New
Snap ToggleDraggable
A reviewer facepile in which every face owns the part of the frame nearest to it. Overlap is impossible rather than prevented, so nothing has to be re-tuned per head count — drag one face into a corner and its share collapses while the rest swell to take it up.
'use client';
import './lloyd-avatars.css';
import { useEffect, useRef, useState, type KeyboardEvent } from 'react';
import {
useCanvasScene,
useReducedMotion,
type SceneDrawContext,
type SceneSetupContext,
} from '@/hooks/use-canvas-scene';
/**
* A reviewer group whose packing is solved rather than authored.
*
* Each face is a Voronoi site in the frame, and the tile it owns is the set of points
* closer to it than to anybody else:
*
* V_i = { p in F : |p − s_i| <= |p − s_j| for all j != i }
*
* which is an intersection of half-planes, one per other face, each bounded by the
* perpendicular bisector of that pair — so a tile is the frame polygon clipped once
* against every other site. The arrangement then walks downhill on the energy of a
* centroidal Voronoi tessellation,
*
* E(s) = sum_i integral_{V_i} |p − s_i|^2 dA, dE/ds_i = 2 * A_i * (s_i − c_i)
*
* where A_i is the tile's area and c_i its area centroid, both read straight off the
* clipped polygon by the shoelace formula. One Lloyd iteration
*
* s_i <- s_i + L * (c_i − s_i)
*
* is therefore a gradient step preconditioned by the tile's own mass, −(L/2A_i) dE/ds_i,
* and its fixed point is the centroidal condition s_i = c_i: every face sitting at the
* centre of mass of its own territory. Integrated at a fixed 1/120 s step so the same
* drag settles the same way on a 60 Hz and a 144 Hz screen.
*
* This is not a grid under a rounded mask, not an eased keyframe between two authored
* layouts, and not a force-directed cluster with a collision check. What follows from
* actually solving it:
*
* - Overlap is impossible rather than prevented. Two tiles are separated by the
* bisector of their two faces, so they are disjoint by construction: there is no
* collision test to lose, at any head count, mid-drag, at any frame rate.
* - Nothing is authored per head count. Seat an eighth face and the neighbours' tiles
* each gain one more half-plane; unseat one and the hole closes because the same
* twenty lines now solve a seven-site problem.
*
* The face a press picks up is the one whose tile the press landed in, because that is
* what a Voronoi diagram is. It is then pinned to the pointer while the other seven keep
* descending around it.
*/
/** Seconds per iteration. The descent is first order and stable for any L <= 1, so the
* fixed step is here for reproducibility, not for stability. */
const STEP = 1 / 120;
/** Iterations per frame, capped. The 0.05 s delta clamp already bounds a frame to six of
* them; twelve is the backstop for a clock that jumped, not a budget. */
const MAX_STEPS = 12;
/** L: the fraction of the way to its centroid a face moves per iteration. Time constant
* STEP/L = 0.12 s, which is the lag on the other faces while one is dragged. L = 1 is
* plain Lloyd and lands within a frame, too fast to read; 0.02 takes three seconds. */
const RELAX = 0.07;
/** Reduced motion runs that same iteration to its fixed point instead. A twentieth of a
* pixel of movement is converged at this size, and the measured worst case — eight faces
* from the stacked start — is 54 iterations, so 120 is a ceiling with room over it. */
const SETTLE_TOL = 0.05;
const SETTLE_MAX = 120;
/** Seconds for a newly seated face's art to come up. Only the art fades: the site joins
* the tessellation on the frame it is seated, which is the whole point. */
const FADE = 0.22;
/** Frame corner radius in px, and arc samples per corner. Five segments hold the polygon
* within CORNER * (1 − cos 9deg) = 0.17px of a true arc, under one device pixel at 2x. */
