Chandrupatla’s root-finding methodSidi’s root-finding methodRegular numbersDruidJS workerNatural breaksDistance to a segmentRay out of a convex hullWord Tour: 40k words and their friendsHello, @thi.ng/grid-iteratorsHead/tail breaksPseudo-blue noise shaderHow fast does walk-on-spheres converge?AoC 12: shortest path under constraintsKDE estimationPlot: Correlation heatmapPoisson Finish 2Poisson disk sampling functionsWoS with transportSimple and surprising sortLocal medianTime series topological subsamplingUnion-FindLevel set experiment 1Mean value coordinatesPoisson potentialMiddle-squareWorld of squares (spherical)World of squaresLargest Inscribed SquareHello, PyWaveletsGeothmetic meandianHello, Reorder.jsGeometric MedianImage FFTTransport to a mapDisc TransportTP3: Power Diagram and Semi-Discrete Optimal TransportThe blue waveHello, genetic-jsSliced Optimal TransportDruidJSSelf-Organizing Maps meet DelaunayHello, polygon-clippingseedrandom, minimalWalk on Spheres 2Walk on SpheresHello, AutoencoderKaprekar’s numberVoronoiMap2DHello, ccwt.jsPolygon TriangulationQuantile.invert?Linear congruential generatorHue blurNeedle in a haystackMoving average blurApollo 11 implementation of trigonometric functions, by Margaret H. Hamilton (march 1969)2D curves intersectionThe 2D approximate Newton-Raphson methodInverting Lee’s Tetrahedral projectionLinde–Buzo–Gray stipplingMean shift clustering with kd-tree2D point distributionsShortest pathKahan SummationHello, delatinDijkstra’s algorithm in gpu.jsLloyd’s relaxation on a graphManhattan DiameterManhattan VoronoiMobility landscapes — an introductionDijkstra’s shortest-path treeH3 odditiesProtein MatrixConvex Spectral WeightsKrigingDelaunay.findTrianglen-dimensions binning?Travelling with a self-organizing mapUMAP-o-MaticMNIST & UMAP-jsHello UMAP-jsMean shift clusteringLevenshtein transitionRd quasi-random sequencesAutomated label placement (countries)Phyllotaxis explainedMotionrugsPlanar hull (Andrew’s monotone chain algorithm)South Africa’s medial axisTravelling salesperson approximation with t-SNEDistance to shoreWorkerngraph: pagerank, louvain…t-SNE VoronoiCloud ContoursCircular function drawingKruskal MazeMyceliumTravelling salesperson approximation on the globe, with t-SNEtsne.jstsne.js & worker
Sort stuff by similarity
sorted = order_by_distance(points)
function* order_by_distance(nodes, distance) {
const n = nodes.length;
const m = new Map(),
connect = [];
if (distance === undefined) distance = euclidian2;
function D(i, j) {
return distance(nodes[i], nodes[j]);
}
const links = [];
for (var i = 0; i < nodes.length; i++) {
for (var j = i + 1; j < nodes.length; j++) {
const d = distance(nodes[i], nodes[j]);
links.push([i, j, d]);
}
}
links.sort((a, b) => a[2] - b[2]);
for (const l of links) {
const [i, j, dist] = l,
s0 = m.get(i),
s1 = m.get(j);
if (s0 && s0 === s1) continue; // i and j are already linked
if (s0 && !s1) {
const s = s0,
a = j;
m.set(a, s);
if (D(a, s[0]) < D(a, s[s.length - 1])) {
connect.push({ left: [a, a], right: [s[0], s[s.length - 1]], dist });
s.unshift(a);
} else {
connect.push({ left: [s[0], s[s.length - 1]], right: [a, a], dist });
s.push(a);
}
} else if (s1 && !s0) {
const s = s1,
a = i;
m.set(a, s);
if (D(a, s[0]) < D(a, s[s.length - 1])) {
connect.push({ left: [a, a], right: [s[0], s[s.length - 1]], dist });
s.unshift(a);
} else {
connect.push({ left: [s[0], s[s.length - 1]], right: [a, a], dist });
s.push(a);
}
} else if (!s0 && !s1) {
const s = [i, j];
m.set(i, s);
m.set(j, s);
connect.push({ left: [i, i], right: [j, j], dist });
} else {
// join the two segments by the shortest link between their extremities
const d00 = D(s0[0], s1[0]),
