27:null 28:["$","title",null,{"children":"dot | LiangweiOIO | Observable"}] 2d:T6b5,// Create a Clifford Algebra with 2,0,1 metric. Algebra(2,0,1,()=>{ const point = (x,y)=>!(1e0 + x*1e1 + y*1e2); const line = (a,b,c)=>a*1e1 + b*1e2 + c*1e0; const scaleP =(P,s) => point((1e1|!P)*s, (1e2|!P)*s); const normalizeP = (P) => scaleP(P, 1 / (!P).Length); const xAxis = line(0,1,0); const A = point( 0.8,1.1); const An = () => normalizeP(A); const An1 = () => (xAxis << An) ^ xAxis; const B = point(1.1,0.5); const Bn = () => normalizeP(B); const Bn1 = () => (xAxis << Bn) ^ xAxis; const O = point(0, 0); const ob = () => O & B const perpObAn = () => ob << An; const projAnOb = () => perpObAn ^ ob; const perpObAn1 = () => ob << An1; const paraObAn1 = () => (ob << An1) / An1; const projAnParaObAn1 = () => paraObAn1 ^ perpObAn; const projAn1Ob = () => perpObAn1 ^ ob; return this.graph([ 'Drag A or B', 0x000000, [O, An], [O, A], [O, Bn], [O, B], [O, projAnOb], [O, projAn1Ob], 0xCCFFFF, [O, Bn, Bn1], 0x888888, [Bn, Bn1], [An, An1], [An, projAnParaObAn1], [An1, projAn1Ob], [O,An1], [An1, projAnParaObAn1], [projAnOb, An], 0xAAFFFF, [O, An1, projAn1Ob], [An, An1, projAnParaObAn1], 0x000000, An, 'An', Bn, 'Bn', 0x8884400, projAnOb, 0x004488, A,'A', B, 'B', ],{ grid : true, // Display a grid labels : true, // Label the grid lineWidth : 3, // Custom lineWidth (default=1) pointRadius : 1, // Custon point radius (default=1) fontSize : 1, // Custom font size (default=1) scale : 1.6, // Custom scale (default=1), mousewheel. }); });2e:Tc4e,Algebra(3,0,1,()=>{ // in 3D PGA, grade-1 elements or vectors (e0,e1,e2) represent // reflections AND planes (the invariant of a reflection) var plane = (a, b, c, d) => a * 1e1 + b * 1e2 + c * 1e3 + d * 1e0; var line = (...plucker) => plucker * [1e01, 1e02, 1e03, 1e12, 1e13, 1e23]; var point = (x, y, z) => !(1e0 + x * 1e1 + y * 1e2 + z * 1e3); const scaleP = (P, s) => point(-(1e1 | !P) * s, -(1e2 | !P) * s, -(1e3 | !P) * s); const normalizeP = (P) => scaleP(P, 1 / (!P).Length); const x0plane = plane(1, 0, 0, 0); const y0plane = plane(0, 1, 0, 0); const z0plane = plane(0, 0, 1, 0); const xAxis = y0plane ^ z0plane; const yAxis = z0plane ^ x0plane; const zAxis = x0plane ^ y0plane; const A = point(-0.5, 0.8, 0.7), B = point(-1.1, 0.65, 0.7), O = point(0, 0, 0); // const A = point(-0.5, 1, 0.9), B = point(-1.1, 0.5, 1), O = point(0, 0, 0); const An = () => normalizeP(A), Bn = () => normalizeP(B); const proj = (P, on) => () => (on << P) / on; const rej = (P, off) => (off << P); const parall = (line, P) => () => line << P / P; const coord = (P) => [1e1, 1e2, 1e3].map(e => { const c = -(e | (!P)) / P.Length; return c[0].toFixed(3); }).join(' '); const Anx = () => proj(An, xAxis); const An0y = () => proj(An, y0plane); const [Bnx, Bny, Bnz] = [xAxis, yAxis, zAxis].map((axis) => proj(Bn, axis)); const ob = () => O & B; const projx = proj(Anx, ob); const topz = () => parall(Anx & projx, An0y) ^ (zAxis & Bn); const projz = proj(An0y, ob); const topy = () => parall(An0y & projz, An) ^ (yAxis & Bn); const projy = proj(An, ob); return this.graph(()=>{ return [ `Drag A or B`, // light grey lines 0xAABBBB, xAxis, 'x', yAxis, 'y', zAxis, 'z', // light grey surfaces 0xDDDDDD, [projz,topz,An0y], [projy,topy,An], // magenta surfaces 0xFFCCFF, [O, Bn, Bnx], [O, Anx, projx], // green surfaces 0xDDFFCC, [O, Bn, Bnz], [projz, projx, topz], // blue surfaces 0xCCFFFF, [O, Bn, Bny], [projz, projy, topy], 0xFFAAAA,// light pink // grey lines 0x888888, [Anx, An0y], [An0y, projz], [An0y, topz], [An0y, An], [An, projy], [An, topy], 0x000000, [O, An], [O, A], [O, B],[O, Bn], // blue lines 0x00DDDD, [projz, projy], [projy, topy], [topy, projz], [Bn, Bny], [Bny, O], 0xFF00FF, //magenta [O, Anx], [Anx, projx],[projx,O], [Bn, Bnx], [Bnx, O], 0x11EE00, //green [projz, projx], [projx, topz], [topz, projz], [Bn, Bnz], [Bnz, O], // black points 0x000000, O, 'O', An, "An", Bn, "Bn", // blue points 0x224488, A,"A",B,"B", ] },{ grid : true, // Display a grid labels : true, // Label the grid h : 0.8, // Heading p : -0.35,// Pitching lineWidth : 2, // Custom lineWidth (default=1) pointRadius : 1, // Custon point radius (default=1) fontSize : 1, // Custom font size (default=1) scale : 2, // Custom scale (default=1), mousewheel. // animate: true, }); 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