From d39244d308513230ba2dd51e9c2b00bf4553a088 Mon Sep 17 00:00:00 2001 From: Aaron Fenyes Date: Sat, 6 Jul 2024 21:35:09 -0700 Subject: [PATCH] Host Ganja.js locally --- engine-proto/ConstructionViewer.jl | 8 +- engine-proto/gram-test/ganja-1.0.204.js | 1913 +++++++++++++++++++++++ 2 files changed, 1919 insertions(+), 2 deletions(-) create mode 100644 engine-proto/gram-test/ganja-1.0.204.js diff --git a/engine-proto/ConstructionViewer.jl b/engine-proto/ConstructionViewer.jl index bdd35fd..29af212 100644 --- a/engine-proto/ConstructionViewer.jl +++ b/engine-proto/ConstructionViewer.jl @@ -65,8 +65,12 @@ mutable struct ConstructionViewer } """) - # load Ganja.js - loadjs!(win, "https://unpkg.com/ganja.js") + # load Ganja.js. for an automatically updated web-hosted version, load from + # + # https://unpkg.com/ganja.js + # + # instead + loadjs!(win, "http://localhost:8000/ganja-1.0.204.js") # create global functions and variables script!(win, """ diff --git a/engine-proto/gram-test/ganja-1.0.204.js b/engine-proto/gram-test/ganja-1.0.204.js new file mode 100644 index 0000000..1e95e42 --- /dev/null +++ b/engine-proto/gram-test/ganja-1.0.204.js @@ -0,0 +1,1913 @@ +/** Ganja.js - Geometric Algebra - Not Just Algebra. + * @author Enki + * @link https://github.com/enkimute/ganja.js + */ + +/*********************************************************************************************************************/ +// +// Ganja.js is an Algebra generator for javascript. It generates a wide variety of Algebra's and supports operator +// overloading, algebraic literals and a variety of graphing options. +// +// Ganja.js is designed with prototyping and educational purposes in mind. Clean mathematical syntax is the primary +// target. +// +// Ganja.js exports only one function called *Algebra*. This function is used to generate Algebra classes. (say complex +// numbers, minkowski or 3D CGA). The returned class can be used to create, add, multiply etc, but also to upgrade +// javascript functions with algebraic literals, operator overloading, vectors, matrices and much more. +// +// As a simple example, multiplying two complex numbers 3+2i and 1+4i could be done like this : +// +// var complex = Algebra(0,1); +// var a = new complex([3,2]); +// var b = new complex([1,3]); +// var result = a.Mul(b); +// +// But the same can be written using operator overloading and algebraic literals. (where scientific notation with +// lowercase e is overloaded to directly specify generators (e1, e2, e12, ...)) +// +// var result = Algebra(0,1,()=>(3+2e1)*(1+4e1)); +// +// Please see github for user documentation and examples. +// +/*********************************************************************************************************************/ + +// Documentation below is for implementors. I'll assume you know about Clifford Algebra's, grades, its products, etc .. +// I'll also assume you are familiar with ES6. My style may feel a bith mathematical, advise is to read slow. + +(function (name, context, definition) { + if (typeof module != 'undefined' && module.exports) module.exports = definition(); + else if (typeof define == 'function' && define.amd) define(name, definition); + else context[name] = definition(); +}('Algebra', this, function () { + +/** Some helpers for eigenvalues for bivector split in high-d spaces **/ + function QR(M) { + // helpers + const {abs,sqrt} = Math; + const hyp = (a,b)=>abs(a)>abs(b)?abs(a)*sqrt(1+(b/a)**2):b==0?0:abs(b)*sqrt(1+(a/b)**2); + const [m,n] = [M.length, M[0].length]; + var qr = M.map(r=>r.map(c=>c)), Q = M.map(r=>r.map(c=>0)), R = M.map(r=>r.map(c=>0)), d = [], k, i, j, nrm; + // helper matrix + for (k=0; k=0; --k) { + for (i=0; i{ + var res = A.map(r=>r.map(c=>0)); + for(let i=0;iA[i][i]); + } + +/** The Algebra class generator. Possible calling signatures : + * Algebra([func]) => algebra with no dimensions, i.e. R. Optional function for the translator. + * Algebra(p,[func]) => 'p' positive dimensions and an optional function to pass to the translator. + * Algebra(p,q,[func]) => 'p' positive and 'q' negative dimensions and optional function. + * Algebra(p,q,r,[func]) => 'p' positive, 'q' negative and 'r' zero dimensions and optional function. + * Algebra({ => for custom basis, cayley, mixing, etc pass in an object as first parameter. + * [p:p], => optional 'p' for # of positive dimensions + * [q:q], => optional 'q' for # of negative dimensions + * [r:r], => optional 'r' for # of zero dimensions + * [metric:array], => alternative for p,q,r. e.g. ([1,1,1,-1] for spacetime) + * [basis:array], => array of strings with basis names. (e.g. ['1','e1','e2','e12']) + * [Cayley:Cayley], => optional custom Cayley table (strings). (e.g. [['1','e1'],['e1','-1']]) + * [mix:boolean], => Allows mixing of various algebras. (for space efficiency). + * [graded:boolean], => Use a graded algebra implementation. (automatic for +6D) + * [baseType:Float32Array] => optional basetype to use. (only for flat generator) + * },[func]) => optional function for the translator. + **/ + return function Algebra(p,q,r) { + // Resolve possible calling signatures so we know the numbers for p,q,r. Last argument can always be a function. + var fu=arguments[arguments.length-1],options=p; if (options instanceof Object) { + q = (p.q || (p.metric && p.metric.filter(x=>x==-1).length))| 0; + r = (p.r || (p.metric && p.metric.filter(x=>x==0).length)) | 0; + p = p.p === undefined ? (p.metric && p.metric.filter(x=>x==1).length) || 0 : p.p || 0; + } else { options={}; p=p|0; r=r|0; q=q|0; }; + + // Support for multi-dual-algebras + if (options.dual || (p==0 && q==0 && r<0)) { r=options.dual=options.dual||-r; // Create a dual number algebra if r<0 (old) or options.dual set(new) + options.basis = [...Array(r+1)].map((a,i)=>i?'e0'+i:'1'); options.metric = [1,...Array(r)]; options.tot=r+1; + options.Cayley = [...Array(r+1)].map((a,i)=>[...Array(r+1)].map((y,j)=>i*j==0?((i+j)?'e0'+(i+j):'1'):'0')); + } + if (options.over) options.baseType = Array; + + // Calculate the total number of dimensions. + var tot = options.tot = (options.tot||(p||0)+(q||0)+(r||0)||(options.basis&&options.basis.length))|0; + + // Unless specified, generate a full set of Clifford basis names. We generate them as an array of strings by starting + // from numbers in binary representation and changing the set bits into their relative position. + // Basis names are ordered first per grade, then lexically (not cyclic!). + // For 10 or more dimensions all names will be double digits ! 1e01 instead of 1e1 .. + var basis=(options.basis&&(options.basis.length==2**tot||r<0||options.Cayley)&&options.basis)||[...Array(2**tot)] // => [undefined, undefined, undefined, undefined, undefined, undefined, undefined, undefined] + .map((x,xi)=>(((1<<30)+xi).toString(2)).slice(-tot||-1) // => ["000", "001", "010", "011", "100", "101", "110", "111"] (index of array in base 2) + .replace(/./g,(a,ai)=>a=='0'?'':String.fromCharCode(66+ai-(r!=0)))) // => ["", "3", "2", "23", "1", "13", "12", "123"] (1 bits replaced with their positions, 0's removed) + .sort((a,b)=>(a.toString().length==b.toString().length)?(a>b?1:b>a?-1:0):a.toString().length-b.toString().length) // => ["", "1", "2", "3", "12", "13", "23", "123"] (sorted numerically) + .map(x=>x&&'e'+(x.replace(/./g,x=>('0'+(x.charCodeAt(0)-65)).slice(tot>9?-2:-1) ))||'1') // => ["1", "e1", "e2", "e3", "e12", "e13", "e23", "e123"] (converted to commonly used basis names) + + // See if the basis names start from 0 or 1, store grade per component and lowest component per grade. + var low=basis.length==1?1:basis[1].match(/\d+/g)[0]*1, + grades=options.grades||(options.dual&&basis.map((x,i)=>i?1:0))||basis.map(x=>tot>9?(x.length-1)/2:x.length-1), + grade_start=grades.map((a,b,c)=>c[b-1]!=a?b:-1).filter(x=>x+1).concat([basis.length]); + + // String-simplify a concatenation of two basis blades. (and supports custom basis names e.g. e21 instead of e12) + // This is the function that implements e1e1 = +1/-1/0 and e1e2=-e2e1. The brm function creates the remap dictionary. + var simplify = (s,p,q,r)=>{ + var sign=1,c,l,t=[],f=true,ss=s.match(tot>9?/(\d\d)/g:/(\d)/g);if (!ss) return s; s=ss; l=s.length; + while (f) { f=false; + // implement Ex*Ex = metric. + for (var i=0; i=(p+r)) sign*=-1; else if ((s[i]-low)t[i+1]) { c=t[i];t[i]=t[i+1];t[i+1]=c;sign*=-1;f=true; break;} if (f) { s=t;t=[];l=s.length; } + } + var ret=(sign==0)?'0':((sign==1)?'':'-')+(t.length?'e'+t.join(''):'1'); return (brm&&brm[ret])||(brm&&brm['-'+ret]&&'-'+brm['-'+ret])||ret; + }, + brm=(x=>{ var ret={}; for (var i in basis) ret[basis[i]=='1'?'1':simplify(basis[i],p,q,r)] = basis[i]; return ret; })(basis); + + // As an alternative to the string fiddling, one can also bit-fiddle. In this case the basisvectors are represented by integers with 1 bit per generator set. + var simplify_bits = (A,B,p2)=>{ var n=p2||(p+q+r),t=0,ab=A&B,res=A^B; if (ab&((1<>1); t&=B; t^=ab>>(p+r); t^=t>>16; t^=t>>8; t^=t>>4; return [1-2*(27030>>(t&15)&1),res]; }, + bc = (v)=>{ v=v-((v>>1)& 0x55555555); v=(v&0x33333333)+((v>>2)&0x33333333); var c=((v+(v>>4)&0xF0F0F0F)*0x1010101)>>24; return c }; + + if (!options.graded && tot <= 6 || options.graded===false || options.Cayley) { + // Faster and degenerate-metric-resistant dualization. (a remapping table that maps items into their duals). + var drm=basis.map((a,i)=>{ return {a:a,i:i} }) + .sort((a,b)=>a.a.length>b.a.length?1:a.a.lengthx.i).reverse(), + drms=drm.map((x,i)=>(x==0||i==0)?1:simplify(basis[x]+basis[i])[0]=='-'?-1:1); + + /// Store the full metric (also for bivectors etc ..) + var metric = options.Cayley&&options.Cayley.map((x,i)=>x[i]) || basis.map((x,xi)=>simplify(x+x,p,q,r)|0); metric[0]=1; + + /// Generate multiplication tables for the outer and geometric products. + var mulTable = options.Cayley||basis.map(x=>basis.map(y=>(x==1)?y:(y==1)?x:simplify(x+y,p,q,r))); + + // subalgebra support. (must be bit-order basis blades, does no error checking.) + if (options.even) options.basis = basis.filter(x=>x.length%2==1); + if (options.basis && !options.Cayley && r>=0 && options.basis.length != 2**tot) { + metric = metric.filter((x,i)=>options.basis.indexOf(basis[i])!=-1); + mulTable = mulTable.filter((x,i)=>options.basis.indexOf(basis[i])!=-1).map(x=>x.filter((x,i)=>options.basis.indexOf(basis[i])!=-1)); + basis = options.basis; + } + + /// Convert Cayley table to product matrices. The outer product selects the strict sum of the GP (but without metric), the inner product + /// is the left contraction. + var gp=basis.map(x=>basis.map(x=>'0')), cp=gp.map(x=>gp.map(x=>'0')), cps=gp.map(x=>gp.map(x=>'0')), op=gp.map(x=>gp.map(x=>'0')), gpo={}; // Storage for our product tables. + basis.forEach((x,xi)=>basis.forEach((y,yi)=>{ var n = mulTable[xi][yi].replace(/^-/,''); if (!gpo[n]) gpo[n]=[]; gpo[n].push([xi,yi]); })); + basis.forEach((o,oi)=>{ + gpo[o].forEach(([xi,yi])=>op[oi][xi]=(grades[oi]==grades[xi]+grades[yi])?((mulTable[xi][yi]=='0')?'0':((mulTable[xi][yi][0]!='-')?'':'-')+'b['+yi+']*this['+xi+']'):'0'); + gpo[o].forEach(([xi,yi])=>{ + gp[oi][xi] =((gp[oi][xi]=='0')?'':gp[oi][xi]+'+') + ((mulTable[xi][yi]=='0')?'0':((mulTable[xi][yi][0]!='-')?'':'-')+'b['+yi+']*this['+xi+']'); + cp[oi][xi] =((cp[oi][xi]=='0')?'':cp[oi][xi]+'+') + ((grades[oi]==grades[yi]-grades[xi])?gp[oi][xi]:'0'); + cps[oi][xi]=((cps[oi][xi]=='0')?'':cps[oi][xi]+'+') + ((grades[oi]==Math.abs(grades[yi]-grades[xi]))?gp[oi][xi]:'0'); + }); + }); + + /// Flat Algebra Multivector Base Class. + var generator = class MultiVector extends (options.baseType||Float32Array) { + /// constructor - create a floating point array with the correct number of coefficients. + constructor(a) { super(a||basis.length); return this; } + + /// grade selection - return a only the part of the input with the specified grade. + Grade(grade,res) { res=res||new this.constructor(); for (var i=0,l=res.length; i1e-10) res.push(((this[i]==1)&&i?'':((this[i]==-1)&&i)?'-':(this[i].toFixed(10)*1))+(i==0?'':tot==1&&q==1?'i':basis[i].replace('e','e_'))); return res.join('+').replace(/\+-/g,'-')||'0'; } + + /// Reversion, Involutions, Conjugation for any number of grades, component acces shortcuts. + get Negative (){ var res = new this.constructor(); for (var i=0; ia[drm[i]]*drms[i]); var res = new this.constructor(); res[res.length-1]=1; return this.Mul(res); }; + get UnDual (){ if (r) return this.map((x,i,a)=>a[drm[i]]*drms[a.length-i-1]); var res = new this.constructor(); res[res.length-1]=1; return this.Div(res); }; + get Length (){ return options.over?Math.sqrt(Math.abs(this.Mul(this.Conjugate).s.s)):Math.sqrt(Math.abs(this.Mul(this.Conjugate).s)); }; + get VLength (){ var res = 0; for (var i=0; i'res['+xi+']=b['+xi+']+this['+xi+']').join(';\n').replace(/(b|this)\[(.*?)\]/g,(a,b,c)=>options.mix?'('+b+'.'