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Create n-dimentional plexispheres!
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(function() { | |
var arr = function(length, fill) { | |
var arr = []; | |
for (var i = 0; i < length; i++) | |
{ | |
arr.push(fill); | |
} | |
return arr; | |
}; | |
var arrbut = function(arr, but) { | |
var out = []; | |
for (var i in arr) { | |
if (i != but) | |
{ | |
out.push(arr[i]); | |
} | |
} | |
return out; | |
} | |
var mixverts = function(verts) { | |
var dim = verts[0].length; | |
var vert = arr(dim, 0); | |
for (var i in verts) | |
{ | |
for (var j in verts[i]) | |
{ | |
vert[j] += verts[i][j] / verts.length; | |
} | |
} | |
return vert; | |
} | |
var simplex = function(dim) { | |
var geo = {verts: [], facets: []}; | |
for (var i = 0; i < dim + 1; i++) | |
{ | |
geo.verts.push(arr(dim, null)); | |
for (var j = i + 1; j < dim; j++) | |
{ | |
geo.verts[i][j] = 0; | |
} | |
} | |
//https://en.wikipedia.org/wiki/Simplex#Cartesian_coordinates_for_regular_n-dimensional_simplex_in_Rn | |
var dotsolve = 1; | |
var dotrem = -1 / dim; | |
for (var i = 0; i < dim; i++) | |
{ | |
var ssum = 0; | |
for (var j = 0; j < i; j++) | |
{ | |
ssum += geo.verts[i][j] * geo.verts[i][j]; | |
} | |
var pythsolve = geo.verts[i][i] = Math.sqrt(1 - ssum); | |
dotsolve = dotrem / pythsolve; | |
for (var j = i + 1; j < dim + 1; j++) | |
{ | |
geo.verts[j][i] = dotsolve; | |
} | |
dotrem -= dotsolve * dotsolve; | |
} | |
for (var i = 0; i < dim + 1; i++) | |
{ | |
var facet = []; | |
for (var j = 0; j < dim + 1; j++) | |
{ | |
if (i != j) | |
{ | |
facet.push(j); | |
} | |
} | |
geo.facets.push(facet); | |
} | |
return geo; | |
}; | |
var sub = { | |
center: function (geo, dim) { | |
var newfacets = []; | |
for (var i in geo.facets) | |
{ | |
var facet = geo.facets[i]; | |
var vertind = geo.verts.length; | |
var verts = []; | |
for (var j = 0; j < dim; j++) | |
{ | |
var newfacet = []; | |
for (var k = 0; k < dim; k++) | |
{ | |
verts.push(geo.verts[facet[j]]); | |
if (k != j) | |
{ | |
newfacet.push(facet[k]); | |
} | |
} | |
newfacet.push(vertind); | |
newfacets.push(newfacet); | |
} | |
geo.verts.push(mixverts(verts)); | |
} | |
geo.facets = newfacets; | |
return geo; | |
}, | |
edge: function (geo, dim) { | |
var edges = {}; | |
for (var i in geo.facets) | |
{ | |
var facet = geo.facets[i]; | |
var newfacet = []; | |
for (var j = 0; j < facet.length; j++) | |
{ | |
var sel = arrbut(facet, j); | |
sel.sort(); | |
var edge = edges[sel]; | |
if (!edge) | |
{ | |
var verts = []; | |
for (var k in sel) | |
{ | |
verts.push(geo.verts[sel[k]]); | |
} | |
edge = geo.verts.length; | |
edges[sel] = edge; | |
geo.verts.push(mixverts(verts)); | |
} | |
newfacet.push(edge); | |
} | |
for (var j = 0; j < facet.length; j++) | |
{ | |
var nextfacet = [facet[j]]; | |
for (var k = 0; k < facet.length; k++) | |
{ | |
if (k != j) | |
{ | |
nextfacet.push(newfacet[k]); | |
} | |
} | |
geo.facets.push(nextfacet); | |
} | |
geo.facets[i] = newfacet; | |
} | |
return geo; | |
} | |
}; | |
var norm = function (vert) | |
{ | |
var ssum = 0; | |
for (var i in vert) | |
{ | |
ssum += vert[i] * vert[i]; | |
} | |
ssum = Math.sqrt(ssum); | |
for (var i in vert) | |
{ | |
vert[i] /= ssum; | |
} | |
return vert; | |
} | |
plexisphere = function(pos, radius, subdiv, mode, normmode) { | |
var dim = pos.length; | |
if (!sub[mode]) | |
{ | |
console.log("fail"); | |
return; | |
} | |
var geo = simplex(dim); | |
for (var i = 0; i < subdiv; i++) | |
{ | |
geo = sub[mode](geo, dim); | |
if (normmode == "each") | |
{ | |
for (var j in geo.verts) | |
{ | |
norm(geo.verts[j]); | |
} | |
} | |
} | |
if (normmode == "last") | |
{ | |
for (var i in geo.verts) | |
{ | |
norm(geo.verts[i]); | |
} | |
} | |
for (var i in geo.verts) | |
{ | |
for (var j = 0; j < dim; j++) | |
{ | |
geo.verts[i][j] *= radius; | |
geo.verts[i][j] += pos[j]; | |
} | |
} | |
return geo; | |
}; | |
})(); | |
var toobj = function(geo) | |
{ | |
var obj = ""; | |
for (var i in geo.verts) | |
{ | |
var vert = geo.verts[i]; | |
obj += "v"; | |
for (var j in vert) | |
{ | |
obj += " " + vert[j]; | |
} | |
obj += "\n"; | |
} | |
for (var i in geo.facets) | |
{ | |
obj += "\n"; | |
var facet = geo.facets[i]; | |
obj += "f"; | |
for (var j in facet) | |
{ | |
obj += " " + (facet[j] + 1); | |
} | |
} | |
return obj; | |
} |
toobj(plexisphere([0, 0, 0], 5, 6, "edge", "last")); //nice 3-d plexisphere as a .obj model
plexisphere([0, 0, 0, 0], 5, 3, "center", "each"); //wtf 5-d thing
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