points from p to far away // if even your outside const p1 = [0.1, -1000]; let int = 0; for (let i=0, l=this.cp.length; i<l; i++) { if (vec2_find_segment_intersect(p, p1, this.cp[i], this.cp[(i+1)%l])) { int ++; } } return int & 1; } Polygon.prototype.boolean = function(p, diff = true) { // very naive polygon diff algorithm - made this up myself const ndp = []; for (let i=0, l=this.dp.length; i<l; i++) { const ls = this.dp[i]; // find all intersections with clip path const int = []; for (let j=0, cl=p.cp.length; j<cl; j++) { const pint = vec2_find_segment_intersect(ls.p1,ls.p2,p.cp[j],p.cp[(j+1)%cl]); if (pint) { int.push(pint); } } if (int.length == 0) { // 0 intersections, inside or outside? if (diff == !p.inside(ls.p1)) { ndp.push(ls); } } else { int.push(ls.p1); int.push(ls.p2); // order intersection points on line ls.p1 to ls.p2 const cmp = [ls.p2[0]-ls.p1[0], ls.p2[1]-ls.p1[1]]; int.sort( (a,b) => { const db = vec2_dot([b[0]-ls.p1[0], b[1]-ls.p1[1]], cmp); const da = vec2_dot([a[0]-ls.p1[0], a[1]-ls.p1[1]], cmp); return da - db; }); for (let j=0; j<int.length-1; j++) { if (!vec2_equal(int[j], int[j+1])) { if (diff == !p.inside([(int[j][0]+int[j+1][0])/2,(int[j][1]+int[j+1][1])/2])) { ndp.push(new LineSegment(int[j], int[j+1])); } } } } } this.dp = ndp; return this.dp.length > 0; } // vec functions const vec2_equal = (a,b) => vec2_dist_sqr(a,b) < 0.01; const vec2_dot = (a, b) => a[0]*b[0]+a[1]*b[1]; const vec2_dist_sqr = (a, b) => (a[0]-b[0])*(a[0]-b[0]) + (a[1]-b[1])*(a[1]-b[1]); //port of http://paulbourke.net/geometry/pointlineplane/Helpers.cs function vec2_find_segment_intersect(l1p1, l1p2, l2p1, l2p2) { const d = (l2p2[1] - l2p1[1]) * (l1p2[0] - l1p1[0]) - (l2p2[0] - l2p1[0]) * (l1p2[1] - l1p1[1]); const n_a = (l2p2[0] - l2p1[0]) * (l1p1[1] - l2p1[1]) - (l2p2[1] - l2p1[1]) * (l1p1[0] - l2p1[0]); const n_b = (l1p2[0] - l1p1[0]) * (l1p1[1] - l2p1[1]) - (l1p2[1] - l1p1[1]) * (l1p1[0] - l2p1[0]); if (d == 0) { return false; } const ua = n_a / d; const ub = n_b / d; if (ua >= 0 && ua <= 1 && ub >= 0 && ub <= 1) { return [l1p1[0] + (ua * (l1p2[0] - l1p1[0])), l1p1[1] + (ua * (l1p2[1] - l1p1[1])) ]; } return false; }