+(c|0?basis[c]:'s')+'||0)':a)+';\nreturn res') + generator.prototype.Scale = new Function('b,res','res=res||new this.constructor();\n'+basis.map((x,xi)=>'res['+xi+']=b*this['+xi+']').join(';\n').replace(/(b|this)\[(.*?)\]/g,(a,b,c)=>options.mix?'('+b+'.'+(c|0?basis[c]:'s')+'||0)':a)+';\nreturn res') + generator.prototype.Sub = new Function('b,res','res=res||new this.constructor();\n'+basis.map((x,xi)=>'res['+xi+']=this['+xi+']-b['+xi+']').join(';\n').replace(/(b|this)\[(.*?)\]/g,(a,b,c)=>options.mix?'('+b+'.'+(c|0?basis[c]:'s')+'||0)':a)+';\nreturn res') + generator.prototype.Mul = new Function('b,res','res=res||new this.constructor();\n'+gp.map((r,ri)=>'res['+ri+']='+r.join('+').replace(/\+\-/g,'-').replace(/(\w*?)\[(.*?)\]/g,(a,b,c)=>options.mix?'('+b+'.'+(c|0?basis[c]:'s')+'||0)':a).replace(/\+0/g,'')+';').join('\n')+'\nreturn res;'); + generator.prototype.LDot = new Function('b,res','res=res||new this.constructor();\n'+cp.map((r,ri)=>'res['+ri+']='+r.join('+').replace(/\+\-/g,'-').replace(/\+0/g,'').replace(/(\w*?)\[(.*?)\]/g,(a,b,c)=>options.mix?'('+b+'.'+(c|0?basis[c]:'s')+'||0)':a)+';').join('\n')+'\nreturn res;'); + generator.prototype.Dot = new Function('b,res','res=res||new this.constructor();\n'+cps.map((r,ri)=>'res['+ri+']='+r.join('+').replace(/\+\-/g,'-').replace(/\+0/g,'').replace(/(\w*?)\[(.*?)\]/g,(a,b,c)=>options.mix?'('+b+'.'+(c|0?basis[c]:'s')+'||0)':a)+';').join('\n')+'\nreturn res;'); + generator.prototype.Wedge = new Function('b,res','res=res||new this.constructor();\n'+op.map((r,ri)=>'res['+ri+']='+r.join('+').replace(/\+\-/g,'-').replace(/\+0/g,'').replace(/(\w*?)\[(.*?)\]/g,(a,b,c)=>options.mix?'('+b+'.'+(c|0?basis[c]:'s')+'||0)':a)+';').join('\n')+'\nreturn res;'); +// generator.prototype.Vee = new Function('b,res','res=res||new this.constructor();\n'+op.map((r,ri)=>'res['+drm[ri]+']='+r.map(x=>x.replace(/\[(.*?)\]/g,function(a,b){return '['+(drm[b|0])+']'})).join('+').replace(/\+\-/g,'-').replace(/\+0/g,'').replace(/(\w*?)\[(.*?)\]/g,(a,b,c)=>options.mix?'('+b+'.'+(c|0?basis[c]:'s')+'||0)':a)+';').join('\n')+'\nreturn res;'); + /// Conforms to the new Chapter 11 now. + generator.prototype.Vee = new Function('b,res',('res=res||new this.constructor();\n'+op.map((r,ri)=>'res['+drm[ri]+']='+drms[ri]+'*('+r.map(x=>x.replace(/\[(.*?)\]/g,function(a,b){return '['+(drm[b|0])+']'+(drms[b|0]>0?"":"*-1")})).join('+').replace(/\+\-/g,'-').replace(/\+0/g,'').replace(/(\w*?)\[(.*?)\]/g,(a,b,c)=>options.mix?'('+b+'.'+(c|0?basis[c]:'s')+'||0)':a)+');').join('\n')+'\nreturn res;').replace(/(b\[)|(this\[)/g,a=>a=='b['?'this[':'b[')); + generator.prototype.eigenValues = eigenValues; + + /// Add getter and setters for the basis vectors/bivectors etc .. + basis.forEach((b,i)=>Object.defineProperty(generator.prototype, i?b:'s', { + configurable: true, get(){ return this[i] }, set(x){ this[i]=x; } + })); + + /// Graded generator for high-dimensional algebras. + } else { + + /// extra graded lookups. + var basisg = grade_start.slice(0,grade_start.length-1).map((x,i)=>basis.slice(x,grade_start[i+1])); + var counts = grade_start.map((x,i,a)=>i==a.length-1?0:a[i+1]-x).slice(0,tot+1); + var basis_bits = basis.map(x=>x=='1'?0:x.slice(1).match(tot>9?/\d\d/g:/\d/g).reduce((a,b)=>a+(1<<(b-low)),0)), + bits_basis = []; basis_bits.forEach((b,i)=>bits_basis[b]=i); + var metric = basisg.map((x,xi)=>x.map((y,yi)=>simplify_bits(basis_bits[grade_start[xi]+yi],basis_bits[grade_start[xi]+yi])[0])); + var drms = basisg.map((x,xi)=>x.map((y,yi)=>simplify_bits(basis_bits[grade_start[xi]+yi],(~basis_bits[grade_start[xi]+yi])&((1<(typeof x=="string")?"-"+x:-x):undefined):this[i]; + else { if (r[i]==undefined) r[i]=[]; for(var j=0,m=Math.max(this[i].length,b[i].length);jx&&x.map(y=>typeof y=="string"?y+"*"+s:y*s)); } + + // geometric product. + Mul(b,r) { + r=r||new this.constructor(); var gotstring=false; + for (var i=0,x,gsx; gsx=grade_start[i],x=this[i],ig.map(e=>e&&(!(e+'').match(/-{0,1}\w+/))?'('+e+')':e)) + return r; + } + // outer product. + Wedge(b,r) { + r=r||new this.constructor(); + for (var i=0,x,gsx; gsx=grade_start[i],x=this[i],ix).sort((a,b)=>((a.match(/\d+/)[0]|0)-(b.match(/\d+/)[0]|0))||((a.match(/\d+$/)[0]|0)-(b.match(/\d+$/)[0]|0))).map(x=>x.replace(/\/\/\d+$/,'')); + var r2 = 'float sum=0.0; float res=0.0;\n', g=0; + r.forEach(x=>{ + var cg = x.match(/\d+/)[0]|0; + if (cg != g) r2 += "sum += res*res;\nres = 0.0;\n"; + r2 += x.replace(/\[\d+\]/,'') + '\n'; + g=cg; + }); + r2+= "sum += res*res;\n"; + return r2; + } + // Inner product glsl output. + IPNS_GLSL(b,point_source) { + var r='',count=0,curg; + for (var i=0,x,gsx; gsx=grade_start[i],x=this[i],ix).sort((a,b)=>((a.match(/\d+/)[0]|0)-(b.match(/\d+/)[0]|0))||((a.match(/\d+$/)[0]|0)-(b.match(/\d+$/)[0]|0))).map(x=>x.replace(/\/\/\d+$/,'')); + var r2 = 'float sum=0.0; float res=0.0;\n', g=0; + r.forEach(x=>{ + var cg = x.match(/\d+/)[0]|0; + if (cg != g) r2 += "sum += res*res;\nres = 0.0;\n"; + r2 += x.replace(/\[\d+\]/,'') + '\n'; + g=cg; + }); + r2+= "sum += res*res;\n"; + return r2; + } + // Left contraction. + LDot(b,r) { + r=r||new this.constructor(); + for (var i=0,x,gsx; gsx=grade_start[i],x=this[i],ig&&g.map((c,ci)=>!c?undefined:((c+'').match(/[\+\-\*]/)?'('+c+')':c)+(gi==0?"":basisg[gi][ci])).filter(x=>x).join('+')).filter(x=>x).join('+').replace(/\+\-/g,'-')||"0"; } + get s () { if (this[0]) return this[0][0]||0; return 0; } + get Length () { var res=0; this.forEach((g,gi)=>g&&g.forEach((e,ei)=>res+=(e||0)**2*metric[gi][ei])); return Math.abs(res)**.5; } + get VLength () { var res=0; this.forEach((g,gi)=>g&&g.forEach((e,ei)=>res+=(e||0)**2)); return Math.abs(res)**.5; } + get Reverse () { var r=new this.constructor(); this.forEach((x,gi)=>x&&x.forEach((e,ei)=>{if(!r[gi])r[gi]=[]; r[gi][ei] = this[gi][ei]*[1,1,-1,-1][gi%4]; })); return r; } + get Involute () { var r=new this.constructor(); this.forEach((x,gi)=>x&&x.forEach((e,ei)=>{if(!r[gi])r[gi]=[]; r[gi][ei] = this[gi][ei]*[1,-1,1,-1][gi%4]; })); return r; } + get Conjugate () { var r=new this.constructor(); this.forEach((x,gi)=>x&&x.forEach((e,ei)=>{if(!r[gi])r[gi]=[]; r[gi][ei] = this[gi][ei]*[1,-1,-1,1][gi%4]; })); return r; } + get Dual() { var r=new this.constructor(); this.forEach((g,gi)=>{ if (!g) return; r[tot-gi]=[]; g.forEach((e,ei)=>r[tot-gi][counts[gi]-1-ei]=drms[gi][ei]*e); }); return r; } + get Normalized () { return this.Scale(1/this.Length); } + } + + + // This generator is UNDER DEVELOPMENT - I'm publishing it so I can test on observable. + } + + // Generate a new class for our algebra. It extends the javascript typed arrays (default float32 but can be specified in options). + var res = class Element extends generator { + + // constructor - create a floating point array with the correct number of coefficients. + constructor(a) { super(a); if (this.upgrade) this.upgrade(); return this; } + + // Grade selection. (implemented by parent class). + Grade(grade,res) { res=res||new Element(); return super.Grade(grade,res); } + + // Right and Left divide - Defined on the elements, shortcuts to multiplying with the inverse. + Div (b,res) { return this.Mul(b.Inverse,res); } + LDiv (b,res) { return b.Inverse.Mul(this,res); } + + + // Bivector split - we handle all real cases, still have to add the complex cases for those exception scenarios. + Split (iter=50) { + var k = Math.floor((p+q+r)/2), OB = this.map(x=>x), B = this.map(x=>x), m = 1; + var Wi = [...Array(k)].map((r,i)=>{ m = m*(i+1); var Wi = B.Scale(1/m); B = B.Wedge(OB); return Wi; }); + if (k<3) { // The quadratic case is easy to solve. (for spaces <6D) + var TDT = this.Dot(this).s, TWT = this.Wedge(this); + if (TWT.VLength < 1E-5) return [this]; // bivector was simple. + var D = 0.5*Math.sqrt( TDT**2 - TWT.Mul(TWT).s ); + var eigen = [0.5*TDT + D, 0.5*TDT - D].sort((a,b)=>Math.abs(a)6D, closed form solutions of the characteristic polyn. are impossible, use eigenvalues of companion matrix. + var Wis = Wi.map((W,i)=>W.Mul(W).s*(-1)**(k-i+(k%2)) ); + var matrix = [...Array(k)].map((r,i)=>[...Array(k)].map((c,j)=>(j == k-1)?Wis[k-i-1]:(i-1==j)?1:0)); + var eigen = eigenValues(matrix,iter).sort((a,b)=>Math.abs(a){ + var r = Math.floor(k/2), N = Element.Scalar(0), DN = Element.Scalar(0); + for (var i=0; i<=r; ++i) { N.Add( Wi[2*i+1].Scale(v**(r-i)), N); DN.Add( Wi[2*i].Scale(v**(r-i)), DN); } + if (DN.VLength == 0) return Element.Scalar(0); + var ret = N.Div(DN); sum.Add(ret, sum); return ret; + }); + return [this.Sub(sum),...res]; // Smallest eigvalue becomes B-rest + } + + // Factorize a motor + Factorize (iter=50) { + var S = this.Grade(2).Split(iter); + var P = this.Scale(1); + // if (P.s) { + var R = S.slice(0,S.length-1).map((Si,i)=>{ + var Mi = Element.Scalar(P.s).Add(Si); + var scale = Math.sqrt(Mi.Reverse.Mul(Mi).s); + return Mi.Scale(1/scale); + }); + R.push( R.reduce((tot,fact)=>tot.Mul(fact.Reverse), Element.Scalar(1)).Mul(P) ); + // } + return R; + } + + // exp - closed form exp. + Exp (taylor = false) { + if (r==1 && tot<=4 && Math.abs(this[0])<1E-9 && !options.over && !taylor) { + // https://www.researchgate.net/publication/360528787_Normalization_Square_Roots_and_the_Exponential_and_Logarithmic_Maps_in_Geometric_Algebras_of_Less_than_6D + // 0 1 2 3 4 5 + // 5 6 7 8 9 10 + var l = (this[8]*this[8] + this[9]*this[9] + this[10]*this[10]); + if (l==0) return new Element([1, 0,0,0,0, this[5], this[6], this[7], 0, 0, 0, 0,0,0,0, 0]); + var m = (this[5]*this[10] + this[6]*this[9] + this[7]*this[8]), a = Math.sqrt(l), c = Math.cos(a), s = Math.sin(a)/a, t = m/l*(c-s); + var test = Element.Element(c, 0,0,0,0, s*this[5] + t*this[10], s*this[6] + t*this[9], s*this[7] + t*this[8], s*this[8], s*this[9], s*this[10], 0,0,0,0, m*s); + //return test; // tbc .. investigate pss coeff?? + + var u = Math.sqrt(Math.abs(this.Dot(this).s)); if (Math.abs(u)<1E-5) return this.Add(Element.Scalar(1)); + var v = this.Wedge(this).Scale(-1/(2*u)); + var res2 = Element.Add(Element.Sub(Math.cos(u),v.Scale(Math.sin(u))),Element.Div(Element.Mul((Element.Add(Math.sin(u),v.Scale(Math.cos(u)))),this),(Element.Add(u,v)))); + //if ([...test].map(x=>x.toFixed(1))+'' != [...res2].map(x=>x.toFixed(1))+'') { console.log(test, res2); debugger } + + return res2; + } + if (!taylor && Math.abs(this[0])<1E-9 && !options.over) { + return this.Grade(2).Split().reduce((total,simple)=>{ + var square = simple.Mul(simple).s, len = Math.sqrt(Math.abs(square)); + if (len <= 1E-5) return total.Mul(Element.Scalar(1).Add(simple)); + if (square < 0) return total.Mul(Element.Scalar(Math.cos(len)).Add(simple.Scale(Math.sin(len)/len)) ); + return total.Mul(Element.Scalar(Math.cosh(len)).Add(simple.Scale(Math.sinh(len)/len)) ); + },Element.Scalar(1)); + } + if (options.dual) { var f=Math.exp(this.s); return this.map((x,i)=>i?x*f:f); } + var res = Element.Scalar(1), y=1, M= this.Scale(1), N=this.Scale(1); for (var x=1; x<15; x++) { res=res.Add(M.Scale(1/y)); M=M.Mul(N); y=y*(x+1); }; + return res; + } + + // Log - only for up to 3D PGA for now + Log (compat = false) { + if (options.over) return; + if (!compat) { + if (tot==4 && q==0 && r==1 && !options.over) { // https://www.researchgate.net/publication/360528787_Normalization_Square_Roots_and_the_Exponential_and_Logarithmic_Maps_in_Geometric_Algebras_of_Less_than_6D + if (Math.abs(this.s)>=.99999) return Element.Bivector(this[5],this[6],this[7],0,0,0).Scale(Math.sign(this.s)); + var a = 1/(1 - this[0]*this[0]), b = Math.acos(this[0])*Math.sqrt(a), c = a*this[15]*(1 - this[0]*b); + return Element.Bivector( c*this[10] + b*this[5], -c*this[9] + b*this[6], c*this[8] + b*this[7], b*this[8], b*this[9], b*this[10] ); + } + return this.Factorize().reduce((sum,bi)=>{ + var [ci,si] = [bi.s, bi.Grade(2)]; + var square = si.Mul(si).s; + var len = Math.sqrt(Math.abs(square)); + if (Math.abs(square) < 1E-5) return sum.Add(si); + if (square < 0) return sum.Add(si.Scale(Math.acos(ci)/len)); + return sum.Add(si.Scale(Math.acosh(ci)/len)); + },Element.Scalar(0)); + } + var b = this.Grade(2), bdb = Element.Dot(b,b).s; + if (Math.abs(bdb)<=1E-5) return this.s<0?b.Scale(-1):b; + var s = Math.sqrt(-bdb), bwb = Element.Wedge(b,b); + if (Math.abs(bwb[bwb.length-1])<=1E-5 || Math.abs(this.s)<=1E-5) return b.Scale(Math.atan2(s,this.s)/s); + var p = bwb.Scale(-1/(2*s)); + return Element.Mul(Element.Mul((Element.Add(Math.atan2(s,this.s),p.Scale(1/this.s))),b),Element.Sub(s,p)).Scale(1/(s*s)); + } + + // Helper for efficient inverses. (custom involutions - negates grades in arguments). + Map () { var res=new Element(); return super.Map(res,...arguments); } + + // Factories - Make it easy to generate vectors, bivectors, etc when using the functional API. None of the examples use this but + // users that have used other GA libraries will expect these calls. The Coeff() is used internally when translating algebraic literals. + static Element() { return new Element([...arguments]); }; + static Coeff() { return (new Element()).Coeff(...arguments); } + static Scalar(x) { return (new Element()).Coeff(0,x); } + static Vector() { return (new Element()).nVector(1,...arguments); } + static Bivector() { return (new Element()).nVector(2,...arguments); } + static Trivector() { return (new Element()).nVector(3,...arguments); } + static nVector(n) { return (new Element()).nVector(...arguments); } + + // Static operators. The parser will always translate operators to these static calls so that scalars, vectors, matrices and other non-multivectors can also be handled. + // The static operators typically handle functions and matrices, calling through to element methods for multivectors. They are intended to be flexible and allow as many + // types of arguments as possible. If performance is a consideration, one should use the generated element methods instead. (which only accept multivector arguments) + static toEl(x) { if (x instanceof Function) x=x(); if (!