const CORNER = 14;
const ARC_SEGS = 5;
/** How close to the frame edge a site may be pushed, px. A site on the boundary owns a
* wedge with no room for a monogram, and nine is the least a legible disc needs. */
const EDGE_KEEP = 9;
/** Half the seam between two tiles, px. A tile is its cell eroded by this, so the 6px
* gutter is geometry that the clipper produced and not a stroke laid over a join. */
const GUTTER = 3;
/** Monogram radius as a fraction of the site's clearance to its own cell edge. Under a
* half, so a disc cannot cross a seam whatever shape the cell around it takes. */
const DISC = 0.46;
/** Least clearance, px, at which a tile is worth lettering. The stacked start never gets
* tighter than 15px of room, so the monograms are there from the first frame at a third
* of their settled size and grow as the tiles open up. */
const MIN_ROOM = 13;
/** Arrow-key step, px. A site's move carries every boundary it shares half as far, so
* one press shifts a seam by exactly one gutter — visible, and ten presses cross a tile. */
const NUDGE = 12;
/** Vertex capacity per polygon. The frame is a 24-gon, seven bisector clips can add one
* vertex each, and the erosion at most one per edge again: 62 worst case, doubled. */
const VERTS = 128;
/** Two colours and a tint — ink, one accent, and that accent under a tenth of an alpha. */
const INK = '234, 243, 255';
const ACCENT = '134, 224, 203';
const TAU = Math.PI * 2;
/** The roster. Distinct initials A–H, so a monogram is one legible letter at tile size. */
const ROSTER = [
{ first: 'Ana', last: 'Reyes' },
{ first: 'Ben', last: 'Okafor' },
{ first: 'Cleo', last: 'Marsh' },
{ first: 'Devi', last: 'Rao' },
{ first: 'Eli', last: 'Nakamura' },
{ first: 'Farah', last: 'Osman' },
{ first: 'Gil', last: 'Andrade' },
{ first: 'Hana', last: 'Weiss' },
];
/** Seats taken on load: seven in, one open, so the eighth can be seated and watched. */
const SEATED = 7;
/** One face: its site, the cell that site owns, and what the shoelace pass read off it. */
interface Tile {
readonly member: number;
x: number;
y: number;
/** The cell as a flat x,y loop, rebuilt every iteration. */
readonly cell: Float64Array;
cellLen: number;
area: number;
cx: number;
cy: number;
/** Distance from the site to the nearest edge of its own cell — the room it has. */
room: number;
fade: number;
}
interface LloydState {
/** The frame as a convex polygon. Every cell starts life as a copy of it. */
readonly frame: Float64Array;
readonly frameLen: number;
/** The frame eroded by EDGE_KEEP: the region a site is allowed to stand in. */
readonly roam: Float64Array;
readonly roamLen: number;
/** Ping-pong buffers for the clipper, so a frame of this allocates nothing. */
readonly bufA: Float64Array;
readonly bufB: Float64Array;
readonly midX: number;
readonly midY: number;
tiles: Tile[];
/** Roster index held by the pointer, pinned by the keyboard, and lit by the roster. */
heldMember: number;
pinMember: number;
spot: number;
/** Site minus pointer at the moment of the grab, so taking hold never jumps a face. */
grabX: number;
grabY: number;
clock: number;
carry: number;
/** Solve to the fixed point instead of stepping toward it. Set under reduced motion,
* where the loop never runs and one L per repaint would never arrive anywhere. */
snap: boolean;
}
/**
* The frame as a convex polygon: a rounded rectangle sampled ARC_SEGS times per corner.
* Convex is the entire requirement — clipping a convex polygon by a half-plane leaves a
* convex polygon, which is what keeps every cell a single simple loop with no bookkeeping.
* Wound so the shoelace area comes out positive (clockwise on screen, y down), and
* Sutherland-Hodgman preserves winding, so the inward normal of any edge of any cell
* derived from this is always (−dy, dx).
