Public
Edited
Aug 10, 2022
Importers
14 stars
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 coordinatesMiddle-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 WeightsSort stuff by similarityKrigingDelaunay.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
Poisson potential
function potential(
graph,
charges,
{ alpha = 0.3, precision = 1e-8, maxSteps = 20000 } = {}
) {
const n = charges.length;
const D = new Float64Array(n); // differences
const A = new Float64Array(n);
const q = d3.mean(charges);
// normalize the flow by the count of valid neighbors
const nneighbors = new Uint16Array(n);
for (let s = 0; s < graph.sources.length; s++) {
const i = graph.sources[s];
const j = graph.targets[s];
if (!isNaN(charges[j])) nneighbors[i]++;
if (!isNaN(charges[i])) nneighbors[j]++;
}
// impedance normalization
const conductance = graph.costs
? Float32Array.from(graph.costs, (d) => 1 / d)
: null;
const Q = charges.map(
(d, i) =>
alpha *
(d - q) *
(!nneighbors[i]
? 0 // special case isolated points
: 1 / nneighbors[i])
);
const E = precision * A.length;
let steps = 0,
error,
c;
const { sources, targets } = graph;
do {
// add charges
for (let i = 0; i < D.length; i++) D[i] = Q[i];
// diffuse
for (let s = 0; s < sources.length; s++) {
const i = sources[s];
const j = targets[s];
// let d = alpha * (A[j] - A[i]); // Jacobi
let d = alpha * (D[j] + A[j] - D[i] - A[i]); // SOR
if (conductance) d *= conductance[s];
if (!isNaN(d)) {
D[i] += d;
D[j] -= d;
}
}
for (let i = 0; i < D.length; i++) A[i] += D[i];
// measure change
error = d3.sum(D, (d) => d * d);
steps++;
} while (error > E && steps < maxSteps);
return Object.assign(A, { steps, error, E });
}
P = potential(graph, C)
points = [...pick2d(width, height, npoints, distributionType)]
C = {
const C = new Float32Array(points.length);
for (const i of pointIndex.slice(0, sources)) {
const v = 1 + (!sourcesOnly && i % 2 ? -3 : 1);
C[i] += v;
graph.sources.forEach((k, s) => {
let j = graph.targets[s];
if (j === i) (j = k), (k = i);
if (k === i) C[j] += v * 0.6;
});
}
return C;
}
C.filter((d) => d)
pointIndex = d3.shuffle(d3.range(points.length))
// the voronoi partition defines the graph *and* is useful to draw the chart
voronoi = d3.Delaunay.from(points).voronoi([0, 0, width, height])
graph = {
let links = d3
.range(points.length)
.flatMap((i) => Array.from(voronoi.neighbors(i), (j) => [i, j]));
// on the square grid, remove diagonals
if (distributionType === "grid") {
let stride;
points.find((d, i) => d[0] > 0 && (stride = i));
links = links.filter(([i, j]) => [1, stride].includes(Math.abs(i - j)));
}
return {
sources: Uint16Array.from(links, ([i]) => i),
targets: Uint16Array.from(links, ([, j]) => j)
// costs (defaults to ...1)
};
}
import { pick2d } from "@fil/2d-point-distributions"
function fade(context, alpha) {
const { globalAlpha, globalCompositeOperation } = context;
context.globalCompositeOperation = "destination-out";
context.fillStyle = "white";
context.globalAlpha = alpha || 1;
context.fillRect(0, 0, context.canvas.width, context.canvas.height);
context.globalAlpha = globalAlpha;
context.globalCompositeOperation = globalCompositeOperation;
}
nodes = {
const random = d3.randomNormal(0, 1000);
return Array.from({ length: Math.min(width * 10, npoints * 2) }, () => ({
x: width / 2 + random(),
y: height / 2 + random()
}));
}
viewof image0 = {
const V = new Float32Array(width * height).fill(NaN);
// fill all triangles, interpolate via barycentric coordinates
const delaunay = d3.Delaunay.from(points);
for (let i = 0; i < delaunay.triangles.length; i += 3) {
const [a, b, c] = delaunay.triangles.slice(i, i + 3);