(x instanceof Element)) x=Element.Scalar(x); return x; } + + // Addition and subtraction. Subtraction with only one parameter is negation. + static Add(a,b,res) { + // Resolve expressions passed in. + while(a.call)a=a(); while(b.call)b=b(); if (a.Add && b.Add) return a.Add(b,res); + // If either is a string, the result is a string. + if ((typeof a=='string')||(typeof b=='string')) return a.toString()+b.toString(); + // If only one is an array, add the other element to each of the elements. + if ((a instanceof Array && !a.Add)^(b instanceof Array && !b.Add)) return (a instanceof Array)?a.map(x=>Element.Add(x,b)):b.map(x=>Element.Add(a,x)); + // If both are equal length arrays, add elements one-by-one + if ((a instanceof Array)&&(b instanceof Array)&&a.length==b.length) return a.map((x,xi)=>Element.Add(x,b[xi])); + // If they're both not elements let javascript resolve it. + if (!(a instanceof Element || b instanceof Element)) return a+b; + // Here we're left with scalars and multivectors, call through to generated code. + a=Element.toEl(a); b=Element.toEl(b); return a.Add(b,res); + } + + static Sub(a,b,res) { + // Resolve expressions passed in. + while(a.call)a=a(); while(b&&b.call) b=b(); if (a.Sub && b && b.Sub) return a.Sub(b,res); + // If only one is an array, add the other element to each of the elements. + if (b&&((a instanceof Array)^(b instanceof Array))) return (a instanceof Array)?a.map(x=>Element.Sub(x,b)):b.map(x=>Element.Sub(a,x)); + // If both are equal length arrays, add elements one-by-one + if (b&&(a instanceof Array)&&(b instanceof Array)&&a.length==b.length) return a.map((x,xi)=>Element.Sub(x,b[xi])); + // Negation + if (arguments.length==1) return Element.Mul(a,-1); + // If none are elements here, let js do it. + if (!(a instanceof Element || b instanceof Element)) return a-b; + // Here we're left with scalars and multivectors, call through to generated code. + a=Element.toEl(a); b=Element.toEl(b); return a.Sub(b,res); + } + + // The geometric product. (or matrix*matrix, matrix*vector, vector*vector product if called with 1D and 2D arrays) + static Mul(a,b,res) { + // Resolve expressions + while(a.call&&!a.length)a=a(); while(b.call&&!b.length)b=b(); if (a.Mul && b.Mul) return a.Mul(b,res); + // still functions -> experimental curry style (dont use this.) + if (a.call && b.call) return (ai,bi)=>Element.Mul(a(ai),b(bi)); + // scalar mul. + if (Number.isFinite(a) && b.Scale) return b.Scale(a); else if (Number.isFinite(b) && a.Scale) return a.Scale(b); + // Handle matrices and vectors. + if ((a instanceof Array)&&(b instanceof Array)) { + // vector times vector performs a dot product. (which internally uses the GP on each component) + if((!(a[0] instanceof Array) || (a[0] instanceof Element)) &&(!(b[0] instanceof Array) || (b[0] instanceof Element))) { var r=tot?Element.Scalar(0):0; a.forEach((x,i)=>r=Element.Add(r,Element.Mul(x,b[i]),r)); return r; } + // Array times vector + if(!(b[0] instanceof Array)) return a.map((x,i)=>Element.Mul(a[i],b)); + // Array times Array + var r=a.map((x,i)=>b[0].map((y,j)=>{ var r=tot?Element.Scalar(0):0; x.forEach((xa,k)=>r=Element.Add(r,Element.Mul(xa,b[k][j]))); return r; })); + // Return resulting array or scalar if 1 by 1. + if (r.length==1 && r[0].length==1) return r[0][0]; else return r; + } + // Only one is an array multiply each of its elements with the other. + if ((a instanceof Array)^(b instanceof Array)) return (a instanceof Array)?a.map(x=>Element.Mul(x,b)):b.map(x=>Element.Mul(a,x)); + // Try js multiplication, else call through to geometric product. + var r=a*b; if (!isNaN(r)) return r; + a=Element.toEl(a); b=Element.toEl(b); return a.Mul(b,res); + } + + // The inner product. (default is left contraction). + static LDot(a,b,res) { + // Expressions + while(a.call)a=a(); while(b.call)b=b(); //if (a.LDot) return a.LDot(b,res); + // Map elements in array + if (b instanceof Array && !(a instanceof Array)) return b.map(x=>Element.LDot(a,x)); + if (a instanceof Array && !(b instanceof Array)) return a.map(x=>Element.LDot(x,b)); + // js if numbers, else contraction product. + if (!(a instanceof Element || b instanceof Element)) return a*b; + a=Element.toEl(a);b=Element.toEl(b); return a.LDot(b,res); + } + + // The symmetric inner product. (default is left contraction). + static Dot(a,b,res) { + // Expressions + while(a.call)a=a(); while(b.call)b=b(); //if (a.LDot) return a.LDot(b,res); + // js if numbers, else contraction product. + if (!(a instanceof Element || b instanceof Element)) return a|b; + a=Element.toEl(a);b=Element.toEl(b); return a.Dot(b,res); + } + + // The outer product. (Grassman product - no use of metric) + static Wedge(a,b,res) { + // normal behavior for booleans/numbers + if (typeof a in {boolean:1,number:1} && typeof b in {boolean:1,number:1}) return a^b; + // Expressions + while(a.call)a=a(); while(b.call)b=b(); if (a.Wedge) return a.Wedge(Element.toEl(b),res); + // The outer product of two vectors is a matrix .. internally Mul not Wedge ! + if (a instanceof Array && b instanceof Array) return a.map(xa=>b.map(xb=>Element.Mul(xa,xb))); + // js, else generated wedge product. + if (!(a instanceof Element || b instanceof Element)) return a*b; + a=Element.toEl(a);b=Element.toEl(b); return a.Wedge(b,res); + } + + // The regressive product. (Dual of the outer product of the duals). + static Vee(a,b,res) { + // normal behavior for booleans/numbers + if (typeof a in {boolean:1,number:1} && typeof b in {boolean:1,number:1}) return a&b; + // Expressions + while(a.call)a=a(); while(b.call)b=b(); if (a.Vee) return a.Vee(Element.toEl(b),res); + // js, else generated vee product. (shortcut for dual of wedge of duals) + if (!(a instanceof Element || b instanceof Element)) return 0; + a=Element.toEl(a);b=Element.toEl(b); return a.Vee(b,res); + } + + // The sandwich product. Provided for convenience (>>> operator) + static sw(a,b) { + // Skip strings/colors + if (typeof b == "string" || typeof b =="number") return b; + // Expressions + while(a.call)a=a(); while(b.call)b=b(); if (a.sw) return a.sw(b); + // Map elements in array + if (b instanceof Array && !b.Add) return b.map(x=>Element.sw(a,x)); + // Call through. no specific generated code for it so just perform the muls. + a=Element.toEl(a); b=Element.toEl(b); return a.Mul(b).Mul(a.Reverse); + } + + // Division - scalars or cal through to element method. + static Div(a,b,res) { + // Expressions + while(a.call)a=a(); while(b.call)b=b(); + // For DDG experiments, I'll include a quick cholesky on matrices here. (vector/matrix) + if ((a instanceof Array) && (b instanceof Array) && (b[0] instanceof Array)) { + // factor + var R = b.flat(), i, j, k, sum, i_n, j_n, n=b[0].length, s=new Array(n), x=new Array(n), yi; + for (i=0;i=0; i--) for (x[i] /= R[i*n+i], j=i+1; ja.map((r,ri)=>Element.Conjugate(a[ri][ci]))); return Element.toEl(a).Conjugate; } + static Normalize(a) { return Element.toEl(a).Normalized; }; + static Length(a) { return Element.toEl(a).Length }; + + // Comparison operators always use length. Handle expressions, then js or length comparison + static eq(a,b) { if (!(a instanceof Element)||!(b instanceof Element)) return a==b; while(a.call)a=a(); while(b.call)b=b(); for (var i=0; i(b instanceof Element?b.Length:b); } + static lte(a,b) { while(a.call)a=a(); while(b.call)b=b(); return (a instanceof Element?a.Length:a)<=(b instanceof Element?b.Length:b); } + static gte(a,b) { while(a.call)a=a(); while(b.call)b=b(); return (a instanceof Element?a.Length:a)>=(b instanceof Element?b.Length:b); } + + // Debug output and printing multivectors. + static describe(x) { if (x===true) console.log(`Basis\n${basis}\nMetric\n${metric.slice(1,1+tot)}\nCayley\n${mulTable.map(x=>(x.map(x=>(' '+x).slice(-2-tot)))).join('\n')}\nMatrix Form:\n`+gp.map(x=>x.map(x=>x.match(/(-*b\[\d+\])/)).map(x=>x&&((x[1].match(/-/)||' ')+String.fromCharCode(65+1*x[1].match(/\d+/)))||' 0')).join('\n')); return {basis:basisg||basis,metric,mulTable,matrix:gp.map(x=>x.map(x=>x.replace(/\*this\[.+\]/,'').replace(/b\[(\d+)\]/,(a,x)=>(metric[x]==-1||metric[x]==0&&grades[x]>1&&(-1)**grades[x]==(metric[basis.indexOf(basis[x].replace('0',''))]||(-1)**grades[x])?'-':'')+basis[x]).replace('--','')))} } + + // Direct sum of algebras - experimental + static sum(B){ + var A = Element; + // Get the multiplication tabe and basis. + var T1 = A.describe().mulTable, T2 = B.describe().mulTable; + var B1 = A.describe().basis, B2 = B.describe().basis; + // Get the maximum index of T1, minimum of T2 and rename T2 if needed. + var max_T1 = B1.filter(x=>x.match(/e/)).map(x=>x.match(/\d/g)).flat().map(x=>x|0).sort((a,b)=>b-a)[0]; + var max_T2 = B2.filter(x=>x.match(/e/)).map(x=>x.match(/\d/g)).flat().map(x=>x|0).sort((a,b)=>b-a)[0]; + var min_T2 = B2.filter(x=>x.match(/e/)).map(x=>x.match(/\d/g)).flat().map(x=>x|0).sort((a,b)=>a-b)[0]; + // remapping .. + T2 = T2.map(x=>x.map(y=>y.match(/e/)?y.replace(/(\d)/g,(x)=>(x|0)+max_T1):y.replace("1","e"+(1+max_T2+max_T1)))); + B2 = B2.map((y,i)=>i==0?y.replace("1","e"+(1+max_T2+max_T1)):y.replace(/(\d)/g,(x)=>(x|0)+max_T1)); + // Build the new basis and multable.. + var basis = [...B1,...B2]; + var Cayley = T1.map((x,i)=>[...x,...T2[0].map(x=>"0")]).concat(T2.map((x,i)=>[...T1[0].map(x=>"0"),...x])) + // Build the new algebra. + var grades = [...B1.map(x=>x=="1"?0:x.length-1),...B2.map((x,i)=>i?x.length-1:0)]; + var a = Algebra({basis,Cayley,grades,tot:Math.log2(B1.length)+Math.log2(B2.length)}) + // And patch up .. + a.Scalar = function(x) { + var res = new a(); + for (var i=0; i function of 1 parameter will be called with that parameter from -1 to 1 and graphed on a canvas. Returned values should also be in the [-1 1] range + // graph(function(x,y)) => functions of 2 parameters will be called from -1 to 1 on both arguments. Returned values can be 0-1 for greyscale or an array of three RGB values. + // graph(array) => array of algebraic elements (points, lines, circles, segments, texts, colors, ..) is graphed. + // graph(function=>array) => same as above, for animation scenario's this function is called each frame. + // An optional second parameter is an options object { width, height, animate, camera, scale, grid, canvas } + static graph(f,options) { + // Store the original input + if (!f) return; var origf=f; + // generate default options. + options=options||{}; options.scale=options.scale||1; options.camera=options.camera||(tot!=4?Element.Scalar(1): ( Element.Bivector(0,0,0,0,0,options.p||0).Exp() ).Mul( Element.Bivector(0,0,0,0,options.h||0,0).Exp()) ); + if (options.conformal && tot==4) var ni = options.ni||this.Coeff(4,1,3,1), no = options.no||this.Coeff(4,0.5,3,-0.5), minus_no = no.Scale(-1); + var ww=options.width, hh=options.height, cvs=options.canvas, tpcam=new Element([0,0,0,0,0,0,0,0,0,0,0,-5,0,0,1,0]),tpy=this.Coeff(4,1),tp=new Element(), + // project 3D to 2D. This allows to render 3D and 2D PGA with the same code. + project=(o)=>{ if (!o) return o; while (o.call) o=o(); +// if (o instanceof Element && o.length == 32) o = new Element([o[0],o[1],o[2],o[3],o[4],o[6],o[7],o[8],o[10],o[11],o[13],o[16],o[17],o[19],o[22],o[26]]); + // Clip 3D lines so they don't go past infinity. + if (o instanceof Element && o.length == 16 && o[8]**2+o[9]**2+o[10]**2>0.0001) { + o = [[options.clip||2,1,0,0],[-(options.clip||2),1,0,0],[options.clip||2,0,1,0],[-(options.clip||2),0,1,0],[options.clip||2,0,0,1],[-(options.clip||2),0,0,1]].map(v=>{ + var r = Element.Vector(...v).Wedge(o); return r[14]?r.Scale(1/r[14], r):undefined; + }).filter(x=>x && Math.abs(x[13])<= (options.clip||2)+0.001 && Math.abs(x[12]) <= (options.clip||2)+0.001 && Math.abs(x[11]) <= (options.clip||2) + 0.001).slice(0,2); + return o.map(o=>(tpcam).Vee(options.camera.Mul(o).Mul(options.camera.Conjugate)).Wedge(tpy)); + } + // Convert 3D planes to polies. + if (o instanceof Element && o.length == 16 && o.Grade(1).Length>0.01) { + var m = Element.Add(1, Element.Mul(o.Normalized, Element.Coeff(3,1))).Normalized, e0 = 0; + o=Element.sw(m,[[-1,-1],[-1,1],[1,1],[-1,-1],[1,1],[1,-1]].map(([x,z])=>Element.Trivector(x*o.Length,e0,z*o.Length,1))); + return o.map(o=>(tpcam).Vee(options.camera.Mul(o).Mul(options.camera.Conjugate)).Wedge(tpy)); + } + return (tot==4 && o instanceof Element && o.length==16)?