// created by florian berger (flockaroo) - 2019 // 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" const polygons = Polygons(); const Subdiv=Math.floor(Math.random()*1.999); // the high subdivs were a bit edgy, but now more detail thanks to reinders optimizations //const RadialSegs=4; //const TangentialSegs=11; const RadialSegs=6.-2*Subdiv; //const RadialSegs=2; const TangentialSegs=9+9*(2-Subdiv); const RandomDive=Math.random()>0.2; const randQuat=getRandQuat(); const objQuat=getRandQuat(); Canvas.setpenopacity(1.); const PI2 = Math.PI*2.0; function getRandQuat() { q=[Math.random(),Math.random(),Math.random(),Math.random()]; ql=Math.sqrt(q[0]*q[0]+q[1]*q[1]+q[2]*q[2]+q[3]*q[3]); q[0]/=ql; q[1]/=ql; q[2]/=ql; q[3]/=ql; return q; } // Global code will be evaluated once. const turtle = new Turtle(); const polygonList = []; const quads = []; function vec3(a,b,c) { return [a,b,c]; } function vec2(a,b) { return [a,b]; } function transformVecByQuat( v, q ) { //return v + 2.0 * cross( q.xyz, cross( q.xyz, v ) + q.w*v ); return add3(v, scale3(cross( q, add3(cross( q, v ) , scale3(v,q[3]) )) ,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 mul2(a,b) { return [a[0]*b[0],a[1]*b[1]]; } 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) { pos=transformVecByQuat( pos, randQuat ); 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.)); if(!RandomDive) 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); } // cubic bezier curve in 2 dimensions // equivalent to the function above, just in a more intuitive form function bezierCurvePos(p, t) { // combination of 2 quadric beziers var q=[]; var r=[]; for(var i=0;i<3;i++) q.push(mix3(p[i],p[i+1],t)); for(var i=0;i<2;i++) r.push(mix3(q[i],q[i+1],t)); return mix3(r[0],r[1],t); } function tanCurve(p1, p2, t1, t2, x) { var d1=Math.abs(dot3(t1,normalize3(sub3(p2,p1)))); var d2=Math.abs(dot3(t2,normalize3(sub3(p2,p1)))); var p=[]; p.push(p1); p.push(add3(p1,scale3(t1,length3(sub3(p2,p1))*mymix(.7,.25,d1)))); p.push(sub3(p2,scale3(t2,length3(sub3(p2,p1))*mymix(.7,.25,d2)))); p.push(p2); return bezierCurvePos(p,x); } function geomTangentZopf(pos1, pos2, tan1, tan2, r1, r2, rSegNum, tSegNum, vIdx, parity, zopfPeriods) { var l = length3(sub3(pos1,pos2)); l*=.4; var i=Math.floor(vIdx/3/2)%tSegNum; var zi = Math.floor(vIdx/3/2/tSegNum/rSegNum)%3; //{ // converted some loops into proper vertex index values var fact, fact2; fact=Math.max(0.,(i)/(tSegNum)); // force >=0 because of sqrt below fact2=Math.max(0.,(i+1)/(tSegNum)); // force >=0 because of sqrt below var ta = mix3(tan1,tan2,fact); var tn = mix3(tan1,tan2,fact2); var p1=tanCurve(pos1,pos2,tan1,tan2,fact); var p2=tanCurve(pos1,pos2,tan1,tan2,fact2); var p1d=tanCurve(pos1,pos2,tan1,tan2,fact+.001); var p2d=tanCurve(pos1,pos2,tan1,tan2,fact2+.001); var ta = normalize3(sub3(p1d,p1)); var tn = normalize3(sub3(p2d,p2)); 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)*.5; var r_2 = mymix(r1,r2,fact2)*.5; var j=Math.floor(vIdx/3/2/tSegNum)%rSegNum; var s1=(dot3(tan1,pos1))>0.?1.:-1.; var s2=(dot3(tan2,pos2))>0.?1.:-1.; //s2=s1=1.; //var zi=0; var zang; var cs; zang = .6666*fact*PI2*s1*zopfPeriods + PI2*.3333*zi; cs=scale2(mul2(vec2(.5,1),mul2(cos2(add2(scale2(vec2(2,1),zang),vec2(0,-PI2*.1666))),vec2(1,parity))),r_1*1.5); var dp1=add3(scale3(b2,cs[0]),scale3(b1,cs[1])); zang = .6666*fact2*PI2*s2*zopfPeriods + PI2*.3333*zi; cs=scale2(mul2(vec2(.5,1),mul2(cos2(add2(scale2(vec2(2,1),zang),vec2(0,-PI2*.1666))),vec2(1,parity))),r_2*1.5); var