*/
function framePolygon(width: number, height: number, out: Float64Array): number {
// Inset by the hairline the frame is stroked with, so the stroke lands inside the
// canvas instead of losing half its width off the edge.
const x0 = 1;
const y0 = 1;
const x1 = width - 1;
const y1 = height - 1;
const r = Math.max(0, Math.min(CORNER, (x1 - x0) / 2, (y1 - y0) / 2));
let n = 0;
const arc = (cx: number, cy: number, from: number) => {
for (let i = 0; i <= ARC_SEGS; i += 1) {
const a = from + (Math.PI / 2) * (i / ARC_SEGS);
out[n * 2] = cx + r * Math.cos(a);
out[n * 2 + 1] = cy + r * Math.sin(a);
n += 1;
}
};
arc(x1 - r, y0 + r, -Math.PI / 2);
arc(x1 - r, y1 - r, 0);
arc(x0 + r, y1 - r, Math.PI / 2);
arc(x0 + r, y0 + r, Math.PI);
return n;
}
/**
* Sutherland-Hodgman against one half-plane, keeping { p : n.p <= c }. Every piece of
* geometry in this file is this function: a cell is the frame clipped by one of these per
* other face, and a tile is that cell clipped by one per edge of itself.
*/
function clipHalfPlane(
src: Float64Array,
n: number,
nx: number,
ny: number,
c: number,
out: Float64Array,
): number {
let m = 0;
for (let i = 0; i < n; i += 1) {
const j = (i + 1) % n;
const ax = src[i * 2];
const ay = src[i * 2 + 1];
const bx = src[j * 2];
const by = src[j * 2 + 1];
const da = nx * ax + ny * ay - c;
const db = nx * bx + ny * by - c;
if (da <= 0) {
out[m * 2] = ax;
out[m * 2 + 1] = ay;
m += 1;
}
// Strict signs on both ends: an endpoint exactly on the plane is already kept above,
// and emitting it twice would leave a zero-length edge in the loop.
if ((da < 0 && db > 0) || (da > 0 && db < 0)) {
const t = da / (da - db);
out[m * 2] = ax + (bx - ax) * t;
out[m * 2 + 1] = ay + (by - ay) * t;
m += 1;
}
}
return m;
}
/** Trace a flat polygon as a path. */
function tracePoly(context: CanvasRenderingContext2D, p: Float64Array, n: number): void {
context.beginPath();
context.moveTo(p[0], p[1]);
for (let i = 1; i < n; i += 1) context.lineTo(p[i * 2], p[i * 2 + 1]);
context.closePath();
}
/**
* Erode a convex polygon by `gap`: clip it against each of its own edges pushed inward,
* which for a convex polygon is exactly the inward offset. The planes are read off `src`
* throughout, since a half-plane intersection does not care what order it is taken in, and
* the answer is left in `a`. Returns 0 when the gap has eaten the polygon, which is the
* right answer for a sliver of a cell.
*/
function erodeInto(
src: Float64Array,
n: number,
gap: number,
a: Float64Array,
b: Float64Array,
): number {
let from = a;
let to = b;
let m = n;
for (let i = 0; i < n * 2; i += 1) a[i] = src[i];
for (let i = 0; i < n; i += 1) {
const j = (i + 1) % n;
const ax = src[i * 2];
const ay = src[i * 2 + 1];
const dx = src[j * 2] - ax;
const dy = src[j * 2 + 1] - ay;
const len = Math.hypot(dx, dy);
if (len < 1e-6) continue;
// The outward unit normal: the inward one, (−dy, dx)/len, negated.
const nx = dy / len;
const ny = -dx / len;
m = clipHalfPlane(from, m, nx, ny, nx * ax + ny * ay - gap, to);
if (m < 3) return 0;
const swap = from;
from = to;
to = swap;
}
if (from !== a) for (let i = 0; i < m * 2; i += 1) a[i] = from[i];
return m;
}
/** Area, area centroid and the site's clearance to its own cell edge, in one pass. */
function measure(tile: Tile): void {
const p = tile.cell;
const n = tile.cellLen;
if (n < 3) {
tile.area = 0;
tile.cx = tile.x;
tile.cy = tile.y;
tile.room = 0;
return;
}
let twice = 0;
let cx = 0;
let cy = 0;
let room = Number.POSITIVE_INFINITY;
for (let i = 0; i < n; i += 1) {
const j = (i + 1) % n;
const ax = p[i * 2];
const ay = p[i * 2 + 1];
const bx = p[j * 2];
const by = p[j * 2 + 1];
// Each cross term is twice the signed area of the triangle back to the origin, and the
// centroid is those crosses weighted by the edge midpoints — the origin cancels out.
