30:T666,canvas = CGA.inline((choice,tresh,show_start_end)=>{ // We start by defining a null basis, and upcasting for points var ni = 1e4+1e5, no = .5e5-.5e4, nino = ni^no; var up = (x)=> no + x + .5*x*x*ni; // for OPNS viz we also need an up version that uses only basis blades : var upviz = ["x","y","z",".5*(x*x+y*y+z*z)-.5",".5*(x*x+y*y+z*z)+.5"]; // some elments. switch (choice) { case "1": var e1 = (!(no-2*ni) & !(up(1e2+1e1)-4*ni)).Normalized; var e2 = (up(1e1)^up(1e2)^up(-1e1)).Normalized; break; case "2": var e1 = (!(no-2*ni) & !(up(1e2+1e1)-4*ni)).Normalized; var e2 = -1*(up(1e3)^up(1e2)^up(-1e3)).Normalized; break; case "3": var e1 = (!(no-2*ni) & !(up(1e2+1e1)-4*ni)).Normalized; var e2 = (up(1e1)^ni^up(-1e1)).Normalized; break; case "4": var e1 = (!(no-.5*ni) & !(up(1e2+1e1)-3.7*ni)).Normalized; var e2 = (up(1e1)^up(1e2)^up(-1e1)).Normalized; break; } // graph it. (directly accessing the OPNS visualizer) return this.graphGL2(()=>{ var i = Math.max(0,Math.min(1, 0.5+0.6*Math.sin(performance.now()/2100))); return [ 0xffffff, up(1e1+1e2+1e3), // GRADE 1 : gray point 0xff0000, up(1e2)^up(1e3), // GRADE 2 : red point pair. 0x0000ff, up(-1e2)^ni, // GRADE 2 : point pair with infinity blue 0xff00ff, up(1e2+1e1)^ni^up(-1e2+1e1), // GRADE 3 : purple line show_start_end?e1:"",show_start_end?e2:"", 0x00ff00,(i*e1 + (1-i)*e2).Normalized, ] },{up:upviz,animate:true,stepSize:0.15,maxSteps:128,tresh:0.15*(tresh/50)}) })(choice,tresh,show_start_end)31:T59c,parametric_version = Algebra(4,1).inline((choice,tresh,show_start_end)=>{ // We start by defining a null basis, and upcasting for points var ni = 1e4+1e5, no = .5e5-.5e4, nino = ni^no; var up = (x)=> no + (x.e1*1e2 + x.e2*1e1 + x.e3*1e3) + .5*x*x*ni; // for OPNS viz we also need an up version that uses only basis blades : var upviz = ["x","y","z",".5*(x*x+y*y+z*z)-.5",".5*(x*x+y*y+z*z)+.5"]; // some elments. switch (choice) { case "1": var e1 = (!(no-2*ni) & !(up(1e2+1e1)-4*ni)).Normalized; var e2 = (up(1e1)^up(1e2)^up(-1e1)).Normalized; break; case "2": var e1 = (!(no-2*ni) & !(up(1e2+1e1)-2*ni)).Normalized; var e2 = -1*(up(1e3)^up(1e2)^up(-1e3)).Normalized; break; case "3": var e1 = (!(no-2*ni) & !(up(1e2+1e1)-4*ni)).Normalized; var e2 = (up(1e1)^ni^up(-1e1)).Normalized; break; case "4": var e1 = (!(no-.5*ni) & !(up(1e2+1e1)-3.7*ni)).Normalized; var e2 = (up(1e1)^up(1e2)^up(-1e1)).Normalized; break; } // graph it. (directly accessing the OPNS visualizer) return this.graph(()=>{ var i = Math.max(0,Math.min(1, 0.5+0.6*Math.sin(performance.now()/2100))); return [ show_start_end?e1:"",show_start_end?e2:"", 0x00ff00,(i*e1 + (1-i)*e2).Normalized, ] },{gl:true,conformal:true,animate:true,stepSize:0.15,maxSteps:160,tresh:0.15*(tresh/50)}) })(choice,tresh,show_start_end)32:[] 2e:{"title":"CGA OPNS","cells":[{"id":0,"value":"md`# CGA OPNS\n\nfor Joan and Hugo`","pinned":false,"hidden":false,"mode":"ojs"},{"id":276,"value":"md`This notebook allows you to experiment with direct visualization of the outer product null space of various CGA objects. Feel free to fork and edit. (Observable notebooks are great - with integrated latex, markdown and GA math and visualizations)\n\nThey consist out of a collection of cells, and you can click and edit any of them easily. To do GA in a notebook, we start off by including ganja.js in one of those cells :`","pinned":false,"hidden":false,"mode":"ojs"},{"id":4,"value":"Algebra = require('ganja.js')","pinned":true,"hidden":false,"mode":"ojs"},{"id":50,"value":"md`The OPNS visualizer only works with the graded algebra generator. That one is automatic for dimensions higher than 6, but for CGA you have to specify it :`","pinned":false,"hidden":false,"mode":"ojs"},{"id":6,"value":"CGA = Algebra({p:4,q:1,graded:true})","pinned":true,"hidden":false,"mode":"ojs"},{"id":52,"value":"md`Then the only extra thing you need is to tell the visualizer how to convert euclidean xyz to the correct grade-1 multivector.\n\nThat's the **upviz** in the block below (called canvas).\n\nThis visualizer also only does OPNS - IPNS coming soon ;). For non-manifold objects (i.e. circles, lines), a **tresh** option allows you to determine how thick they will be rendered. For now only grade 4 and grade 3 elements will be rendered. (rest coming soon - **has been added in v1.0.82**)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":278,"value":"md`In the block below we're interpolating between some grade 3 elements and examine the exact shape of the outer product null space of the interpolated result. Use the inputs below to explore.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":224,"value":"viewof choice = html``","pinned":false,"hidden":false,"mode":"ojs"},{"id":238,"value":"viewof tresh = html``","pinned":false,"hidden":false,"mode":"ojs"},{"id":247,"value":"viewof show_start_end = { \n var lbl=html`show start/end states`\n var cb = lbl.firstChild;\n lbl.value = false;\n cb.onclick = ()=>{\n lbl.value = !lbl.value;\n lbl.dispatchEvent(new CustomEvent(\"input\"));\n }\n return lbl\n} ","pinned":false,"hidden":false,"mode":"ojs"},{"id":8,"value":"$30","pinned":false,"hidden":false,"mode":"ojs"},{"id":291,"value":"md`I still have to match the camera's between the visualizers .. but here's the old school parametric version of the same thing .. \n\n(this is using pretty much the GA 'interprete' to generate parametric geometry)\n\nIt shows mostly how its not really an accurate representation of inbetween states when interpolating.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":282,"value":"$31","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W32","stdlib":"1","titling":"auto"}