dp2=add3(scale3(b4,cs[0]),scale3(b3,cs[1])); //dp1=[0,0,0]; //dp2=[0,0,0]; //{ var ph = (j)*dph; var ph2 = ph+dph; var v1 = add3(dp1,add3(p1,scale3(add3(scale3(b1,mcos(ph )),scale3(b2,msin(ph ))),r_1))); var v2 = add3(dp1,add3(p1,scale3(add3(scale3(b1,mcos(ph2)),scale3(b2,msin(ph2))),r_1))); var v3 = add3(dp2,add3(p2,scale3(add3(scale3(b3,mcos(ph )),scale3(b4,msin(ph ))),r_2))); var v4 = add3(dp2,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; } // FIXME: why is this necessary - very seldom actually!? if(dot3(cross(sub3(p2,p1),sub3(p3,p1)),p1)>0.0) { var dummy; dummy=p2; p2=p3; p3=dummy; } var tubeNum=rSegNum*tSegNum*2*3 * 3; var parity=-1.; var zopfPeriods = 1.; var i=Math.floor(idx/(tubeNum))%trNum; { var pos1, pos2, tan1, tan2; var R0 = .23; if (i==0) { pos1=mix3(p1,p2,R0); pos2=mix3(p1,p3,R0); parity=-1.; zopfPeriods = 1.; tan1=scale3(normalize3(add3(cross(pos1,sub3(p2,p1)),scale3(pos1,.25))),-1.); tan2=scale3(normalize3(add3(cross(pos2,sub3(p3,p1)),scale3(pos2,.25))),-1.); } if (i==1) { pos1=mix3(p1,p2,1.-R0); pos2=mix3(p1,p3,1.-R0); parity=1.; zopfPeriods = 3.; tan1=scale3(normalize3(add3(cross(pos1,sub3(p2,p1)),scale3(pos1,-.25))),-1.); tan2=scale3(normalize3(add3(cross(pos2,sub3(p3,p1)),scale3(pos2,-.25))),-1.); } if (i==2) { pos1=mix3(p2,p3,R0); pos2=mix3(p3,p2,R0); parity=-1.; zopfPeriods = 3.; tan1=scale3(normalize3(add3(cross(pos1,sub3(p3,p2)),scale3(pos1,.25))),-1.); tan2=scale3(normalize3(add3(cross(pos2,sub3(p2,p3)),scale3(pos2,.25))),-1.); } var pn = geomTangentZopf(pos1,pos2,tan1,tan2,radius,radius,rSegNum,tSegNum, idx%tubeNum,parity,zopfPeriods); 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 * 3; // 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(RadialSegs,TangentialSegs,Subdiv,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 = RadialSegs*TangentialSegs*3*20*Math.pow(4,Subdiv)*3; 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=transformVecByQuat(p0,objQuat); p1=transformVecByQuat(p1,objQuat); p2=transformVecByQuat(p2,objQuat); p3=transformVecByQuat(p3,objQuat); 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 = polygons.create(); p.addPoints([p0[0], p0[1]], [p1[0], p1[1]], [p2[0], p2[1]], [p3[0], p3[1]]); p.addSegments([p0[0], p0[1]], [p1[0], p1[1]], [p2[0], p2[1]], [p3[0], p3[1]]); polygons.draw(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" // Optimizations and code clean-up by ge1doot //////////////////////////////////////////////////////////////// function Polygons() { const polygonList = []; const linesDrawn = []; const Polygon = class { constructor() { this.cp = []; // clip path: array of [x,y] pairs this.dp = []; // 2d line to draw this.aabb = []; // AABB bounding box } addPoints(...points) { for (let i = 0; i < points.length; i++) this.cp.push(points[i]); this.aabb = this.AABB(); } addSegments(...points) { for (let i = 0; i < points.length; i++) this.dp.push(points[i]); } addOutline(s = 0) { for (let i = s, l = this.cp.length; i < l; i++) { this.dp.push(this.cp[i], this.cp[(i + 1) % l]); } } createPoly(x, y, c, r, a) { this.cp.length = 0; 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 ]); } this.aabb = this.AABB(); } draw(t) { if (this.dp.length === 0) return; for (let i = 0, l = this.dp.length; i < l; i+=2) { const d0 = this.dp[i]; const d1 = this.dp[i + 1]; const line_hash = Math.min(d0[0], d1[0]).toFixed(2) + "-" + Math.max(d0[0], d1[0]).toFixed(2) + "-" + Math.min(d0[1], d1[1]).toFixed(2) + "-" + Math.max(d0[1], d1[1]).toFixed(2); if (!linesDrawn[line_hash]) { t.penup(); t.goto(d0); t.pendown(); t.goto(d1); linesDrawn[line_hash] = true; } } } AABB() { let xmin = 2000; let xmax = -2000; let ymin = 2000; let ymax = -2000; for (let i = 0, l = this.cp.length; i < l; i++) { const x = this.cp[i][0]; const y = this.cp[i][1]; if (x < xmin) xmin = x; if (x > xmax) xmax = x; if (y < ymin) ymin = y; if (y > ymax) ymax = y; } // Bounding box: center x, center y, half w, half h return [ (xmin + xmax) * 0.5, (ymin + ymax) * 0.5, (xmax - xmin) * 0.5, (ymax - ymin) * 0.5 ]; } addHatching(a, d) { const tp = new Polygon(); tp.cp.push( [this.aabb[0] - this.aabb[2], this.aabb[1] - this.aabb[3]], [this.aabb[0] + this.aabb[2], this.aabb[1] - this.aabb[3]], [this.aabb[0] + this.aabb[2], this.aabb[1] + this.aabb[3]], [this.aabb[0] - this.aabb[2], this.aabb[1] + this.aabb[3]] ); const dx = Math.sin(a) * d, dy = Math.cos(a) * d; const cx = Math.sin(a) * 200, cy = Math.cos(a) * 200; for (let i = 0.5; i < 150 / d; i++) { tp.dp.push([dx * i + cy, dy * i - cx], [dx * i - cy, dy * i + cx]); tp.dp.push([-dx * i + cy, -dy * i - cx], [-dx * i - cy, -dy * i + cx]); } tp.boolean(this, false); for (let i = 0, l = tp.dp.length; i < l; i++) this.dp.push(tp.dp[i]); } inside(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 ( this.vec2_find_segment_intersect( p, p1, this.cp[i], this.cp[(i + 1) % l] ) !== false ) { int++; } } return int & 1; } boolean(p, diff = true) { // polygon diff algorithm (narrow phase) const ndp = []; for (let i = 0, l = this.dp.length; i < l; i+=2) { const ls0 = this.dp[i]; const ls1 = this.dp[i + 1]; // find all intersections with clip path const int = []; for (let j = 0, cl = p.cp.length; j < cl; j++) { const pint = this.vec2_find_segment_intersect( ls0, ls1, p.cp[j], p.cp[(j + 1) % cl] ); if (pint !== false) { int.push(pint); } } if (int.length === 0) { // 0 intersections, inside or outside? if (diff === !p.inside(ls0)) { ndp.push(ls0, ls1); } } else { int.push(ls0, ls1); // order intersection points on line ls.p1 to ls.p2 const cmpx = ls1[0] - ls0[0]; const cmpy = ls1[1] - ls0[1]; for (let i = 0, len = int.length; i < len; i++) { let j = i; const item = int[j]; for ( const db = (item[0] - ls0[0]) * cmpx + (item[1] - ls0[1]) * cmpy; j > 0 && (int[j - 1][0] - ls0[0]) * cmpx + (int[j - 1][1] - ls0[1]) * cmpy < db; j-- ) int[j] = int[j - 1]; int[j] = item; } for (let j = 0; j < int.length - 1; j++) { if ( (int[j][0] - int[j + 1][0]) ** 2 + (int[j][1] - int[j + 1][1]) ** 2 >= 0.01 ) { if ( diff === !p.inside([ (int[j][0] + int[j + 1][0]) / 2, (int[j][1] + int[j + 1][1]) / 2 ]) ) { ndp.push(int[j], int[j + 1]); } } } } } this.dp = ndp; return this.dp.length > 0; } //port of http://paulbourke.net/geometry/pointlineplane/Helpers.cs 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]); if (d === 0) return false; 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]); 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; } }; return { list() { return polygonList; }, create() { return new Polygon(); }, draw(turtle, p) { let vis = true; for (let j = 0; j < polygonList.length; j++) { const p1 = polygonList[j]; // AABB overlapping test - still O(N2) but very fast if ( Math.abs(p1.aabb[0] - p.aabb[0]) - (p.aabb[2] + p1.aabb[2]) < 0 && Math.abs(p1.aabb[1] - p.aabb[1]) - (p.aabb[3] + p1.aabb[3]) < 0 ) { if (p.boolean(p1) === false) { vis = false; break; } } } if (vis) { p.draw(turtle); polygonList.push(p); } } }; }