const cross = ax * by - bx * ay;
twice += cross;
cx += (ax + bx) * cross;
cy += (ay + by) * cross;
const dx = bx - ax;
const dy = by - ay;
const len = Math.hypot(dx, dy);
if (len > 1e-6) {
const gap = (-dy * (tile.x - ax) + dx * (tile.y - ay)) / len;
if (gap < room) room = gap;
}
}
tile.area = twice / 2;
tile.cx = twice === 0 ? tile.x : cx / (3 * twice);
tile.cy = twice === 0 ? tile.y : cy / (3 * twice);
tile.room = Number.isFinite(room) ? Math.max(0, room) : 0;
}
/** One face's cell: the frame clipped by the bisector of it and every other face. */
function cellOf(state: LloydState, tile: Tile): void {
const { frame, frameLen, bufA, bufB } = state;
let from = bufA;
let to = bufB;
let n = frameLen;
for (let i = 0; i < frameLen * 2; i += 1) bufA[i] = frame[i];
const own = tile.x * tile.x + tile.y * tile.y;
for (const other of state.tiles) {
if (other === tile) continue;
const dx = other.x - tile.x;
const dy = other.y - tile.y;
// Two faces on the same pixel have no bisector between them. That pair simply divides
// nothing this iteration, and the next one moves them apart.
if (dx * dx + dy * dy < 1e-9) continue;
// |p − s|^2 <= |p − o|^2 rearranges to 2(o − s).p <= |o|^2 − |s|^2.
const c = other.x * other.x + other.y * other.y - own;
n = clipHalfPlane(from, n, 2 * dx, 2 * dy, c, to);
if (n < 3) break;
const swap = from;
from = to;
to = swap;
}
tile.cellLen = n < 3 ? 0 : n;
for (let i = 0; i < tile.cellLen * 2; i += 1) tile.cell[i] = from[i];
}
/** Rebuild every cell against the current sites and measure them. No motion. */
function tessellate(state: LloydState): void {
for (const tile of state.tiles) {
cellOf(state, tile);
measure(tile);
}
}
/** Held by the pointer or pinned by the keyboard: either way the solver leaves it alone. */
function pinned(state: LloydState, tile: Tile): boolean {
return tile.member === state.heldMember || tile.member === state.pinMember;
}
/**
* One Lloyd iteration. Every cell is built against the same set of positions and only then
* is anything moved — a Jacobi sweep rather than Gauss-Seidel, so the arrangement cannot
* depend on the order the roster happens to be in. Returns the largest step taken, which
* at L = 1 is the residual and is the convergence test below.
*/
function relax(state: LloydState, lambda: number): number {
tessellate(state);
let largest = 0;
for (const tile of state.tiles) {
if (pinned(state, tile) || tile.cellLen < 3) continue;
const dx = lambda * (tile.cx - tile.x);
const dy = lambda * (tile.cy - tile.y);
tile.x += dx;
tile.y += dy;
const step = Math.hypot(dx, dy);
if (step > largest) largest = step;
}
return largest;
}
/** The answer rather than the route to it: plain Lloyd, L = 1, run to its fixed point. */
function settle(state: LloydState): void {
for (let i = 0; i < SETTLE_MAX; i += 1) {
if (relax(state, 1) < SETTLE_TOL) break;
}
// Nothing here is on its way anywhere, so nothing may be mid-fade either.
for (const tile of state.tiles) tile.fade = 1;
}
/** A tile with its own clipping buffer. Allocated when a face is seated, never per frame. */
function makeTile(member: number, x: number, y: number, fade: number): Tile {
return {
member,
x,
y,
cell: new Float64Array(VERTS * 2),
cellLen: 0,
area: 0,
cx: x,
cy: y,
room: 0,
fade,
};
}
/**
* Put a face at (x, y), or at the nearest point of the region a site is allowed to stand
* in. The out-of-bounds case is a true projection onto the boundary rather than a clamp
* per edge: a pointer under capture is regularly a long way outside the frame, and pushing
* it back along one edge normal at a time accumulates across the twenty-four of them and
* lands the face somewhere the pointer never was.