(tpcam).Vee(options.camera.Mul(o).Mul(options.camera.Conjugate)).Wedge(tpy):(o.length==2**tot)?Element.sw(options.camera,o):o; + }; + // gl escape. + if (options.gl && !(tot==4 && options.conformal)) return Element.graphGL(f,options); if (options.up) return Element.graphGL2(f,options); + // if we get an array or function without parameters, we render c2d or p2d SVG points/lines/circles/etc + if (!(f instanceof Function) || f.length===0) { + // Our current cursor, color, animation state and 2D mapping. + var lx,ly,lr,color,res,anim=false,to2d=(tot==5)?[0, 8, 11, 13, 19, 17, 22, 26]:(tot==3)?[0,1,2,3,4,5,6,7]:[0,7,9,10,13,12,14,15]; + // Make sure we have an array of elements. (if its an object, convert to array with elements and names.) + if (f instanceof Function) f=f(); if (!(f instanceof Array)) f=[].concat.apply([],Object.keys(f).map((k)=>typeof f[k]=='number'?[f[k]]:[f[k],k])); + // The build function generates the actual SVG. It will be called everytime the user interacts or the anim flag is set. + function build(f,or) { + // Make sure we have an aray. + if (or && f && f instanceof Function) f=f(); + // Reset position and color for cursor. + lx=-2;ly=options.conformal?-1.85:1.85;lr=0;color='#444'; + // Create the svg element. (master template string till end of function) + var svg=new DOMParser().parseFromString(` + ${// Add a grid (option) + options.grid?(()=>{ + if (tot==4 && !options.conformal) { + const lines3d = (n,from,to,j,l=0, ox=0, oy=0, alpha=1)=>[``,...[...Array(n+1)].map((x,i)=>{ + var f=from.map((x,i)=>x*(i==3?1:(options.gridSize||1))), t=to.map((x,i)=>x*(i==3?1:(options.gridSize||1))); f[j] = t[j] = (i-(n/2))/(n/2) * (options.gridSize||1); + var D3a = Element.Trivector(...f), D2a = project(D3a), D3b = Element.Trivector(...t), D2b = project(D3b); + var lx=options.scale*D2a[drm[2]]/D2a[drm[1]]; if (drm[1]==6||drm[1]==14) lx*=-1; var ly=-options.scale*D2a[drm[3]]/D2a[drm[1]]; + var lx2=options.scale*D2b[drm[2]]/D2b[drm[1]]; if (drm[1]==6||drm[1]==14) lx2*=-1; var ly2=-options.scale*D2b[drm[3]]/D2b[drm[1]]; + var r = ``; + if (l && i && i!= n) r += `${((from[j]<0?-1:1)*(i-(n/2))/(n/2)*(options.gridSize||1)).toFixed(1)}` + return r; + }),'']; + var front = Element.sw(options.camera,Element.Trivector(1,0,0,0)).Dual.Dot(Element.Vector(0,0,0,1)).s, ff = front>0?1:-1; + var left = Element.sw(options.camera,Element.Trivector(0,0,1,0)).Dual.Dot(Element.Vector(0,0,0,1)).s, ll = left>0?1:-1; + var fa = Math.max(0,Math.min(1,5*Math.abs(left))), la = Math.max(0,Math.min(1,5*Math.abs(front))); + return [ + ...lines3d(20,[-1,-1,-1,1],[1,-1,1,1],2,options.labels?ff:0, 0, 0.05), + ...lines3d(20,[-1,-1,-1,1],[1,-1,1,1],0,options.labels?ll:0, 0, 0.05), + ...lines3d(20,[-1,-1,ll,1],[1,1,ll,1],0,0,0,0,fa), + ...lines3d(20,[-1,1,ll,1],[1,-1,ll,1],1,!options.labels?0:(ff!=-1)?1:2, ll*ff*-0.05, 0, fa), + ...lines3d(20,[ff,1,-1,1],[ff,-1,1,1],1,!options.labels?0:(ll!=-1)?1:2, ll*ff*0.05, 0, la), + ...lines3d(20,[ff,-1,-1,1],[ff,1,1,1],2,0,0,0,la), + ].join(''); + } + const s = options.scale, n = (10/s)|0, cx = options.camera.e02, cy = options.camera.e01, alpha = Math.min(1,(s-0.2)*10); if (options.scale<0.1) return; + const lines = (n,dir,space,width,color)=>[...Array(2*n+1)].map((x,xi)=>``) + return [``,...lines(n*2,0,0.2,0.005,'#DDD'),...lines(n*2,1,0.2,0.005,'#DDD'),...lines(n,0,1,0.005,'#AAA'),...lines(n,1,1,0.005,'#AAA'),...lines(n,0,5,0.005,'#444'),...lines(n,1,5,0.005,'#444')] + .concat(options.labels?[...Array(4*n+1)].map((x,xi)=>(xi-n*2==0)?``:`${((xi-n*2)*0.2).toFixed(1)}`):[]) + .concat(options.labels?[...Array(4*n+1)].map((x,xi)=>`${((xi-n*2)*-0.2).toFixed(1)}`):[]).join('')+''; + })():''} + // Handle conformal 2D elements. + ${options.conformal?f.map&&f.map((o,oidx)=>{ + // Optional animation handling. + if((o==Element.graph && or!==false)||(oidx==0&&options.animate&&or!==false)) { anim=true; requestAnimationFrame(()=>{var r=build(origf,(!res)||(document.body.contains(res))).innerHTML; if (res) res.innerHTML=r; }); if (!options.animate) return; } + // Resolve expressions passed in. + while (o.call) o=o(); + if (options.ipns && o instanceof Element) o = o.Dual; + var sc = options.scale; + var lineWidth = options.lineWidth || 1; + var pointRadius = options.pointRadius || 1; + var dash_for_r2 = (r2, render_r, target_width) => { + // imaginary circles are dotted + if (r2 >= 0) return 'none'; + var half_circum = render_r*Math.PI; + var width = half_circum / Math.max(Math.round(half_circum / target_width), 1); + return `${width} ${width}`; + }; + // Arrays are rendered as segments or polygons. (2 or more elements) + if (o instanceof Array) { lx=ly=lr=0; o=o.map(o=>{ while(o.call)o=o(); return o.Scale(-1/o.Dot(ni).s); }); o.forEach((o)=>{lx+=sc*(o.e1);ly+=sc*(-o.e2)});lx/=o.length;ly/=o.length; return o.length>2?``:``; } + // Allow insertion of literal svg strings. + if (typeof o =='string' && o[0]=='<') { return o; } + // Strings are rendered at the current cursor position. + if (typeof o =='string') { var res2=(o[0]=='_')?'':` ${o} `; ly+=0.14; return res2; } + // Numbers change the current color. + if (typeof o =='number') { color='#'+(o+(1<<25)).toString(16).slice(-6); return ''; }; + // All other elements are rendered .. + var ni_part = o.Dot(no.Scale(-1)); // O_i + n_o O_oi + var no_part = ni.Scale(-1).Dot(o); // O_o + O_oi n_i + if (ni_part.VLength * 1e-6 > no_part.VLength) { + // direction or dual - nothing to render + return ""; + } + var no_ni_part = no_part.Dot(no.Scale(-1)); // O_oi + var no_only_part = ni.Wedge(no_part).Dot(no.Scale(-1)); // O_o + + /* Note: making 1e-6 smaller increases the maximum circle radius before they are drawn as lines */ + if (no_ni_part.VLength * 1e-6 > no_only_part.VLength) { + var is_flat = true; + var direction = no_ni_part; + } + else { + var is_flat = false; + var direction = no_only_part; + } + // normalize to make the direction unitary + var dl = direction.Length; + o = o.Scale(1/dl); + direction = direction.Scale(1/dl) + + var b0=direction.Grade(0).VLength>0.001,b1=direction.Grade(1).VLength>0.001,b2=direction.Grade(2).VLength>0.001; + if (!is_flat && b0 && !b1 && !b2) { + // Points + if (direction.s < 0) { o = Element.Sub(o); } + lx=sc*(o.e1); ly=sc*(-o.e2); lr=0; return res2=``; + } else if (is_flat && !b0 && b1 && !b2) { + // Lines. + var loc=minus_no.LDot(o).Div(o), att=ni.Dot(o); + lx=sc*(-loc.e1); ly=sc*(loc.e2); lr=Math.atan2(-o[14],o[13])/Math.PI*180; return ``; + } else if (!is_flat && !b0 && !b1 && b2) { + // Circles + var loc=o.Div(ni.LDot(o)); lx=sc*(-loc.e1); ly=sc*(loc.e2); + var r2=o.Mul(o.Conjugate).s; + var r = Math.sqrt(Math.abs(r2))*sc; + return ``; + } else if (!is_flat && !b0 && b1 && !b2) { + // Point Pairs. + lr=0; var ei=ni,eo=no, nix=o.Wedge(ei), sqr=o.LDot(o).s/nix.LDot(nix).s, r=Math.sqrt(Math.abs(sqr)), attitude=((ei.Wedge(eo)).LDot(nix)).Normalized.Mul(Element.Scalar(r)), pos=o.Div(nix); pos=pos.Div( pos.LDot(Element.Sub(ei))); + if (nix==0) { pos = o.Dot(Element.Coeff(4,-1)); sqr=-1; } + lx=sc*(pos.e1); ly=sc*(-pos.e2); + if (sqr==0) return ``; + // Draw imaginary pairs hollow + if (sqr > 0) var fill = color||'green', stroke = 'none', dash_array = 'none'; + else var fill = 'none', stroke = color||'green'; + lx=sc*(pos.e1+attitude.e1); ly=sc*(-pos.e2-attitude.e2); + var res2=``; + lx=sc*(pos.e1-attitude.e1); ly=sc*(-pos.e2+attitude.e2); + return res2+``; + } else { + /* Unrecognized */ + return ""; + } + // Handle projective 2D and 3D elements. + }):f.map&&f.map((o,oidx)=>{ if((o==Element.graph && or!==false)||(oidx==0&&options.animate&&or!==false)) { anim=true; requestAnimationFrame(()=>{var r=build(origf,(!res)||(document.body.contains(res))).innerHTML; if (res) res.innerHTML=r; }); if (!options.animate) return; } while (o instanceof Function) o=o(); o=(o instanceof Array)?o.map(project):project(o); if (o===undefined) return; + // dual option dualizes before render + if (options.dual && o instanceof Element) o = o.Dual; + // line segments and polygons + if (o instanceof Array && o.length>1) { lx=ly=lr=0; o.forEach((o)=>{while (o.call) o=o(); lx+=options.scale*((drm[1]==6||drm[1]==14)?-1:1)*o[drm[2]]/o[drm[1]];ly+=options.scale*o[drm[3]]/o[drm[1]]});lx/=o.length;ly/=o.length; return o.length>2?``:``; } + // svg + if (typeof o =='string' && o[0]=='<') { return o; } + // Labels + if (typeof o =='string') { var res2=(o[0]=='_')?'':` ${o} `; ly-=0.14; return res2; } + // Colors + if (typeof o =='number') { color='#'+(o+(1<<25)).toString(16).slice(-6); return ''; }; + // Points + if (o[to2d[6]]**2 >0.0001) { lx=options.scale*o[drm[2]]/o[drm[1]]; if (drm[1]==6||drm[1]==14) lx*=-1; ly=options.scale*o[drm[3]]/o[drm[1]]; lr=0; var res2=``; ly+=0.05; lx-=0.1; return res2; } + // Lines + if (o[to2d[2]]**2+o[to2d[3]]**2>0.0001) { var l=Math.sqrt(o[to2d[2]]**2+o[to2d[3]]**2); o[to2d[2]]/=l; o[to2d[3]]/=l; o[to2d[1]]/=l; lx=0.5; ly=options.scale*((drm[1]==6)?-1:-1)*o[to2d[1]]; lr=-Math.atan2(o[to2d[2]],o[to2d[3]])/Math.PI*180; var res2=``; ly+=0.05; return res2; } + // Vectors + if (o[to2d[4]]**2+o[to2d[5]]**2>0.0001) { lr=0; ly+=0.05; lx+=0.1; var res2=``; ly=ly+o.e01/4*3-0.05; lx=lx-o.e02/4*3; return res2; } + }).join()}`,'text/html').body; + // return the inside of the created svg element. + return svg.removeChild(svg.firstChild); + }; + // Create the initial svg and install the mousehandlers. + res=build(f); res.value=f; res.options=options; res.setAttribute("stroke-width",options.lineWidth*0.005||0.005); + res.remake = (animate)=>{ options.animate = animate; if (animate) { var r=build(origf,(!res)||(document.body.contains(res))).innerHTML; if (res) res.innerHTML=r; }; return res;}; + //onmousedown="if(evt.target==this)this.sel=undefined" + var mousex,mousey,cammove=false; + res.onwheel=(e)=>{ e.preventDefault(); options.scale = Math.min(5,Math.max(0.1,(options.scale||1)-e.deltaY*0.0001)); if (!anim) {var r=build(origf,(!res)||(document.body.contains(res))).innerHTML; if (res) res.innerHTML=r; } } + res.onmousedown=(e)=>{ if (e.target == res) res.sel=undefined; mousex = e.clientX; mousey = e.clientY; cammove = true; } + res.onmousemove=(e)=>{ + if (cammove && tot==4 && !options.conformal) { + if (!e.buttons) { cammove=false; return; }; + var [dx,dy] = [(options.scale || 1)*(e.clientX - mousex)*3, 3*(options.scale || 1)*(e.clientY - mousey)]; + [mousex,mousey] = [e.clientX,e.clientY]; + if (res.sel !== undefined && f[res.sel].set) { + var [cw,ch] = [res.clientWidth, res.clientHeight]; + var ox = (1/(options.scale || 1)) * ((e.offsetX / cw) - 0.5) * (cw>ch?(cw/ch):1); + var oy = (1/(options.scale || 1)) * ((e.offsetY / ch) - 0.5) * (ch>cw?(ch/cw):1); + var tb = Element.sw(options.camera,f[res.sel]); + var z = -(tb.e012/tb.e123+5)/5*4; tb.e023 = ox*z*tb.e123; tb.e013 = oy*z*tb.e123; + f[res.sel].set(Element.sw(options.camera.Reverse, tb)); + //f[res.sel].set( Element.sw(Element.sw(options.camera.Reverse,Element.Bivector(-dx/res.clientWidth,dy/res.clientHeight,0,0,0,0).Exp()),f[res.sel]) ); + } else { + options.h = (options.h||0) + dx/300; + options.p = (options.p||0) - dy/600; + if (options.camera) options.camera.set( ( Element.Bivector(0,0,0,0,0,options.p).Exp() ).Mul( Element.Bivector(0,0,0,0,options.h,0).Exp() )/*.Mul(options.camera)*/ ) + } + if (!anim) {var r=build(origf,(!res)||(document.body.contains(res))).innerHTML; if (res) res.innerHTML=r; } + return; + } + if (res.sel===undefined || f[res.sel] == undefined || f[res.sel].set == undefined || !e.buttons) return; + var resx=res.getBoundingClientRect().width,resy=res.getBoundingClientRect().height, + x=((e.clientX-res.getBoundingClientRect().left)/(resx/4||128)-2)*(resx>resy?resx/resy:1),y=((e.clientY-res.getBoundingClientRect().top)/(resy/4||128)-2)*(resy>resx?resy/resx:1); + x/=options.scale;y/=options.scale; + if (options.conformal) { f[res.sel].set(this.Coeff(1,x,2,-y).Add(no).Add(ni.Scale(0.5*(x*x+y*y))) ) } + else { f[res.sel][drm[2]]=((drm[1]==6)?-x:x)-((tot<4)?2*options.camera.e01:0); f[res.sel][drm[3]]=-y+((tot<4)?2*options.camera.e02:0); f[res.sel][drm[1]]=1; f[res.sel].set(f[res.sel].Normalized)} + if (!anim) {var r=build(origf,(!res)||(document.body.contains(res))).innerHTML; if (res) res.innerHTML=r; } + res.dispatchEvent(new CustomEvent('input')) }; + return res; + } + // 1d and 2d functions are rendered on a canvas. + cvs=cvs||document.createElement('canvas'); if(ww)cvs.width=ww; if(hh)cvs.height=hh; var w=cvs.width,h=cvs.height,context=cvs.getContext('2d'), data=context.getImageData(0,0,w,h); + // Grid support for the canvas. + const [x_from,x_to,y_from,y_to]=options.range||[-1,1,1,-1]; + function drawGrid() { + const [X,Y]=[x=>(x-x_from)*w/(x_to-x_from),y=>(y-y_from)*h/(y_to-y_from)] + context.strokeStyle = "#008800"; context.lineWidth = 1; + // X and Y axis + context.beginPath(); + context.moveTo(X(x_from), Y(0)); context.lineTo(X(x_to ), Y(0)); context.stroke(); + context.moveTo(X(0), Y(y_from)); context.lineTo(X(0), Y(y_to )); context.stroke(); + // Draw ticks + context.strokeStyle = "#00FF00"; context.lineWidth = 2; context.font = "10px Arial"; context.fillStyle = "#448844"; + for (var i=x_from,j=y_from,ii=0; ii<=10; ++ii) { + context.beginPath(); j+= (y_to-y_from)/10; i+=(x_to-x_from)/10; + context.moveTo(X(i), Y(-(y_to - y_from)/200)); context.lineTo(X(i), Y((y_to - y_from)/200)); context.stroke(); + if(i.toFixed(1)!