Visiting Research at NYU Shanghai; previously @ Nest, Apple, AOL; faculty @ Olin College, NYU Shanghai.
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d3 = require("d3@6")
import { p5 } from "@tmcw/p5"
import {debounce} from "@mbostock/debouncing-input"
import {Range} from "@observablehq/inputs"
sin = x => Math.sin(x * Math.PI / 180)
map = (x, a, b, c, d) => ((x - a) / (b - a)) * (d - c) + c;
periodic = {
const rec = (a, b) => b ? a + rec(b-a) : a/2 + a/2 * Math.sin(now / 2000);
return rec;
}
// Return a function that runs fn() immediately, the first time. This handles thumbnails.
// Then run it only once the cell is visible.
async function whenVisible(fn) {
return async function(...args) {
if (this) await visibility();
return fn(...args);
};
}
function thisCached(key, thunk) {
if (!this) return thunk();
let cache = this.__thisCache;
if (!cache) {
this.__thisCache = cache = new Map();
}
if (cache.has(key)) {
return cache.get(key);
} else {
let value = thunk();
this.set(key, value);
return value;
}
}
sinWave = whenVisible(async function({
bias = 0,
amp = 1,
period = 1,
phase = 0,
yRange,
yScale = 1,
axes = true
}) {
const lineWidth = 2;
const range = yRange || [-100, 100];
const height = range[1] - range[0] + 10;
const xd = -range[1] + lineWidth;
const fn = x => bias + amp * sin(x / period + phase);
const y = x => yScale * fn(x);
const data = Array(width)
.fill()
.map((_, x) => [x, y(x)]);
const path = data
.map(p => `L${p.join(' ')}`)
.join(' ')
.replace('L', 'M');
function createSvg() {
const svg = d3.create("svg").attr("viewBox", [0, 0, width, height]);
const g = svg.append("g").attr("transform", `translate(50, ${height / 2})`);
if (axes) {
const xscale = d3
.scaleLinear()
.domain([0, width])
.range([0, width]);
const x_axis = d3
.axisBottom()
.scale(xscale)
.ticks();
svg
.append("g")
.attr("transform", `translate(50, ${height / 2})`)
.call(x_axis);
const yscale = d3
.scaleLinear()
.domain([range[0] / yScale, range[1] / yScale])
.range(range);
const y_axis = d3
.axisLeft()
.scale(yscale)
.ticks();
g.call(y_axis);
}
g.append("path").attr("fill", "none");
return svg;
}
const svg = thisCached('svg', createSvg);
svg
.select("g")
.select("path")
.attr("d", path)
.attr("stroke-width", lineWidth)
.attr("stroke", "blue");
const fmt = d3.format("0.1f");
const phaseStr = d3.format("0.0f")( phase );
const eqn = `${fmt(amp)} * \\sin (x° / ${fmt(period)} + ${phaseStr}°) + ${fmt(bias)}`;
const code = `${fmt(amp)} * sin(x / ${fmt(period)} + ${phaseStr}) + ${fmt(bias)}`;
return md`
${svg.node()}
<table style="width: 100%">
<tr>
<th style="width: 5%"></th>
<th style="width: 25%">Math</th>
<th style="width: 25%">Code</th>
</tr>
<tr>
<td style="width: 5%"></td>
<td style="width: 25%">
${tex`y = ${simplifyEqn(eqn).replace(' * ', '')}`}</td>
<td style="width: 25%">
${md`\`\`\`javascript
let y = ${simplifyEqn(code)}
\`\`\``}
</td>
</tr>
</table>
`;
})
sinWave({ amp: 100, bias: -10 })
function sinWaveFill(phase = 0, suffix = "") {
const period = 1;
const height = 100;
const svg = d3.create("svg").attr("viewBox", [0, 0, width, height]);
const fn = x => 25 + 25 * sin(x / period + phase);
const pts = [
[0, height],
...Array(width)
.fill()
.map((_, x) => [x, fn(x)]),
[width, height]
];
const path = pts
.map(([x, y]) => `L${x},${y}`)
.join(" ")
.replace("L", "M");
svg
.append("path")
.attr("d", path)
.attr("fill", "blue");
const eqn = `map(sin(x / ${period.toFixed(
0