*/
function pinTo(state: LloydState, tile: Tile, x: number, y: number): void {
const p = state.roam;
const n = state.roamLen;
if (n < 3) {
// A frame too small to hold a face clear of its own edge. The middle is the only
// defensible answer, and it keeps the cell non-empty.
tile.x = state.midX;
tile.y = state.midY;
return;
}
let inside = true;
for (let i = 0; i < n && inside; i += 1) {
const j = (i + 1) % n;
const ax = p[i * 2];
const ay = p[i * 2 + 1];
const dx = p[j * 2] - ax;
const dy = p[j * 2 + 1] - ay;
if (-dy * (x - ax) + dx * (y - ay) < 0) inside = false;
}
if (inside) {
tile.x = x;
tile.y = y;
return;
}
let best = Number.POSITIVE_INFINITY;
for (let i = 0; i < n; i += 1) {
const j = (i + 1) % n;
const ax = p[i * 2];
const ay = p[i * 2 + 1];
const dx = p[j * 2] - ax;
const dy = p[j * 2 + 1] - ay;
const span = dx * dx + dy * dy;
const t = span < 1e-9 ? 0 : Math.max(0, Math.min(1, ((x - ax) * dx + (y - ay) * dy) / span));
const px = ax + dx * t;
const py = ay + dy * t;
const d = (x - px) * (x - px) + (y - py) * (y - py);
if (d < best) {
best = d;
tile.x = px;
tile.y = py;
}
}
}
/** The face nearest a point, which is the face whose tile the point is in. */
function tileAt(state: LloydState, x: number, y: number): Tile | null {
let best: Tile | null = null;
let near = Number.POSITIVE_INFINITY;
for (const tile of state.tiles) {
const d = (tile.x - x) * (tile.x - x) + (tile.y - y) * (tile.y - y);
if (d < near) {
near = d;
best = tile;
}
}
return best;
}
function tileOf(state: LloydState, member: number): Tile | null {
for (const tile of state.tiles) if (tile.member === member) return tile;
return null;
}
/**
* Seat a face. The newcomer is dropped half way out toward the far corner of whichever
* tile is largest, so the split it forces begins where there is most room to give — and
* it is never coincident with the site already there, which a bisector needs.
*/
function seat(state: LloydState, member: number): void {
let host: Tile | null = null;
for (const tile of state.tiles) if (!host || tile.area > host.area) host = tile;
let x = state.midX;
let y = state.midY;
if (host && host.cellLen >= 3) {
let far = 0;
for (let i = 0; i < host.cellLen; i += 1) {
const vx = host.cell[i * 2] - host.cx;
const vy = host.cell[i * 2 + 1] - host.cy;
const d = vx * vx + vy * vy;
if (d > far) {
far = d;
x = host.cx + vx * 0.5;
y = host.cy + vy * 0.5;
}
}
}
const tile = makeTile(member, x, y, 0);
pinTo(state, tile, x, y);
state.tiles.push(tile);
}
/** Bring the tessellation in line with the roster: take the leavers out, seat the joiners. */
function reconcile(state: LloydState, seated: readonly boolean[]): void {
for (let i = state.tiles.length - 1; i >= 0; i -= 1) {
const tile = state.tiles[i];
if (seated[tile.member]) continue;
if (state.heldMember === tile.member) state.heldMember = -1;
state.tiles.splice(i, 1);
}
for (let member = 0; member < ROSTER.length; member += 1) {
if (seated[member] && !tileOf(state, member)) seat(state, member);
}
}
/** Everything the scene owns, sized to this frame. Re-run on every resize. */
function build(
{ width, height }: SceneSetupContext,
seated: readonly boolean[],
places: number[],
snap: boolean,
): LloydState {
const frame = new Float64Array(VERTS * 2);
const frameLen = framePolygon(width, height, frame);
const bufA = new Float64Array(VERTS * 2);
const bufB = new Float64Array(VERTS * 2);
const roam = new Float64Array(VERTS * 2);
const roamLen = erodeInto(frame, frameLen, EDGE_KEEP, bufA, bufB);
for (let i = 0; i < roamLen * 2; i += 1) roam[i] = bufA[i];
const state: LloydState = {
frame,
frameLen,
roam,
roamLen,
bufA,
bufB,
midX: width / 2,
midY: height / 2,
tiles: [],
heldMember: -1,
pinMember: -1,
spot: -1,
grabX: 0,
grabY: 0,
clock: 0,
carry: 0,
snap,
};
// Sites come from the fractions of the frame they were last at, not from pixels of the
// old one, so a resize re-seats each face where it already was instead of restarting the
// descent. On the first build those fractions are the overlapped avatar row.