d01 = D(s0[0], s1[s1.length - 1]),
d10 = D(s0[s0.length - 1], s1[0]),
d11 = D(s0[s0.length - 1], s1[s1.length - 1]),
k = Math.min(d00, d01, d10, d11);
var s;
if (k === d00) s = [s1.reverse(), s0];
else if (k === d01) s = [s1, s0];
else if (k === d10) s = [s0, s1];
else if (k === d11) s = [s0, s1.reverse()];
connect.push({
left: [s[0][0], s[0][s[0].length - 1]],
right: [s[1][0], s[1][s[1].length - 1]],
dist
});
s = s.flat();
for (const a of s) m.set(a, s);
}
}
nodes = m.get(0).map(i => nodes[i]);
if (opts.crossover || opts.points) {
do {
yield nodes;
var gain = 0;
for (var i = 0; i < nodes.length - 2; i++) {
for (var j = i + 2; j < nodes.length - 1; j++) {
// no-crossings optimization [i,i+1] vs [j, j+1]
if (opts.crossover) {
const ii1 = distance(nodes[i], nodes[i + 1]),
jj1 = distance(nodes[j], nodes[j + 1]),
ij = distance(nodes[i], nodes[j]),
i1j1 = distance(nodes[j + 1], nodes[i + 1]),
diff = ii1 + jj1 - ij - i1j1;
if (diff > 0) {
gain += diff;
nodes = nodes
.slice(0, i + 1)
.concat(nodes.slice(i + 1, j + 1).reverse())
.concat(nodes.slice(j + 1, Infinity));
}
}
if (opts.points && j < nodes.length - 3) {
const ii1 = distance(nodes[i], nodes[i + 1]),
i1i2 = distance(nodes[i + 1], nodes[i + 2]),
ij1 = distance(nodes[i], nodes[j + 1]),
i1j = distance(nodes[i + 1], nodes[j]),
ii2 = distance(nodes[i], nodes[i + 2]),
i1j1 = distance(nodes[i + 1], nodes[j + 1]),
jj1 = distance(nodes[j], nodes[j + 1]),
j1j2 = distance(nodes[j + 1], nodes[j + 2]),
jj2 = distance(nodes[j], nodes[j + 2]),
diff0 = ii1 + jj1 + j1j2 - (ij1 + i1j1 + jj2),
diff1 = ii1 + jj1 + i1i2 - (i1j + i1j1 + ii2);
if (diff0 > 0) {
/*
i j
>j1
i1 j2 */
gain += diff0;
nodes = nodes
.slice(0, i + 1)
.concat([nodes[j + 1]])
.concat(nodes.slice(i + 1, j + 1))
.concat(nodes.slice(j + 2, Infinity));
} else if (diff1 > 0) {
/*
j i
>i1
j1 i2 */
gain += diff1;
nodes = nodes
.slice(0, i + 1)
.concat(nodes.slice(i + 2, j + 1))
.concat([nodes[i + 1]])
.concat(nodes.slice(j + 1, Infinity));
}
}
}
}
} while (gain);
}
nodes.connect = connect;
yield nodes;
return nodes;
function euclidian2(a, b) {
return a.map((_, i) => (a[i] - b[i]) ** 2).reduce((a, b) => a + b);
}
}
sorted.connect
branchset = {
const branches = [],
m = new Map();
for (const c of sorted.connect) {
const branch = {
name: `${c.left[1]}-${c.right[0]}`,
length: c.dist,
branchset: []
};
branches.push(branch);
let p0 = m.get(c.left[0]),
p1 = m.get(c.right[1]);
if (p0 === undefined) p0 = { name: `${c.left[0]}`, length: 0 };
branch.branchset.push(p0);
if (p1 === undefined) p1 = { name: `${c.right[1]}`, length: 0 };
branch.branchset.push(p1);
m.set(c.left[0], branch);
m.set(c.right[1], branch);
}
return branches[branches.length - 1];
}
import {chart as phylogenetic} with {branchset as data} from "@mbostock/tree-of-life"
phylogenetic
function chart() {
const context = DOM.context2d(height, height),
path = d3.geoPath().context(context),
x = d3.scaleLinear().range([10, height - 10]),
coordinates = sorted.map(d => d.map(x));
context.beginPath();
path({
type: "LineString",
coordinates
});
context.lineWidth = 2;
context.strokeStyle = "lightblue";
context.stroke();
context.lineWidth = 0.5;
context.beginPath();
path.pointRadius(2)({ type: "MultiPoint", coordinates });
context.fillStyle = "white";
context.fill();
context.strokeStyle = "black";
context.stroke();
context.beginPath();
path.pointRadius(4)({
type: "MultiPoint",
coordinates: [coordinates[0], coordinates[coordinates.length - 1]]
});
context.fillStyle = "orange";
context.fill();
context.strokeStyle = "black";
context.stroke();
return context.canvas;
}
height = Math.min(700, width)
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