=0) context.fillText(i.toFixed(1), X(i-(x_to-x_from)/100), Y(-(y_to-y_from)/40)); + context.moveTo(X((x_to-x_from)/200), Y(j)); context.lineTo(X(-(x_to-x_from)/200), Y(j)); context.stroke(); + if(j.toFixed(1)!=0) context.fillText(j.toFixed(1), X((x_to-x_from)/100), Y(j)); + } + } + // two parameter functions .. evaluate for both and set resulting color. + if (f.length==2) for (var px=0; pxx*255).concat([255]),py*w*4+px*4); } + // one parameter function.. go over x range, use result as y. + else if (f.length==1) for (var px=0; px 0 && res < h-1) data.data.set([0,0,0,255],res*w*4+px*4); } + context.putImageData(data,0,0); + if (f.length == 1 || f.length == 2) if (options.grid) drawGrid(); + return cvs; + } + + // webGL2 Graphing function. (for OPNS/IPNS implicit 2D and 1D surfaces in 3D space). + static graphGL2(f,options) { + // Create canvas, get webGL2 context. + var canvas=document.createElement('canvas'); canvas.style.width=options.width||''; canvas.style.height=options.height||''; canvas.style.backgroundColor='#EEE'; + if (options.width && options.width.match && options.width.match(/px/i)) canvas.width = parseFloat(options.width)*(options.devicePixelRatio||devicePixelRatio||1); if (options.height && options.height.match && options.height.match(/px/i)) canvas.height = parseFloat(options.height)*(options.devicePixelRatio||devicePixelRatio||1); + var gl=canvas.getContext('webgl2',{alpha:options.alpha||false,preserveDrawingBuffer:true,antialias:true,powerPreference:'high-performance'}); + var gl2=!!gl; if (!gl) gl=canvas.getContext('webgl',{alpha:options.alpha||false,preserveDrawingBuffer:true,antialias:true,powerPreference:'high-performance'}); + gl.clearColor(240/255,240/255,240/255,1.0); gl.enable(gl.DEPTH_TEST); if (!gl2) { gl.getExtension("EXT_frag_depth"); gl.va = gl.getExtension('OES_vertex_array_object'); } + else gl.va = { createVertexArrayOES : gl.createVertexArray.bind(gl), bindVertexArrayOES : gl.bindVertexArray.bind(gl), deleteVertexArrayOES : gl.deleteVertexArray.bind(gl) } + // Compile vertex and fragment shader, return program. + var compile=(vs,fs)=>{ + var s=[gl.VERTEX_SHADER,gl.FRAGMENT_SHADER].map((t,i)=>{ + var r=gl.createShader(t); gl.shaderSource(r,[vs,fs][i]); gl.compileShader(r); + return gl.getShaderParameter(r, gl.COMPILE_STATUS)&&r||console.error(gl.getShaderInfoLog(r)); + }); + var p = gl.createProgram(); gl.attachShader(p, s[0]); gl.attachShader(p, s[1]); gl.linkProgram(p); + gl.getProgramParameter(p, gl.LINK_STATUS)||console.error(gl.getProgramInfoLog(p)); + return p; + }; + // Create vertex array and buffers, upload vertices and optionally texture coordinates. + var createVA=function(vtx) { + var r = gl.va.createVertexArrayOES(); gl.va.bindVertexArrayOES(r); + var b = gl.createBuffer(); gl.bindBuffer(gl.ARRAY_BUFFER, b); + gl.bufferData(gl.ARRAY_BUFFER, new Float32Array(vtx), gl.STATIC_DRAW); + gl.vertexAttribPointer(0, 3, gl.FLOAT, false, 0, 0); gl.enableVertexAttribArray(0); + return {r,b} + }, + // Destroy Vertex array and delete buffers. + destroyVA=function(va) { + if (va.b) gl.deleteBuffer(va.b); if (va.r) gl.va.deleteVertexArrayOES(va.r); + } + // Drawing function + var M=[1,0,0,0,0,1,0,0,0,0,1,0,0,0,5,1]; + var draw=function(p, tp, vtx, color, color2, ratio, texc, va, b,color3,r,g){ + gl.useProgram(p); gl.uniformMatrix4fv(gl.getUniformLocation(p, "mv"),false,M); + gl.uniformMatrix4fv(gl.getUniformLocation(p, "p"),false, [5,0,0,0,0,5*(ratio||1),0,0,0,0,1,2,0,0,-1,0]) + gl.uniform3fv(gl.getUniformLocation(p, "color"),new Float32Array(color)); + gl.uniform3fv(gl.getUniformLocation(p, "color2"),new Float32Array(color2)); + if (color3) gl.uniform3fv(gl.getUniformLocation(p, "color3"),new Float32Array(color3)); + if (b) gl.uniform1fv(gl.getUniformLocation(p, "b"),(new Float32Array(counts[g])).map((x,i)=>b[g][i]||0)); + if (texc) gl.uniform1i(gl.getUniformLocation(p, "texc"),0); + if (r) gl.uniform1f(gl.getUniformLocation(p,"ratio"),r); + var v; if (!va) v = createVA(vtx); else gl.va.bindVertexArrayOESOES(va.r); + gl.drawArrays(tp, 0, (va&&va.tcount)||vtx.length/3); + if (v) destroyVA(v); + } + // Compile the OPNS renderer. (sphere tracing) + var programs = [], genprog = grade=>compile(`${gl2?"#version 300 es":""} + ${gl2?"in":"attribute"} vec4 position; ${gl2?"out":"varying"} vec4 Pos; uniform mat4 mv; uniform mat4 p; + void main() { Pos=mv*position; gl_Position = p*Pos; }`, + `${!gl2?"#extension GL_EXT_frag_depth : enable":"#version 300 es"} + precision highp float; + uniform vec3 color; uniform vec3 color2; + uniform vec3 color3; uniform float b[${counts[grade]}]; + uniform float ratio; ${gl2?"out vec4 col;":""} + ${gl2?"in":"varying"} vec4 Pos; + float product_len (in float z, in float y, in float x, in float[${counts[grade]}] b) { + ${this.nVector(options.up.length>tot?2:1,[])[options.IPNS?"IPNS_GLSL":"OPNS_GLSL"](this.nVector(grade,[]), options.up)} + return sqrt(abs(sum)); + } + vec3 find_root (in vec3 start, vec3 dir, in float thresh) { + vec3 orig=start; + float lastd = 1000.0; + const int count=${(options.maxSteps||80)}; + for (int i=0; i0.0) { + vec3 n = normalize(vec3( + product_len(d2[0]+h,d2[1],d2[2],b)-product_len(d2[0]-h,d2[1],d2[2],b), + product_len(d2[0],d2[1]+h,d2[2],b)-product_len(d2[0],d2[1]-h,d2[2],b), + product_len(d2[0],d2[1],d2[2]+h,b)-product_len(d2[0],d2[1],d2[2]-h,b) + )); + ${gl2?"gl_FragDepth":"gl_FragDepthEXT"} = dl2/50.0; + ${gl2?"col":"gl_FragColor"} = vec4(max(0.2,abs(dot(n,normalize(L-d2))))*color3 + pow(abs(dot(n,normalize(normalize(L-d2)+dir))),100.0),1.0); + } else discard; + }`),genprog2D = grade=>compile(`${gl2?"#version 300 es":""} + ${gl2?"in":"attribute"} vec4 position; ${gl2?"out":"varying"} vec4 Pos; uniform mat4 mv; uniform mat4 p; + void main() { Pos=mv*position; gl_Position = p*Pos; }`, + `${!gl2?"#extension GL_EXT_frag_depth : enable":"#version 300 es"} + precision highp float; + uniform vec3 color; uniform vec3 color2; + uniform vec3 color3; uniform float b[${counts[grade]}]; + uniform float ratio; ${gl2?"out vec4 col;":""} + ${gl2?"in":"varying"} vec4 Pos; + float product_len (in float z, in float y, in float x, in float[${counts[grade]}] b) { + ${this.nVector(1,[])[options.IPNS?"IPNS_GLSL":"OPNS_GLSL"](this.nVector(grade,[]), options.up)} + return sqrt(abs(sum)); + } + void main() { + vec3 p = -5.0*normalize(color2) -Pos[0]/5.0*color + color2 + vec3(0.0,Pos[1]/5.0*ratio,0.0); + float d2 = 1.0 - 150.0*pow(product_len( p[0]*5.0, p[1]*5.0, p[2]*5.0, b),2.0); + if (d2>0.0) { + ${gl2?"col":"gl_FragColor"} = vec4(color3,d2); + } else discard; + }`) + // canvas update will (re)render the content. + var armed=0; + canvas.update = (x)=>{ + // Start by updating canvas size if needed and viewport. + var s = getComputedStyle(canvas); if (s.width) { canvas.width = parseFloat(s.width)*(options.devicePixelRatio||devicePixelRatio||1); canvas.height = parseFloat(s.height)*(options.devicePixelRatio||devicePixelRatio||1); } + gl.viewport(0,0, canvas.width|0,canvas.height|0); var r=canvas.width/canvas.height; + // Defaults, resolve function input + var a,p=[],l=[],t=[],c=[.5,.5,.5],alpha=0,lastpos=[-2,2,0.2]; gl.clear(gl.COLOR_BUFFER_BIT+gl.DEPTH_BUFFER_BIT); while (x.call) x=x(); + // Loop over all items to render. + for (var i=0,ll=x.length;i>>24)&0xff)/255; c[0]=((e>>>16)&0xff)/255; c[1]=((e>>>8)&0xff)/255; c[2]=(e&0xff)/255; } + if (e instanceof Element){ + var tt = options.spin?-performance.now()*options.spin/1000:-options.h||0; tt+=Math.PI/2; var r = canvas.height/canvas.width; + var g=tot-1; while(!e[g]&&g>1) g--; + if (!programs[tot-1-g]) programs[tot-1-g] = (options.up.find(x=>x.match&&x.match("z")))?genprog(g):genprog2D(g); + gl.enable(gl.BLEND); gl.blendFunc(gl.ONE, gl.ONE_MINUS_SRC_ALPHA); + draw(programs[tot-1-g],gl.TRIANGLES,[-2,-2,0,-2,2,0,2,-2,0,-2,2,0,2,-2,0,2,2,0],[Math.cos(tt),0,-Math.sin(tt)],[Math.sin(tt),0,Math.cos(tt)],undefined,undefined,undefined,e,c,r,g); + gl.disable(gl.BLEND); + } + } + // if we're no longer in the page .. stop doing the work. + armed++; if (document.body.contains(canvas)) armed=0; if (armed==2) return; + canvas.value=x; if (options&&!options.animate) canvas.dispatchEvent(new CustomEvent('input')); + if (options&&options.animate) { requestAnimationFrame(canvas.update.bind(canvas,f,options)); } + if (options&&options.still) { canvas.value=x; canvas.dispatchEvent(new CustomEvent('input')); canvas.im.width=canvas.width; canvas.im.height=canvas.height; canvas.im.src = canvas.toDataURL(); } + } + // Basic mouse interactivity. needs more love. + var sel=-1; canvas.oncontextmenu = canvas.onmousedown = (e)=>{ e.preventDefault(); e.stopPropagation(); sel=-2; + var rc = canvas.getBoundingClientRect(), mx=(e.x-rc.left)/(rc.right-rc.left)*2-1, my=((e.y-rc.top)/(rc.bottom-rc.top)*-4+2)*canvas.height/canvas.width; + canvas.onwheel=e=>{e.preventDefault(); e.stopPropagation(); options.z = (options.z||5)+e.deltaY/100; if (!options.animate) requestAnimationFrame(canvas.update.bind(canvas,f,options));} + canvas.onmouseup=e=>sel=-1; canvas.onmouseleave=e=>sel=-1; + canvas.onmousemove=(e)=>{ + var rc = canvas.getBoundingClientRect(); + var mx =(e.movementX)/(rc.right-rc.left)*2, my=((e.movementY)/(rc.bottom-rc.top)*-2)*canvas.height/canvas.width; + if (sel==-2) { options.h = (options.h||0)+mx; if (!options.animate) requestAnimationFrame(canvas.update.bind(canvas,f,options)); return; }; if (sel < 0) return; + } + } + canvas.value = f.call?f():f; canvas.options = options; + if (options&&options.still) { + var i=new Image(); canvas.im = i; return requestAnimationFrame(canvas.update.bind(canvas,f,options)),i; + } else return requestAnimationFrame(canvas.update.bind(canvas,f,options)),canvas; + + } + + + // webGL Graphing function. (for parametric defined objects) + static graphGL(f,options) { + // Create a canvas, webgl2 context and set some default GL options. + var canvas=document.createElement('canvas'); canvas.style.width=options.width||''; canvas.style.height=options.height||''; canvas.style.backgroundColor='#EEE'; + if (options.width && options.width.match && options.width.match(/px/i)) canvas.width = parseFloat(options.width); if (options.height && options.height.match && options.height.match(/px/i)) canvas.height = parseFloat(options.height); + var gl=canvas.getContext('webgl',{alpha:options.alpha||false,antialias:true,preserveDrawingBuffer:options.still||true,powerPreference:'high-performance'}); + gl.enable(gl.DEPTH_TEST); gl.depthFunc(gl.LEQUAL); if (!options.alpha) gl.clearColor(240/255,240/255,240/255,1.0); gl.getExtension("OES_standard_derivatives"); gl.va=gl.getExtension("OES_vertex_array_object"); + // Compile vertex and fragment shader, return program. + var compile=(vs,fs)=>{ + var s=[gl.VERTEX_SHADER,gl.FRAGMENT_SHADER].map((t,i)=>{ + var r=gl.createShader(t); gl.shaderSource(r,[vs,fs][i]); gl.compileShader(r); + return gl.getShaderParameter(r, gl.COMPILE_STATUS)&&r||console.error(gl.getShaderInfoLog(r)); + }); + var p = gl.createProgram(); gl.attachShader(p, s[0]); gl.attachShader(p, s[1]); gl.linkProgram(p); + gl.getProgramParameter(p, gl.LINK_STATUS)||console.error(gl.getProgramInfoLog(p)); + return p; + }; + // Create vertex array and buffers, upload vertices and optionally texture coordinates. + var createVA=function(vtx, texc, idx, clr) { + var r = gl.va.createVertexArrayOES(); gl.va.bindVertexArrayOES(r); + var b = gl.createBuffer(); gl.bindBuffer(gl.ARRAY_BUFFER, b); + gl.bufferData(gl.ARRAY_BUFFER, new Float32Array(vtx), gl.STATIC_DRAW); + gl.vertexAttribPointer(0, 3, gl.FLOAT, false, 0, 0); gl.enableVertexAttribArray(0); + if (texc){ + var b2=gl.createBuffer(); gl.bindBuffer(gl.ARRAY_BUFFER, b2); + gl.bufferData(gl.ARRAY_BUFFER, new Float32Array(texc), gl.STATIC_DRAW); + gl.vertexAttribPointer(1, 2, gl.FLOAT, false, 0, 0); gl.enableVertexAttribArray(1); + } + if (clr){ + var b3=gl.createBuffer(); gl.bindBuffer(gl.ARRAY_BUFFER, b3); + gl.bufferData(gl.ARRAY_BUFFER, new Float32Array(clr), gl.STATIC_DRAW); + gl.vertexAttribPointer(texc?2:1, 3, gl.FLOAT, false, 0, 0); gl.enableVertexAttribArray(texc?2:1); + } + if (idx) { + var b4=gl.createBuffer(); gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, b4); + gl.bufferData(gl.ELEMENT_ARRAY_BUFFER, new