for (let member = 0; member < ROSTER.length; member += 1) {
if (!seated[member]) continue;
const tile = makeTile(member, state.midX, state.midY, 1);
pinTo(state, tile, places[member * 2] * width, places[member * 2 + 1] * height);
state.tiles.push(tile);
}
if (snap) settle(state);
else tessellate(state);
return state;
}
/** One face: the territory it owns, and the monogram sitting in the middle of it. */
function drawTile(context: CanvasRenderingContext2D, state: LloydState, tile: Tile): void {
const n = erodeInto(tile.cell, tile.cellLen, GUTTER, state.bufA, state.bufB);
if (n < 3) return;
const lit = pinned(state, tile) || tile.member === state.spot;
const fade = tile.fade;
const r = DISC * tile.room;
context.save();
tracePoly(context, state.bufA, n);
// A vignette per panel, centred on the face rather than on the panel, so neighbours read
// apart even where their shared seam crosses empty frame. The base alpha climbs with the
// roster index, which is what keeps eight identical panels from reading as one surface.
const wash = context.createRadialGradient(tile.x, tile.y, 0, tile.x, tile.y, Math.max(8, tile.room * 2.4));
const base = 0.028 + 0.006 * tile.member;
wash.addColorStop(0, lit ? `rgba(${ACCENT}, ${0.095 * fade})` : `rgba(${INK}, ${(base + 0.045) * fade})`);
wash.addColorStop(1, lit ? `rgba(${ACCENT}, ${0.038 * fade})` : `rgba(${INK}, ${base * fade})`);
context.fillStyle = wash;
context.fill();
context.lineWidth = 1;
context.strokeStyle = lit ? `rgba(${ACCENT}, ${0.45 * fade})` : `rgba(${INK}, ${0.11 * fade})`;
context.stroke();
// Everything inside is clipped to the panel, so a monogram is cropped by its own
// territory exactly the way a photograph in a mosaic would be.
context.clip();
if (r >= 4) {
context.beginPath();
context.arc(tile.x, tile.y, r, 0, TAU);
context.fillStyle = lit ? `rgba(${ACCENT}, ${0.16 * fade})` : `rgba(${INK}, ${0.075 * fade})`;
context.fill();
context.strokeStyle = lit ? `rgba(${ACCENT}, ${0.62 * fade})` : `rgba(${INK}, ${0.24 * fade})`;
context.stroke();
}
if (tile.room >= MIN_ROOM) {
context.textAlign = 'center';
context.textBaseline = 'middle';
context.font = `500 ${(r * 1.05).toFixed(1)}px ui-monospace, "SFMono-Regular", Menlo, monospace`;
context.fillStyle = lit ? `rgba(255, 255, 255, ${0.92 * fade})` : `rgba(${INK}, ${0.78 * fade})`;
context.fillText(ROSTER[tile.member].first.charAt(0), tile.x, tile.y);
}
context.restore();
}
function paint(
context: CanvasRenderingContext2D,
state: LloydState,
width: number,
height: number,
): void {
context.clearRect(0, 0, width, height);
context.lineJoin = 'round';
context.lineCap = 'round';
// The frame's own ground, from the very polygon the cells are cut out of.