)}${suffix}), -1, 1, 0, ${height.toFixed(0)})`.replace(/ \/ 1(?=[^\d.])/, '');
return md`${svg.node()}
${`\`\`\`javascript
let y = ${eqn}
\`\`\``}`;
}
async function* bouncingBalls(ballSpecs = [{}, {}]) {
const specs = ballSpecs.map(spec => ({
period: 10,
phase: 0,
radius: 20,
color: "blue",
amp: 75,
...spec
}));
const height = Math.max(
...specs.map(({ radius, amp }) => 2 * (radius + amp))
);
const fn = ({ period, phase, amp }) =>
map(sin(new Date() / period + phase), 0, 1, height / 2, height / 2 + amp);
const svg = d3.create("svg").attr("viewBox", [0, 0, width, height]);
const circles = svg
.selectAll("circle")
.data(specs)
.enter()
.append("circle")
.attr("cx", (_, i) => ((i + 1) * width) / (specs.length + 1))
.attr("r", d => d.radius)
.attr("fill", d => d.color);
while (true) {
svg
.selectAll("circle")
.data(specs)
.attr("cy", fn);
yield svg.node();
}
}
async function* bouncingBallWithEqn({
amp = 150,
period = 10,
radius = 20
} = {}) {
const eqn = md`\`\`\`javascript
let y = map(sin(millis() / ${period.toFixed(0)}), -1, 1, 0, ${amp.toFixed(
0
)})\`\`\``;
const bs = await bouncingBalls([{ radius, period, amp }]);
const div = md`${(await bs.next()).value}\n${eqn}}`;
while (true) {
await bs.next();
yield div;
}
}
false &&
bouncingBalls([
{ phase: phase1, color: "red" },
{ phase: phase1, color: "blue" }
])
function* bounceTrail({ period = 10, radius = 10, height = 200 } = {}) {
const eqn = `\`\`\`javascript
map(sin(millis() / ${period.toFixed(0)}), -1, 1, 0, ${(
height -
2 * radius
).toFixed(0)})\`\`\``;
for (let elt of bouncingBallsWithTrails([{ period }])) {
yield md`${elt}
let y = ${eqn}
`;
}
}
bouncingBallsWithTrails = phases =>
p5(sketch => {
const height = 100;
const radius = 20;
const toObject = n =>
typeof n === 'number' || n.hasOwnProperty("value") ? { phase: n } : n;
const circles = phases.map(objOrValue => ({
period: 10,
phase: 0,
...toObject(objOrValue)
}));
let pg;
let pmillis;
const resolve = value =>
value.hasOwnProperty("value") ? value.value : value;
sketch.setup = () => {
sketch.createCanvas(width, height);
sketch.angleMode(sketch.DEGREES);
sketch.colorMode(sketch.HSB);
sketch.noStroke();
pg = sketch.createGraphics(width, height);
pg.background(255);
pg.colorMode(sketch.HSB);
pg.noStroke();
circles.forEach((obj, i) => {
obj.hue =
obj.hue || circles.length === 1
? 240
: sketch.map(i, 0, circles.length - 1, 0, 240);
});
pmillis = sketch.millis();
};
sketch.draw = () => {
const scroll = sketch.max(
-1,
sketch.round((sketch.millis() - pmillis) / (1000 / 30))
);
pmillis = sketch.millis();
pg.image(pg, -scroll, 0);
sketch.image(pg, 0, 0);
for (const { period, phase, hue, x } of circles) {
const x = width - radius;
const y = sketch.map(
sketch.sin(sketch.millis() / period + resolve(phase)),
-1,
1,
radius,
height - radius
);
pg.fill(hue, 100, 100, .005);
pg.circle(x, y, radius);
pg.fill(hue, 100, 100, .005);
pg.circle(x, y, radius * .8);
sketch.fill(hue, 100, 100);
sketch.circle(x, y, radius);
}
};
})
bouncingBallsWithTrails([0, { period: 90 }])
function simplifyEqn(eqn) {
return eqn
.replace(/\.0+(?=[^\d]|$)/g, '')
.replace(/ 1 \* /, ' ')
.replace(/^1 \* /, '')
.replace(' / 1 ', ' ')
.replace(/^0 \+ /, '')
.replace(/ \+ [−-]/g, ' - ')
.replace(/ \+ 0$/, '')
.replace(/ \+ 0°?(?=[^0-9.])/, '')
.replace(/sin \(([^\+/]+?)\)/, 'sin $1');
}
simplifyEqn("100.0 * sin(x / 1.0 + 0) + −10.0")
// simplifyEqn("x + −10.0")
// "x + 10.0".replace("-", " x-x ")
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