Uint16Array(idx), gl.STATIC_DRAW); + } + return {r,b,b2,b4,b3} + }, + // Destroy Vertex array and delete buffers. + destroyVA=function(va) { + [va.b,va.b2,va.b4,va.b3].forEach(x=>{if(x) gl.deleteBuffer(x)}); if (va.r) gl.va.deleteVertexArrayOES(va.r); + } + // Default modelview matrix, convert camera to matrix (biquaternion->matrix) + var M=[1,0,0,0,0,1,0,0,0,0,1,0,0,0,5,1], mtx = (x,iscam=true)=>{ var t=options.spin?performance.now()*options.spin/1000:-options.h||0, t2=options.p||0; + var ct = Math.cos(t), st= Math.sin(t), ct2 = Math.cos(t2), st2 = Math.sin(t2), xx=options.posx||0, y=options.posy||0, z=options.posz||0, zoom=options.z||5; + if (tot==5) return [ct,st*-st2,st*ct2,0,0,ct2,st2,0,-st,ct*-st2,ct*ct2,0,xx*ct+z*-st,y*ct2+(xx*st+z*ct)*-st2,y*st2+xx*st+z*ct*ct2+zoom,1]; + x=x.Normalized; var y=x.Mul(x.Dual),X=x.e23,Y=-x.e13,Z=-x.e12,W=x.s; + var xx = X*X, xy = X*Y, xz = X*Z, xw = X*W, yy = Y*Y, yz = Y*Z, yw = Y*W, zz = Z*Z, zw = Z*W; + var mtx = [ 1-2*(yy+zz), 2*(xy+zw), 2*(xz-yw), 0, 2*(xy-zw), 1-2*(xx+zz), 2*(yz+xw), 0, 2*(xz+yw), 2*(yz-xw), 1-2*(xx+yy), 0, -2*y.e23, -2*y.e13, 2*y.e12+(iscam?5:0), 1]; + return mtx; + } + // Render the given vertices. (autocreates/destroys vertex array if not supplied). + var draw=function(p, tp, vtx, color, color2, ratio, texc, va, cbuf, allowcull=true){ + gl.useProgram(p); gl.uniformMatrix4fv(gl.getUniformLocation(p, "mv"),false,M); + gl.uniformMatrix4fv(gl.getUniformLocation(p, "p"),false, [5,0,0,0,0,5*(ratio||2),0,0,0,0,1,2,0,0,-1,0]) + gl.uniform3fv(gl.getUniformLocation(p, "color"),new Float32Array(color)); + gl.uniform3fv(gl.getUniformLocation(p, "color2"),new Float32Array(color2)); + //if (texc) gl.uniform1i(gl.getAttribLocation(p, "texc"),0); + var v; if (!va) v = createVA(vtx, texc, undefined, cbuf, p); else gl.va.bindVertexArrayOES(va.r); + if (options.cull && allowcull) gl.enable(gl.CULL_FACE); + if (va && va.b4) { + gl.drawElements(tp, va.tcount, gl.UNSIGNED_SHORT, 0); + } else { + gl.drawArrays(tp, 0, (va&&va.tcount)||vtx.length/3); + } + if (v) destroyVA(v); + if (options.cull) gl.disable(gl.CULL_FACE); + } + // Program for the geometry. Derivative based normals. Basic lambert shading. + var program = compile(`attribute vec4 position; varying vec4 Pos; uniform mat4 mv; uniform mat4 p; + void main() { gl_PointSize=12.0; Pos=mv*position; gl_Position = p*Pos; }`, + `#extension GL_OES_standard_derivatives : enable + precision highp float; uniform vec3 color; uniform vec3 color2; varying vec4 Pos; + void main() { vec3 ldir = normalize(Pos.xyz - vec3(2.0,2.0,-4.0)); + vec3 normal = normalize(cross(dFdx(Pos.xyz), dFdy(Pos.xyz))); float l=dot(normal,ldir); + vec3 E = normalize(-Pos.xyz); vec3 R = normalize(reflect(ldir,normal)); + gl_FragColor = vec4(max(0.0,l)*color+vec3(0.5*pow(max(dot(R,E),0.0),20.0))+color2, 1.0); }`); + var programSphere = compile(`attribute vec4 position; varying vec4 Pos; varying vec3 N; uniform mat4 mv; uniform mat4 p; + void main() { gl_PointSize=12.0; Pos=mv*position; N = normalize(position.xzy); gl_Position = p*Pos; }`, + `#extension GL_OES_standard_derivatives : enable + precision highp float; uniform vec3 color; uniform vec3 color2; varying vec4 Pos; varying vec3 N; + void main() { vec3 ldir = normalize(Pos.xyz - vec3(2.0,2.0,-4.0)); + vec3 normal = N; float l=dot(normal,ldir); + vec3 E = normalize(-Pos.xyz); vec3 R = normalize(reflect(ldir,normal)); + gl_FragColor = vec4(max(0.0,l)*color+vec3(0.5*pow(max(dot(R,E),0.0),20.0))+color2, 1.0); }`); + var programPoint = compile(`attribute vec4 position; varying vec4 Pos; uniform mat4 mv; uniform mat4 p; + void main() { gl_PointSize=${((options.pointRadius||1)*(options.devicePixelRatio||devicePixelRatio||1)*8.0).toFixed(2)}; Pos=mv*position; gl_Position = p*Pos; }`, + `precision highp float; uniform vec3 color; uniform vec3 color2; varying vec4 Pos; + void main() { float distanceToCenter = length(gl_PointCoord - vec2(0.5)); if (distanceToCenter>0.5) discard; + gl_FragColor = vec4(color+color2, (distanceToCenter<0.5?1.0:0.0)); }`); + var programline = compile(` + attribute vec4 position; // current point. + attribute vec2 texc; // x = +w or -w, alternating. y = opacity. + attribute vec4 col; // next point. (extrapolated for end point) + uniform vec3 color; // r=aspect g=thickness + uniform mat4 mv,p; // modelview and projection matrix + varying vec2 tc; + void main() { + // Convert to clipspace. + vec4 cp = p*mv*vec4(position.xyz,1.0); + vec2 cs = cp.xy / abs(cp.w); + vec4 np = p*mv*vec4(col.xyz,1.0); + vec2 ns = np.xy / abs(np.w); + // compensate aspect + cs.x *= color.r; + ns.x *= color.r; + // clipspace line direction. + vec2 dir = normalize(cs-ns); + // Calculate screenspace normal. + vec2 normal = vec2( -dir.y, dir.x); + // Line scaling and aspect fix. + normal *= color.g * 5.0; + normal.x /= color.r; + // Pass through texture coordinates for edge softening + tc = vec2(texc.x / abs(texc.x), texc.y); + gl_Position = cp + vec4(normal*texc.x,0.0,0.0); + }`, + `precision highp float; + uniform vec3 color2; + varying vec2 tc; + void main() { +// gl_FragColor = vec4(abs(tc.x),abs(tc.x),abs(tc.x),1.0-abs(tc.x)); + gl_FragColor = vec4(color2,(1.0-pow(abs(tc.x),2.0))*tc.y); + }`); + var programcol = compile(`attribute vec4 position; attribute vec3 col; varying vec3 Col; varying vec4 Pos; uniform mat4 mv; uniform mat4 p; + void main() { gl_PointSize=6.0; Pos=mv*position; gl_Position = p*Pos; Col=col; }`, + `#extension GL_OES_standard_derivatives : enable + precision highp float; uniform vec3 color; uniform vec3 color2; varying vec4 Pos; varying vec3 Col; + void main() { vec3 ldir = normalize(Pos.xyz - vec3(1.0,1.0,2.0)); + vec3 normal = normalize(cross(dFdx(Pos.xyz), dFdy(Pos.xyz))); float l=dot(normal,ldir); + vec3 E = normalize(-Pos.xyz); vec3 R = normalize(reflect(ldir,normal)); + gl_FragColor = vec4(max(0.3,l)*Col+vec3(pow(max(dot(R,E),0.0),20.0))+color2, 1.0); ${options.shader||''} }`); + var programmot = compile(`attribute vec4 position; attribute vec2 texc; attribute vec3 col; varying vec3 Col; varying vec4 Pos; uniform mat4 mv; uniform mat4 p; uniform vec3 color2; + void main() { gl_PointSize=2.0; float blend=fract(color2.x+texc.r)*0.5; Pos=mv*(position*(1.0-blend) + (blend)*vec4(col,1.0)); gl_Position = p*Pos; Col=vec3(length(col-position.xyz)*1.); gl_PointSize = 8.0 - Col.x; Col.y=sin(blend*2.*3.1415); }`, + `precision highp float; uniform vec3 color; uniform vec3 color2; varying vec4 Pos; varying vec3 Col; + void main() { float distanceToCenter = length(gl_PointCoord - vec2(0.5));gl_FragColor = vec4(1.0-pow(Col.x,2.0),0.0,0.0,(.6-Col.x*0.05)*(distanceToCenter<0.5?1.0:0.0)*Col.y); }`); + gl.lineWidth(options.lineWidth||1); // doesn't work yet (nobody supports it) + // Create a font texture, lucida console or otherwise monospaced. + var fw=33, font = Object.assign(document.createElement('canvas'),{width:(19+94)*fw,height:48}), + ctx = Object.assign(font.getContext('2d'),{font:'bold 48px lucida console, monospace'}), + ftx = gl.createTexture(); gl.activeTexture(gl.TEXTURE0); gl.bindTexture(gl.TEXTURE_2D, ftx); + for (var i=33; i<127; i++) ctx.fillText(String.fromCharCode(i),(i-33)*fw,40); + var specialChars = "∞≅¹²³₀₁₂₃₄₅₆₇₈₉⋀⋁∆⋅"; specialChars.split('').forEach((x,i)=>ctx.fillText(x,(i-33+127)*fw,40)); + // 2.0 gl.texImage2D(gl.TEXTURE_2D,0,gl.RGBA,94*fw,32,0,gl.RGBA,gl.UNSIGNED_BYTE,font); + gl.texImage2D(gl.TEXTURE_2D, 0, gl.RGBA, gl.RGBA, gl.UNSIGNED_BYTE, font); + gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_MAG_FILTER, gl.LINEAR); gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_MIN_FILTER, gl.LINEAR); + gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_WRAP_S, gl.CLAMP_TO_EDGE); gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_WRAP_T, gl.CLAMP_TO_EDGE); + // Font rendering program. Renders billboarded fonts, transforms offset passed as color2. + var program2 = compile(`attribute vec4 position; attribute vec2 texc; varying vec2 tex; varying vec4 Pos; uniform mat4 mv; uniform mat4 p; uniform vec3 color2; + void main() { tex=texc; gl_PointSize=6.0; vec4 o=mv*vec4(color2,0.0); Pos=(-1.0/(o.z-mv[3][2]))*position+vec4(mv[3][0],mv[3][1],mv[3][2],0.0)+o; gl_Position = p*Pos; }`, + `precision highp float; uniform vec3 color; varying vec4 Pos; varying vec2 tex; + uniform sampler2D texm; void main() { vec4 c = texture2D(texm,tex); if (c.a<0.01) discard; gl_FragColor = vec4(color,c.a);}`); + // Helpers for line drawing. Convert line segments to triangles. + const line_to_tri = ([ax,ay,az,bx,by,bz]) => [ax,ay,az,ax,ay,az,bx,by,bz,bx,by,bz,ax,ay,az,bx,by,bz]; + const line_to_tri2 = ([ax,ay,az,bx,by,bz]) => [bx,by,bz,bx,by,bz,2*bx-ax,2*by-ay,2*bz-az,2*bx-ax,2*by-ay,2*bz-az,bx,by,bz,2*bx-ax,2*by-ay,2*bz-az]; + // Conformal space needs a bit extra magic to extract euclidean parametric representations. + if (tot==5 && options.conformal) var ni = Element.Coeff(4,1).Add(Element.Coeff(5,1)), no = Element.Coeff(4,0.5).Sub(Element.Coeff(5,0.5)); + var interprete = (x)=>{ + if (!(x instanceof Element)) return { tp:0 }; + if (options.ipns) x=x.Dual; + // tp = { 0:unknown 1:point 2:line, 3:plane, 4:circle, 5:sphere + var X2 = (x.Mul(x)).s, tp=0, weight2, opnix = ni.Wedge(x), ipnix = ni.LDot(x), + attitude, pos, normal, tg,btg,epsilon = 0.000001/(options.scale||1), I3=Element.Coeff(16,-1); + var x2zero = Math.abs(X2) < epsilon, ipnixzero = ipnix.VLength < epsilon, opnixzero = opnix.VLength < epsilon; + if (opnixzero && ipnixzero) { // free flat + } else if (opnixzero && !ipnixzero) { // bound flat (lines) + attitude = no.Wedge(ni).LDot(x); + weight2 = Math.abs(attitude.LDot(attitude).s)**.5; + pos = attitude.LDot(x.Reverse); //Inverse); + pos = [-pos.e15/pos.e45,-pos.e25/pos.e45,-pos.e34/pos.e45]; + if (x.Grade(3).VLength) { + normal = [attitude.e1/weight2,attitude.e2/weight2,attitude.e3/weight2]; tp=2; + } else if (x.Grade(2).VLength) { // point pair with ni + tp = 1; + } else { + normal = Element.LDot(Element.Mul(attitude,1/weight2),I3).Normalized; + var r=normal.Mul(Element.Coeff(3,1)); if (r[0]==-1) r[0]=1; else {r[0]+=1; r=r.Normalized;} + tg = [...r.Mul(Element.Coeff(1,1)).Mul(r.Conjugate)].slice(1,4); + btg = [...r.Mul(Element.Coeff(2,1)).Mul(r.Conjugate)].slice(1,4); + normal = [...normal.slice(1,4)]; tp=3; + } + } else if (!opnixzero && ipnixzero) { // dual bound flat + } else if (x2zero) { // bound vec,biv,tri (points) + if (options.ipns) x=x.Dual; + attitude = ni.Wedge(no).LDot(ni.Wedge(x)); + pos = [...(Element.LDot(1/(ni.LDot(x)).s,x)).slice(1,4)].map(x=>-x); + tp=1; + } else if (!x2zero) { // round (point pair,circle,sphere) + tp = x.Grade(3).VLength?4:x.Grade(2).VLength?6:5; + var nix = ni.Wedge(x), nix2 = (nix.Mul(nix)).s; + attitude = ni.Wedge(no).LDot(nix); + pos = [...(x.Mul(ni).Mul(x)).slice(1,4)].map(x=>-x/(2.0*nix2)); + weight2 = Math.abs((x.LDot(x)).s / nix2)**.5; + if (tp==4) { + if (x.LDot(x).s < 0) { weight2 = -weight2; } + normal = Element.LDot(Element.Mul(attitude,1/weight2),I3).Normalized; + var r=normal.Mul(Element.Coeff(3,1)); if (r[0]==-1) r[0]=1; else {r[0]+=1; r=r.Normalized;} + tg = [...r.Mul(Element.Coeff(1,1)).Mul(r.Conjugate)].slice(1,4); + btg = [...r.Mul(Element.Coeff(2,1)).Mul(r.Conjugate)].slice(1,4); + normal = [...normal.slice(1,4)]; + } else if (tp==6) { + weight2 = (x.LDot(x).s < 0)?-(weight2):weight2; + normal = Element.Mul(attitude.Normalized,weight2).slice(1,4); + } else { + normal = [...