const [pa, pb, pc] = Array.from([a, b, c], (i) => P[i]);
if (isNaN(pa) || isNaN(pb) || isNaN(pc)) continue;
const [Ax, Bx, Cx] = Array.from([a, b, c], (i) => points[i][0]);
const [Ay, By, Cy] = Array.from([a, b, c], (i) => points[i][1]);
const [x0, x1] = d3.extent([Ax, Bx, Cx]);
const [y0, y1] = d3.extent([Ay, By, Cy]);
const z = (By - Cy) * (Ax - Cx) + (Ay - Cy) * (Cx - Bx);
if (!z) continue;
for (let x = Math.floor(x0); x < x1; x++) {
for (let y = Math.floor(y0); y < y1; y++) {
if (x < 0 || x >= width || y < 0 || y >= height) continue;
const ga = ((By - Cy) * (x - Cx) + (y - Cy) * (Cx - Bx)) / z;
const gb = ((Cy - Ay) * (x - Cx) + (y - Cy) * (Ax - Cx)) / z;
const gc = 1 - ga - gb;
if (ga >= 0 && gb >= 0 && gc >= 0)
V[x + width * y] = ga * pa + gb * pb + gc * pc;
}
}
}
// fill the missing parts with the value of the closest dot
const values = points
.map((d, i) => [...d, P[i]])
.filter(([, , p]) => !isNaN(p));
const quad = d3.quadtree().addAll(values);
for (let x = 0; x < width; x++) {
for (let y = 0; y < height; y++) {
if (isNaN(V[x + width * y])) V[x + width * y] = quad.find(x, y)[2];
}
}
return heatmap(V, {
width,
color: sourcesOnly ? d3.interpolateInferno : d3.interpolateRdYlBu
});
}
import { heatmap } from "@fil/heatmap"
B = require("array-blur")
viewof image1 = heatmap(B.blur().radius(blurRadius).width(width)(image0), {
width,
color: sourcesOnly ? d3.interpolateInferno : d3.interpolateRdYlBu
})
contours = d3.contours().size([width, height])(image1)
// filtered contours
isolines = contours.map(({ value, coordinates }) => ({
type: "MultiLineString",
value,
coordinates: coordinates.flatMap((polygon) =>
polygon.flatMap((ring) => {
const lines = [];
let line = [];
let i;
for (const p of ring) {
i = voronoi.delaunay.find(...p, i);
if (isNaN(P[i])) {
if (line.length > 1) {
lines.push(line);
line = [];
}
} else line.push(p);
}
if (line.length > 1) lines.push(line);
return lines;
})
)
}))
function grad(p, image) {
let x = Math.floor(p[0]),
y = Math.floor(p[1]);
if (x < 0) x = 0;
if (y < 0) y = 0;
if (x === width - 1) x--;
if (y === height - 1) y--;
return [
image[x + width * y] - image[x + 1 + width * y],
image[x + width * y] - image[x + width * (y + 1)]
];
}
gradient = points.map((d, i) => (isNaN(P[i]) ? null : grad(d, image1)))
streaklines = () => {
const visited = new Uint8Array(points.length);
let maxstep = 200000;
const streaklines = [];
for (const i of d3.shuffle(d3.range(points.length))) {
// already visited? drop
if (visited[i]) continue;
const streakline = [[...points[i], 0]];
visited[i] = 1; // logically useless but clearer
let delta;
let x;
let y;
let j = i;
let vx, vy, dx, dy;
for (const direction of [-1, 1]) {
x = points[i][0];
y = points[i][1];
vx = 0;
vy = 0;
do {
dx = vx;
dy = vy;
j = voronoi.delaunay.find(x, y, j);
if (isNaN(P[j])) break;
visited[j] = 1;
[vx, vy] = grad([x, y], image1).map((d) => d * direction);
const delta = Math.hypot(vx, vy);
x += vx / delta;
y += vy / delta;
streakline.push([x, y]);
} while (
vx * dx + vy * dy >= 0 &&
//delta > 1e-12 &&
x > 0 &&
y > 0 &&
x < width &&
y < height &&
maxstep-- > 0
);
streakline.reverse();
}
streaklines.push(streakline);
}
return streaklines;
}
height = 600
One platform to build and deploy the best data apps
Experiment and prototype by building visualizations in live JavaScript notebooks. Collaborate with your team and decide which concepts to build out.
Use Observable Framework to build data apps locally. Use data loaders to build in any language or library, including Python, SQL, and R.
Seamlessly deploy to Observable. Test before you ship, use automatic deploy-on-commit, and ensure your projects are always up-to-date.