((Element.LDot(Element.Mul(attitude,1/weight2),I3)).Normalized).slice(1,4)]; + } + } + return {tp,pos:pos?pos.map(x=>x*(options.scale||1)):[0,0,0],normal,tg,btg,weight2:weight2*(options.scale||1)} + }; + // canvas update will (re)render the content. + var armed=0,sphere,e14 = Element.Coeff(14,1); + canvas.update = (x)=>{ + if (!canvas.parentElement) return; + // restore from still.. + if (options && !options.still && canvas.im && canvas.im.parentElement) { canvas.im.parentElement.insertBefore(canvas,canvas.im); canvas.im.parentElement.removeChild(canvas.im); } + // Start by updating canvas size if needed and viewport. + var s = getComputedStyle(canvas); if (s.width) { canvas.width = parseFloat(s.width)*(options.devicePixelRatio||devicePixelRatio||1); canvas.height = parseFloat(s.height)*(options.devicePixelRatio||devicePixelRatio||1); } + gl.viewport(0,0, canvas.width|0,canvas.height|0); var r=canvas.width/canvas.height; + // Defaults, resolve function input + var a,p=[],l=[],t=[],c=[.5,.5,.5],alpha=0,lastpos=[-1.95,1.5,0,1]; gl.clear(gl.COLOR_BUFFER_BIT+gl.DEPTH_BUFFER_BIT); while (x.call) x=x(); + // Create default camera matrix and initial lastposition (contra-compensated for camera) + M = mtx(options.camera); + var a = new this(); a.set([1,-2,1.90*canvas.height/canvas.width,0],1); a = options.camera.Conjugate.Mul(a.Dual).Mul(options.camera); + lastpos = a.slice(11,14).map((y,i)=>(i<=1?1:-1)*y/a[14]).reverse(); + var linediff = new this(); linediff.set([0,0,-0.12*2000/canvas.width*(options.fontSize||1),0],1); + linediff = options.camera.Conjugate.Mul(linediff.Dual).Mul(options.camera).slice(11,14).map((y,i)=>(i<=1?1:-1)*y/a[14]).reverse(); + // Grid. + if (options.grid) { + const gr = options.gridSize||1; + if (!options.gridLines) { options.gridLines=[[],[],[]]; for (var i=-gr; i<=gr; i+=gr/10) { + options.gridLines[0].push(i,-gr,gr, i,-gr,-gr, gr,-gr,i, -gr,-gr,i); + options.gridLines[1].push(i,gr,gr, i,-gr,gr, gr,i,gr, -gr,i,gr); + options.gridLines[2].push(-gr,i,gr, -gr,i,-gr, -gr,gr,i, -gr,-gr,i); + }} + var ltest = [], ltest2 = [], ttest = []; for (var j=0; j<3; ++j) for (var i=0; i{ while (x.call) x=x.call(); x=interprete(x);l.push.apply(l,x.pos); }); var d = {tp:-1}; } + else if (e instanceof Array && e.length==3) { e.forEach(x=>{ while (x.call) x=x.call(); x=interprete(x);t.push.apply(t,x.pos); }); var d = {tp:-1}; } + else var d = interprete(e); + if (d.tp) lastpos=d.pos; + if (d.tp==1) p.push.apply(p,d.pos); + if (d.tp==2) { l.push.apply(l,d.pos.map((x,i)=>x-d.normal[i]*3)); l.push.apply(l,d.pos.map((x,i)=>x+d.normal[i]*3)); } + if (d.tp==3) { t.push.apply(t,d.pos.map((x,i)=>x+d.tg[i]+d.btg[i])); t.push.apply(t,d.pos.map((x,i)=>x-d.tg[i]+d.btg[i])); t.push.apply(t,d.pos.map((x,i)=>x+d.tg[i]-d.btg[i])); + t.push.apply(t,d.pos.map((x,i)=>x-d.tg[i]+d.btg[i])); t.push.apply(t,d.pos.map((x,i)=>x+d.tg[i]-d.btg[i])); t.push.apply(t,d.pos.map((x,i)=>x-d.tg[i]-d.btg[i])); } + if (d.tp==4) { + var ne=0,la=0; + if (d.weight2<0) { c[0]=1;c[1]=0;c[2]=0; } + for (var j=0; j<65; j++) { + ne = d.pos.map((x,i)=>x+Math.cos(j/32*Math.PI)*d.weight2*d.tg[i]+Math.sin(j/32*Math.PI)*d.weight2*d.btg[i]); if (ne&&la&&(d.weight2>0||j%2==0)) { l.push.apply(l,la); l.push.apply(l,ne); }; la=ne; + } + } + if (d.tp==6) { + if (d.weight2<0) { c[0]=1;c[1]=0;c[2]=0; } + if (options.useUnnaturalLineDisplayForPointPairs) { + l.push.apply(l,d.pos.map((x,i)=>x-d.normal[i]*(options.scale||1))); + l.push.apply(l,d.pos.map((x,i)=>x+d.normal[i]*(options.scale||1))); + } + p.push.apply(p,d.pos.map((x,i)=>x-d.normal[i]*(options.scale||1))); + p.push.apply(p,d.pos.map((x,i)=>x+d.normal[i]*(options.scale||1))); + } + if (d.tp==5) { + if (!sphere) { + var pnts = [], tris=[], S=Math.sin, C=Math.cos, pi=Math.PI, W=96, H=48; + for (var j=0; jx.s); + gl.enable(gl.BLEND); gl.blendFunc(gl.CONSTANT_ALPHA, gl.ONE_MINUS_CONSTANT_ALPHA); gl.blendColor(1,1,1,1-(alpha||0.1)); gl.enable(gl.CULL_FACE) + draw(programSphere,gl.TRIANGLES,undefined,c,[0,0,0],r,undefined,sphere.va); + gl.disable(gl.BLEND); gl.disable(gl.CULL_FACE); + M = oldM; + } + if (i==ll-1 || d.tp==0) { + // render triangles, lines, points. + if (alpha) { gl.enable(gl.BLEND); gl.blendFunc(gl.CONSTANT_ALPHA, gl.ONE_MINUS_CONSTANT_ALPHA); gl.blendColor(1,1,1,1-alpha); } + if (t.length) { draw(program,gl.TRIANGLES,t,c,[0,0,0],r); t.forEach((x,i)=>{ if (i%9==0) lastpos=[0,0,0]; lastpos[i%3]+=x/3; }); t=[]; } + if (l.length) { + var ltest = [], ltest2 = [], ttest = []; for (var li=0; lix%(countx*county))); e.va3.tcount = (countx-1)*county*2*3; + } + if ( e.call && e.length==1 && !e.va2) { var countx=e.dx||256; + var temp=new Float32Array(3*countx),o=new Float32Array(3),et=[]; + for (var ii=0; ii{ + if (e instanceof Array && e.length==3) { tc++; e.forEach(x=>{ while (x.call) x=x.call(); x=interprete(x);et3.push.apply(et3,x.pos); }); var d = {tp:-1}; } + else { + var d = interprete(e); + if (d.tp==1) { pc++; et.push(...d.pos); } + if (d.tp==2) { lc++; et2.push(...d.pos.map((x,i)=>x-d.normal[i]*10),...d.pos.map((x,i)=>x+d.normal[i]*10)); } + } + }); + e.va = createVA(et,undefined); e.va.tcount = pc; + e.va2 = createVA(et2,undefined); e.va2.tcount = lc*2; + e.va3 = createVA(et3,undefined); e.va3.tcount = tc*3; + } + // render the vertex array. + if (e.va && e.va.tcount) { gl.enable(gl.BLEND); gl.blendFunc(gl.SRC_ALPHA, gl.ONE_MINUS_SRC_ALPHA); draw(programPoint,gl.POINTS,undefined,[0,0,0],c,r,undefined,e.va); gl.disable(gl.BLEND); }; + if (e.va2 && e.va2.tcount) draw(program,gl.LINES,undefined,[0,0,0],c,r,undefined,e.va2); + if (e.va3 && e.va3.tcount) draw(program,gl.TRIANGLES,undefined,c,[0,0,0],r,undefined,e.va3); + } + if (alpha) gl.disable(gl.BLEND); // no alpha for text printing. + // setup a new color + if (typeof e == "number") { alpha=((e>>>24)&0xff)/255; c[0]=((e>>>16)&0xff)/255; c[1]=((e>>>8)&0xff)/255; c[2]=(e&0xff)/255; } + if (typeof(e)=='string') { + if (options.htmlText) { + if (!x['_'+i]) { console.log('creating div'); Object.defineProperty(x,'_'+i, {value: document.body.appendChild(document.createElement('div')), enumerable:false }) }; + var rc = canvas.getBoundingClientRect(), div = x['_'+i]; + var pos2 = Element.Mul( [[M[0],M[4],M[8],M[12]],[M[1],M[5],M[9],M[13]],[M[2],M[6],M[10],M[14]],[M[3],M[7],M[11],M[15]]], [...lastpos,1]).map(x=>x.s); + pos2 = Element.Mul( [[5,0,0,0],[0,5*(r||2),0,0],[0,0,1,-1],[0,0,2,0]], pos2).map(x=>x.s).map((x,i,a)=>x/a[3]); + Object.assign(div.style,{position:'fixed',pointerEvents:'none',left:rc.left + (rc.right-rc.left)*(pos2[0]/2+0.5),top: rc.top + (rc.bottom-rc.top)*(-pos2[1]/2+0.5) - 20}); + if (div.last != e) { div.innerHTML = e; div.last = e; if (self.renderMathInElement) self.renderMathInElement(div); } + } else { + gl.enable(gl.BLEND); gl.blendFunc(gl.SRC_ALPHA,gl.ONE_MINUS_SRC_ALPHA); + var fw = 113, mapChar = (x)=>{ var c = x.charCodeAt(0)-33; if (c>=94) c = 94+specialChars.indexOf(x); return c/fw; } + draw(program2,gl.TRIANGLES, + [...Array(e.length*6*3)].map((x,i)=>{ var x=0,z=-0.2, o=x+(i/18|0)*1.1; return (0.05*(options.z||5))*[o,-1,z,o+1.2,-1,z,o,1,z,o+1.2,-1,z,o+1.2,1,z,o,1,z][i%18]}),c,lastpos,r, + [...Array(e.length*6*2)].map((x,i)=>{ var o=mapChar(e[i/12|0]); return [o,1,o+1/fw,1,o,0,o+1/fw,1,o+1/fw,0,o,0][i%12]})); gl.disable(gl.BLEND); lastpos[1]+=linediff[1]; lastpos[0]+=linediff[0]; lastpos[2]+=linediff[2]; + } + } + } + continue; + } + // PGA + if (options.dual && e instanceof Element) e = e.Dual; + // Convert planes to polygons. + if (e instanceof Element && e.Grade(1).Length > 0.001) { + var m = Element.Add(1, Element.Mul(e.Normalized, Element.Coeff(3,1))).Normalized, e0 = 0; + e=Element.sw(m,[[-1,-1],[-1,1],[1,1],[-1,-1],[1,1],[1,-1]].map(([x,z])=>Element.Trivector(x*e.Length,e0,z*e.Length,1))); + } + // Convert lines to line segments. + if (e instanceof Element && e.Grade(2).Length) + e=[e.LDot(e14).Wedge(e).Add(e.Wedge(Element.Coeff(1,1)).Mul(Element.Coeff(0,-(options.clip||3)))),e.LDot(e14).Wedge(e).Add(e.Wedge(Element.Coeff(1,1)).Mul(Element.Coeff(0,options.clip||3)))] + .map(x=>x[14]<0?x.Scale(-1):x); + // If euclidean point, store as point, store line segments and triangles. + if (e.e123) p.push.apply(p,e.slice(11,14).map((y,i)=>(i<=1?1:-1)*y/e[14]).reverse()); + if (e instanceof Array && e.length==2) l=l.concat.apply(l,e.map(x=>[...x.slice(11,14).map((y,i)=>(i<=1?1:-1)*y/x[14]).reverse()])); + if (e instanceof Array && e.length%3==0) t=t.concat.apply(t,e.map(x=>[...x.slice(11,14).map((y,i)=>(i<=1?1:-1)*y/x[14]).reverse()])); + // Render orbits of parametrised motors, as well as lists of points.. + function sw_mot_orig(A,R){ + var a0=A[0],a1=A[5],a2=A[6],a3=A[7],a4=A[8],a5=A[9],a6=A[10],a7=A[15]; + R[2] = -2*(a0*a3+a4*a7-a6*a2-a5*a1); + R[1] = -2*(a4*a1-a0*a2-a6*a3+a5*a7); + R[0] = 2*(a0*a1+a4*a2+a5*a3+a6*a7); + return R + } + if ( e.call && e.length==1) { var count=e.dx||64; + for (var ismot,xx,o=new Float32Array(3),ii=0; ii1) l.push(xx[0],xx[1],xx[2]); + var m = e(ii/(count-1)); + if (ii==0) ismot = m[0]||m[5]||m[6]||m[7]||m[8]||m[9]||m[10]; + xx = ismot?sw_mot_orig(m,o):m.slice(11,14).map((y,i)=>(i<=1?1:-1)*y).reverse(); //Element.sw(e(ii/(count-1)),o); + l.push(xx[0],xx[1],xx[2]); + } + } + if ( e.call && e.length==2 && !e.va) { var countx=e.dx||64,county=e.dy||32; + var temp=new Float32Array(3*countx*county),o=new Float32Array(3),et=[]; + for (var pp=0,ii=0; iix%(countx*county))); e.va.tcount = (countx-1)*county*2*3; + } + // Experimental display of motors using particle systems. + if (e instanceof Object && e.motor) { + if (!e.va || e.recalc) { + var seed = 1; function random() { var x = Math.sin(seed++) * 10000; return x - Math.floor(x); } + e.xRange = e.xRange === undefined ? 1:e.xRange; e.yRange = e.yRange === undefined ? 1:e.yRange; e.zRange = e.zRange === undefined ? 1:e.zRange; + var vtx=[], tx=[], vtx2=[]; + for (var i=0; i<(e.zRange===0?5000:60000); i++) { + var p = Element.Trivector(random()*(2*e.xRange)-e.xRange,random()*2*e.yRange-e.yRange,random()*2*e.zRange-e.zRange,1); +// var p2 = Element.sw(e.motor,p); + var p2 = e.motor.Mul(p).Mul(e.motor.Inverse); + tx.push(random(), random()); + vtx.push(...p.slice(11,14).reverse()); vtx2.push(...p2.slice(11,14).reverse()); + } + e.va = createVA(vtx,tx,undefined,vtx2); e.va.tcount = vtx.length/3; + e.recalc = false; + } + var time = performance.now()/1000; + gl.enable(gl.BLEND); gl.blendFunc(gl.SRC_ALPHA, gl.ONE_MINUS_SRC_ALPHA); gl.disable(gl.DEPTH_TEST); + draw(programmot, gl.POINTS,t,c,[time%1,0,0],r,undefined,e.va); + gl.disable(gl.BLEND); gl.enable(gl.DEPTH_TEST); + } + // we could also be an object with cached vertex array of triangles .. + else if (e.va || (e instanceof Object && e.data)) { + // Create the vertex array and store it for re-use. + if (!e.va) { + if (e.idx) { + var et = e.data.map(x=>[...x.slice(11,14).map((y,i)=>(i<=1?1:-1)*y/x[14]).reverse()]).flat(); + } else { + var et=[]; e.data.forEach(e=>{if (e instanceof Array && e.length==3) et=et.concat.apply(et,e.map(x=>[...x.slice(11,14).map((y,i)=>(i<=1?1:-1)*y/x[14]).reverse()]));}); + } + e.va = createVA(et,undefined,e.idx,e.color?new Float32Array(e.color):undefined); e.va.tcount = (e.idx && e.idx.length)?e.idx.length:e.data.length*3; + } + // render the vertex array. + var M5 = Element.Scalar(1).Add(Element.Coeff(7,2.5)); + if (e.transform) { + var M1 = mtx(e.transform, false); + var M2 = mtx(M5.Mul(options.camera), false); + M = Array(16).fill(0); + for (var ii=0; ii<4; ++ii) for (var jj=0; jj<4; ++jj) for (var kk=0; kk<4; ++kk) M[ii*4+kk] += M1[ii*4+jj] * M2[jj*4+kk]; + } + if (alpha) { gl.enable(gl.BLEND); gl.blendFunc(gl.CONSTANT_ALPHA, gl.ONE_MINUS_CONSTANT_ALPHA); gl.blendColor(1,1,1,1-alpha); } + draw(e.color?programcol:program,gl.TRIANGLES,t,c,[0,0,0],r,undefined,e.va); + if (alpha) gl.disable(gl.BLEND); + if (e.transform) { M=mtx(options.camera); } + } + // if we're a number (color), label or the last item, we output the collected items. + else if (typeof e=='number' || i==ll-1 || typeof e == 'string') { + // render triangles, lines, points. + if (alpha) { gl.enable(gl.BLEND); gl.blendFunc(gl.CONSTANT_ALPHA, gl.ONE_MINUS_CONSTANT_ALPHA); gl.blendColor(1,1,1,1-alpha); } + if (t.length) { draw(program,gl.TRIANGLES,t,c,[0,0,0],r); t.forEach((x,i)=>{ if (i%9==0) lastpos=[0,0,0]; lastpos[i%3]+=x/3; }); t=[]; } + if (l.length) { + var ltest = [], ltest2 = [], ttest = [], w = (options.lineWidth||1); for (var li=0; li>>24)&0xff)/255; c[0]=((e>>>16)&0xff)/255; c[1]=((e>>>8)&0xff)/255; c[2]=(e&0xff)/255; } + // render a label + if (typeof(e)=='string') { + if (options.htmlText) { + if (!canvas['_'+i]) { console.log('creating div'); Object.defineProperty(canvas,'_'+i, {value: document.body.appendChild(document.createElement('div')), enumerable:false }) }; + var rc = canvas.getBoundingClientRect(), div = canvas['_'+i]; + var pos2 = Element.Mul( [[M[0],M[4],M[8],M[12]],[M[1],M[5],M[9],M[13]],[M[2],M[6],M[10],M[14]],[M[3],M[7],M[11],M[15]]], [...lastpos,1]).map(x=>x.s); + pos2 = Element.Mul( [[5,0,0,0],[0,5*(r||2),0,0],[0,0,1,-1],[0,0,2,0]], pos2).map(x=>x.s).map((x,i,a)=>x/a[3]); + Object.assign(div.style,{position:'fixed',pointerEvents:'none',left:rc.left + (rc.right-rc.left)*(pos2[0]/2+0.5),top: rc.top + (rc.bottom-rc.top)*(-pos2[1]/2+0.5) - 20}); + if (div.last != e) { div.innerHTML = e; div.last = e; if (self.renderMathInElement) self.renderMathInElement(div,{output:'html'}); } + } else { + gl.enable(gl.BLEND); gl.blendFunc(gl.SRC_ALPHA,gl.ONE_MINUS_SRC_ALPHA); gl.disable(gl.DEPTH_TEST); + var fw = 113, mapChar = (x)=>{ var c = x.charCodeAt(0)-33; if (c>=94) c = 94+specialChars.indexOf(x); return c/fw; } + draw(program2,gl.TRIANGLES, + [...Array(e.length*6*3)].map((x,i)=>{ var x=0,z=0.2, o=x+(i/18|0)*1.1; return 0.2*(options.fontSize||1)*2000/canvas.width*[o,-1,z,o+1.2,-1,z,o,1,z,o+1.2,-1,z,o+1.2,1,z,o,1,z][i%18]}),c,lastpos,r, + [...Array(e.length*6*2)].map((x,i)=>{ var o=mapChar(e[i/12|0]); return [o,1,o+1/fw,1,o,0,o+1/fw,1,o+1/fw,0,o,0][i%12]})); gl.disable(gl.BLEND); lastpos[0] += linediff[0];lastpos[1] += linediff[1];lastpos[2] += linediff[2]; + if (!options.noZ) gl.enable(gl.DEPTH_TEST); + } + } + } + }; + // if we're no longer in the page .. stop doing the work. + armed++; if (document.body.contains(canvas)) armed=0; if (armed==2) return; + canvas.value=x; if (options&&!options.animate) canvas.dispatchEvent(new CustomEvent('input')); canvas.options=options; + if (options&&options.animate) { requestAnimationFrame(canvas.update.bind(canvas,f,options)); } + if (options&&options.still) { canvas.value=x; canvas.dispatchEvent(new CustomEvent('input')); canvas.im.style.width=canvas.style.width; canvas.im.style.height=canvas.style.height; canvas.im.src = canvas.toDataURL(); + var p=canvas.parentElement; if (p) { p.insertBefore(canvas.im,canvas); p.removeChild(canvas); } + } + } + // Basic mouse interactivity. needs more love. + var sel=-1; canvas.oncontextmenu = canvas.onmousedown = (e)=>{e.preventDefault(); e.stopPropagation(); if (e.detail===0) return; + var rc = canvas.getBoundingClientRect(), mx=(e.x-rc.left)/(rc.right-rc.left)*2-1, my=((e.y-rc.top)/(rc.bottom-rc.top)*4-2)*canvas.height/canvas.width; + sel = (e.button==2)?-3:-2; canvas.value.forEach((x,i)=>{ + if (tot != 5) { if (x[14]) { + var pos2 = Element.Mul( [[M[0],M[4],M[8],M[12]],[M[1],M[5],M[9],M[13]],[M[2],M[6],M[10],M[14]],[M[3],M[7],M[11],M[15]]], [-x[13]/x[14],x[12]/x[14],x[11]/x[14],1]).map(x=>x.s); + pos2 = Element.Mul( [[5,0,0,0],[0,-5*(2),0,0],[0,0,1,-1],[0,0,2,0]], pos2).map(x=>x.s).map((x,i,a)=>x/a[3]); + if ((mx-pos2[0])**2 + ((my)-pos2[1])**2 < 0.001) sel=i; + }} else { + x = interprete(x); if (x.tp==1) { + var pos2 = Element.Mul( [[M[0],M[4],M[8],M[12]],[M[1],M[5],M[9],M[13]],[M[2],M[6],M[10],M[14]],[M[3],M[7],M[11],M[15]]], [...x.pos,1]).map(x=>x.s); + pos2 = Element.Mul( [[5,0,0,0],[0,5*(r||2),0,0],[0,0,1,-1],[0,0,2,0]], pos2).map(x=>x.s).map((x,i,a)=>x/a[3]); + if ((mx-pos2[0])**2 + ((-my)-pos2[1])**2 < 0.01) sel=i; + } + } + }); + canvas.onwheel=e=>{e.preventDefault(); e.stopPropagation(); options.z = (options.z||5)+e.deltaY/100; if (!options.animate) requestAnimationFrame(canvas.update.bind(canvas,f,options));} + canvas.onmouseup=e=>sel=-1; canvas.onmouseleave=e=>sel=-1; + var tx,ty; canvas.ontouchstart = (e)=>{e.preventDefault(); canvas.focus(); var x = e.changedTouches[0].pageX, y = e.changedTouches[0].pageY; tx=x; ty=y; } + canvas.ontouchmove = function (e) { e.preventDefault(); + var x = e.changedTouches[0].pageX, y = e.changedTouches[0].pageY, mx = (x-(tx||x))/1000, my = -(y-(ty||y))/1000; tx=x; ty=y; + options.h = (options.h||0)+mx; options.p = Math.max(-Math.PI/2,Math.min(Math.PI/2, (options.p||0)+my)); if (!options.animate) requestAnimationFrame(canvas.update.bind(canvas,f,options)); return; + }; + canvas.onmousemove=(e)=>{ + var rc = canvas.getBoundingClientRect(),x; if (sel>=0) { if (tot==5) x=interprete(canvas.value[sel]); else { x=canvas.value[sel]; x={pos:[-x[13]/x[14],-x[12]/x[14],x[11]/x[14]]}; }} + var mx =(e.movementX)/(rc.right-rc.left)*2, my=((e.movementY)/(rc.bottom-rc.top)*2)*canvas.height/canvas.width; + if (sel==-2) { options.h = (options.h||0)+(options.conformal?-1:1)*mx/2; options.p = Math.max(-Math.PI/2,Math.min(Math.PI/2, (options.p||0)-my/2)); if (options.camera) options.camera.set( ( Element.Bivector(0,0,0,0,0,options.p).Exp() ).Mul( Element.Bivector(0,0,0,0,options.h,0).Exp() )); if (!options.animate) requestAnimationFrame(canvas.update.bind(canvas,f,options)); return; }; + if (sel==-3) { var ct = Math.cos(options.h||0), st= Math.sin(options.h||0), ct2 = Math.cos(options.p||0), st2 = Math.sin(options.p||0); + if (e.shiftKey) { options.posy = (options.posy||0)+my; } else { options.posx = (options.posx||0)+mx*ct+my*st; options.posz = (options.posz||0)+mx*-st+my*ct*ct2; } if (!options.animate) requestAnimationFrame(canvas.update.bind(canvas,f,options));return; }; if (sel < 0) return; + if (tot==5) { + x.pos[0] += (e.buttons!=2)?Math.cos((options.h||0))*mx:Math.sin(-(options.h||0))*-my; x.pos[1]+=(e.buttons!=2)?-my:0; x.pos[2]+=(e.buttons!=2)?Math.sin((options.h||0))*mx:Math.cos(-(options.h||0))*-my; + canvas.value[sel].set(Element.Mul(ni,(x.pos[0]**2+x.pos[1]**2+x.pos[2]**2)*0.5).Sub(no)); canvas.value[sel].set(x.pos,1); } + else if (x) { + var [cw,ch] = [rc.width, rc.height]; + var ox = (1/(options.scale || 1)) * ((e.offsetX / cw) - 0.5); + var oy = (1/(options.scale || 1)) * ((e.offsetY / ch) - 0.5) * (ch/cw); + var tb = Element.sw(options.camera,canvas.value[sel]); + var z = -(tb.e012/tb.e123+5)/5*4; tb.e023 = ox*z*tb.e123; tb.e013 = oy*z*tb.e123; + canvas.value[sel].set(Element.sw(options.camera.Reverse, tb)); + } + if (!options.animate) requestAnimationFrame(canvas.update.bind(canvas,f,options)); + } + } + canvas.value = f.call?f():f; canvas.options=options; + if (options&&options.still) { + var i=new Image(); canvas.im = i; return requestAnimationFrame(canvas.update.bind(canvas,f,options)),canvas; + } else return requestAnimationFrame(canvas.update.bind(canvas,f,options)),canvas; + } + + // The inline function is a js to js translator that adds operator overloading and algebraic literals. + // It can be called with a function, a string, or used as a template function. + static inline(intxt) { + // If we are called as a template function. + if (arguments.length>1 || intxt instanceof Array) { + var args=[].slice.call(arguments,1); + return res.inline(new Function(args.map((x,i)=>'_template_'+i).join(),'return ('+intxt.map((x,i)=>(x||'')+(args[i]&&('_template_'+i)||'')).join('')+')')).apply(res,args); + } + // Get the source input text. + var txt = (intxt instanceof Function)?intxt.toString():`function(){return (${intxt})}`; + // Our tokenizer reads the text token by token and stores it in the tok array (as type/token tuples). + var tok = [], resi=[], t, possibleRegex=false, c, tokens = [/^[\s\uFFFF]|^[\u000A\u000D\u2028\u2029]|^\/\/[^\n]*\n|^\/\*[\s\S]*?\*\//g, // 0: whitespace/comments + /^\"\"|^\'\'|^\".*?[^\\]\"|^\'.*?[^\\]\'|^\`[\s\S]*?[^\\]\`/g, // 1: literal strings + /^\d+[.]{0,1}\d*[ei][\+\-_]{0,1}\d*|^\.\d+[ei][\+\-_]{0,1}\d*|^e_\d*/g, // 2: literal numbers in scientific notation (with small hack for i and e_ asciimath) + /^\d+[.]{0,1}\d*[E][+-]{0,1}\d*|^\.\d+[E][+-]{0,1}\d*|^0x\d+|^\d+[.]{0,1}\d*|^\.\d+/g, // 3: literal hex, nonsci numbers + /^\/.*?[^\\]\/[gmisuy]?/g, // 4: regex + /^(\.Normalized|\.Length|\.\.\.|>>>=|===|!==|>>>|<<=|>>=|=>|\|\||[<>\+\-\*%&|^\/!\=]=|\*\*|\+\+|\-\-|<<|>>|\&\&|\^\^|^[{}()\[\];.,<>\+\-\*%|&^!~?:=\/]{1})/g, // 5: punctuator + /^[$_\p{L}][$_\p{L}\p{Mn}\p{Mc}\p{Nd}\p{Pc}\u200C\u200D]*/gu] // 6: identifier + while (txt.length) for (t in tokens) { + if (t == 4 && !possibleRegex) continue; + if (resi = txt.match(tokens[t])) { + c = resi[0]; if (t!=0) {possibleRegex = c == '(' || c == '=' || c == '[' || c == ',' || c == ';';} tok.push([t | 0, c]); txt = txt.slice(c.length); break; + }} // tokenise + // Translate algebraic literals. (scientific e-notation to "this.Coeff" + tok=tok.map(t=>(t[0]==2)?[2,'Element.Coeff('+basis.indexOf((!options.Cayley?simplify:(x)=>x)('e'+t[1].split(/e_|e|i/)[1]||1).replace('-',''))+','+(simplify(t[1].split(/e_|e|i/)[1]||1).match('-')?"-1*":"")+parseFloat(t[1][0]=='e'?1:t[1].split(/e_|e|i/)[0])+')']:t); + // String templates (limited support - needs fundamental changes.). + tok=tok.map(t=>(t[0]==1 && t[1][0]=='`')?[1,t[1].replace(/\$\{(.*?)\}/g,a=>"${"+Element.inline(a.slice(2,-1)).toString().match(/return \((.*)\)/)[1]+"}")]:t); + // We support two syntaxes, standard js or if you pass in a text, asciimath. + var syntax = (intxt instanceof Function)?[[['.Normalized','Normalize',2],['.Length','Length',2]],[['~','Conjugate',1],['!','Dual',1]],[['**','Pow',0,1]],[['^','Wedge'],['&','Vee'],['<<','LDot']],[['*','Mul'],['/','Div']],[['|','Dot']],[['>>>','sw',0,1]],[['-','Sub'],['+','Add']],[['%','%']],[['==','eq'],['!=','neq'],['<','lt'],['>','gt'],['<=','lte'],['>=','gte']]] + :[[['pi','Math.PI'],['sin','Math.sin']],[['ddot','this.Reverse'],['tilde','this.Involute'],['hat','this.Conjugate'],['bar','this.Dual']],[['^','Pow',0,1]],[['^^','Wedge'],['*','LDot']],[['**','Mul'],['/','Div']],[['-','Sub'],['+','Add']],[['<','lt'],['>','gt'],['<=','lte'],['>=','gte']]]; + // For asciimath, some fixed translations apply (like pi->Math.PI) etc .. + tok=tok.map(t=>(t[0]!=6)?t:[].concat.apply([],syntax).filter(x=>x[0]==t[1]).length?[6,[].concat.apply([],syntax).filter(x=>x[0]==t[1])[0][1]]:t); + // Now the token-stream is translated recursively. + function translate(tokens) { + // helpers : first token to the left of x that is not of a type in the skip list. + var left = (x=ti-1,skip=[0])=>{ while(x>=0&&~skip.indexOf(tokens[x][0])) x--; return x; }, + // first token to the right of x that is not of a type in the skip list. + right= (x=ti+1,skip=[0])=>{ while(x{tokens.splice(x,y-x+1,[tp,...(sub||tokens.slice(x,y+1))])}, + // match O-C pairs. returns the 'matching bracket' position + match = (O="(",C=")")=>{var o=1,x=ti+1; while(o){if(tokens[x][1]==O)o++;if(tokens[x][1]==C)o--; x++;}; return x-1;}; + // grouping (resolving brackets). + for (var ti=0,t,si;t=tokens[ti];ti++) if (t[1]=="(") glue(ti,si=match(),7,[[5,"("],...translate(tokens.slice(ti+1,si)),[5,")"]]); + // [] dot call and new + for (var ti=0,t,si; t=tokens[ti];ti++) { + if (t[1]=="[") { glue(ti,si=match("[","]"),7,[[5,"["],...translate(tokens.slice(ti+1,si)),[5,"]"]]); if (ti)ti--;} // matching [] + else if (t[1]==".") { glue(left(),right()); ti--; } // dot operator + else if (t[0]==7 && ti && left()>=0 && tokens[left()][0]>=6 && tokens[left()][1]!="return") { glue(left(),ti--) } // collate ( and [ + else if (t[1]=='new') { glue(ti,right()) }; // collate new keyword + } + // ++ and -- + for (var ti=0,t; t=tokens[ti];ti++) if (t[1]=="++" || t[1]=="--") glue(left(),ti); + // unary - and + are handled separately from syntax .. + for (var ti=0,t,si; t=tokens[ti];ti++) + if (t[1]=="-" && (left()<0 || (tokens[left()]||[])[1]=='return'||(tokens[left()]||[5])[0]==5)) glue(ti,right(),6,["Element.Sub(",tokens[right()],")"]); // unary minus works on all types. + else if (t[1]=="+" && (left()<0 || (tokens[left()]||[])[1]=='return'|| (tokens[left()]||[0])[0]==5 && (tokens[left()]||[0])[1][0]!=".")) glue(ti,ti+1); // unary plus is glued, only on scalars. + // now process all operators in the syntax list .. + for (var si=0,s; s=syntax[si]; si++) for (var ti=s[0][3]?tokens.length-1:0,t; t=tokens[ti];s[0][3]?ti--:ti++) for (var opi=0,op; op=s[opi]; opi++) if (t[1]==op[0]) { + // exception case .. ".Normalized" and ".Length" properties are re-routed (so they work on scalars etc ..) + if (op[2]==2) { var arg=tokens[left()]; glue(ti-1,ti,6,["Element."+op[1],"(",arg,")"]); } + // unary operators (all are to the left) + else if (op[2]) { var arg=tokens[right()]; glue(ti, right(), 6, ["Element."+op[1],"(",arg,")"]); } + // binary operators + else { var l=left(),r=right(),a1=tokens[l],a2=tokens[r]; if (op[0]==op[1]) glue(l,r,6,[a1,op[1],a2]); else glue(l,r,6,["Element."+op[1],"(",a1,",",a2,")"]); ti-=2; } + } + return tokens; + } + // Glue all back together and return as bound function. + return eval( ('('+(function f(t){return t.map(t=>t instanceof Array?f(t):typeof t == "string"?t:"").join('');})(translate(tok))+')') ); + } + } + + if ((p==2 || p==3) && (r==1)) { + res.arrow = res.inline(( from_point, to_point, w=0.03, aspect=0.8, camera=1 )=>{ + from_point = from_point/(-from_point|!1e0); to_point = to_point/(-to_point|!1e0); + var line = ( from_point & to_point ), l = line.Length; + var shape = [[0,w],[l-5*w,w],[l-5*w,aspect*5*w],[l,0],[l-5*w,-aspect*5*w],[l-5*w,-w],[0,-w]].map(([x,y])=>!(1e0+x*1e1+y*1e2)); + var sqrt = R => R==-1?1e12:(1+R).Normalized; + var R = ((to_point - from_point).UnDual).Normalized * 1e1; + var R2 = sqrt(from_point/!1e0) * sqrt(R); + var p2 = R2 >>> 1e3; + if (p2 != 0) { var p1 = (((~(camera+0e1) >>> 1e3)|line)/line).Normalized; return sqrt(p1/p2) * R2 >>> shape; } + return R2 >>> shape; + }) + } + + if (options.dual) { + Object.defineProperty(res.prototype, 'Inverse', {configurable:true, get(){ var s = 1/this.s**2; return this.map((x,i)=>i?-x*s:1/x ); }}); + } else { + // Matrix-free inverses up to 5D. Should translate this to an inline call for readability. + // http://repository.essex.ac.uk/17282/1/TechReport_CES-534.pdf + Object.defineProperty(res.prototype, 'Inverse', {configurable: true, get(){ + // Shirokov inverse .. + if (tot > 5) { + for (var N=2**(((tot+1)/2)|0), Uk=this.Scale(1), k=1; kres.prototype[x] = options.over.inline(res.prototype[x])); + res.prototype.Coeff = function() { for (var i=0,l=arguments.length; ix==0?undefined:(i?'('+x+')'+basis[i]:x.toString())).filter(x=>x).join(' + '); } + } + + // Experimental differential operator. + var _D, _DT, _DA, totd = basis.length; + function makeD(transpose=false){ + _DA = _DA || Algebra({ p:p,q:q,r:r,basis:options.basis,even:options.even,over:Algebra({dual:totd})}); // same algebra, but over dual numbers. + return (func)=>{ + var dfunc = _DA.inline(func); // convert input function to dual algebra + return (val,...args)=>{ // return a new function (the derivative w.r.t 1st param) + if (!(val instanceof res)) val = res.Scalar(val); // allow to be called with scalars. + args = args.map(x=>{ var r = _DA.Scalar(0); for (var i=0; ival.slice()); // call the function in the dual algebra. + if (transpose) for (var i=0; i