tracePoly(context, state.frame, state.frameLen);
context.fillStyle = `rgba(${INK}, 0.022)`;
context.fill();
for (const tile of state.tiles) drawTile(context, state, tile);
tracePoly(context, state.frame, state.frameLen);
context.lineWidth = 1;
context.strokeStyle = `rgba(${INK}, 0.16)`;
context.stroke();
}
/** The line an avatar group carries. Real grammar at every count this one can reach. */
function summarise(names: readonly string[]): string {
if (names.length <= 2) return names.join(' and ');
if (names.length === 3) return `${names[0]}, ${names[1]} and ${names[2]}`;
const rest = names.length - 3;
return `${names[0]}, ${names[1]}, ${names[2]} and ${rest} ${rest === 1 ? 'other' : 'others'}`;
}
/**
* A reviewer group. The seat gauge, the frame, the names line and the roster are one
* control over one tessellation: the chips seat and unseat, a press drags whichever face
* it landed on, and the arrow keys pin a face and walk it.
*/
/** `compact` is the 298x240 catalogue card: the same eight faces, the same tessellation and
* the same drag, with the sentence naming the reviewers and the hint dropped. Every seat is
* stored as a fraction of the frame and the frame polygon is measured from the canvas box, so
* the packing is scale-free and a shorter frame is the same solve. See `lloyd-avatars.css`. */
export type LloydAvatarsProps = { compact?: boolean };
export function LloydAvatars({ compact = false }: LloydAvatarsProps) {
const reduced = useReducedMotion();
const [seated, setSeated] = useState<readonly boolean[]>(() =>
ROSTER.map((_, index) => index < SEATED),
);
/**
* Where each face is, as a fraction of the frame. Starts as the overlapped avatar row
* every one of these components is handed — that row is the unsolved state, and the first
* second of the loop is it being solved.
*/
const placesRef = useRef<number[]>(
ROSTER.flatMap((_, index) => [
0.3 + (0.4 * index) / (ROSTER.length - 1),
// Alternated either side of the mid-line. A perfectly collinear start is a symmetric
// configuration and Lloyd preserves symmetry exactly: the row would descend into
// vertical bands, which is a critical point of the energy and not the answer.
index % 2 === 0 ? 0.445 : 0.555,
]),
);
/** Roster index the pointer or focus is over, and the one the keyboard is holding. Refs,
* not state: the canvas is their only reader, so a hover need not re-render the chips. */
const spotRef = useRef(-1);
const pinRef = useRef(-1);
const nudgeRef = useRef<{ member: number; dx: number; dy: number } | null>(null);
const draw = (scene: SceneDrawContext<LloydState>) => {
const { context, width, height, state, pointer } = scene;
state.snap = reduced;
state.spot = spotRef.current;
reconcile(state, seated);
const nudge = nudgeRef.current;
if (nudge) {
nudgeRef.current = null;
const tile = tileOf(state, nudge.member);
// A nudge on its own would be undone by the next iteration, because the centroid is
// an attractor. Pinning is what makes the keyboard the same gesture as the drag.
if (tile) {
pinRef.current = nudge.member;
pinTo(state, tile, tile.x + nudge.dx, tile.y + nudge.dy);
}
}
state.pinMember = pinRef.current;
if (!pointer.down) state.heldMember = -1;
else if (state.heldMember < 0 && pointer.inside) {
const tile = tileAt(state, pointer.x, pointer.y);
if (tile) {
state.heldMember = tile.member;
state.grabX = tile.x - pointer.x;
state.grabY = tile.y - pointer.y;
// One face at a time: taking hold of one lets go of whatever the keys were holding.
pinRef.current = -1;
state.pinMember = -1;
}
}
const held = state.heldMember < 0 ? null : tileOf(state, state.heldMember);
if (held) pinTo(state, held, pointer.x + state.grabX, pointer.y + state.grabY);
const now = performance.now();
const elapsed = state.clock ? Math.min(0.05, (now - state.clock) / 1000) : STEP;
state.clock = now;
if (state.snap) {
settle(state);
state.carry = 0;
} else {
state.carry += elapsed;
const steps = Math.min(MAX_STEPS, Math.floor(state.carry / STEP));
for (let i = 0; i < steps; i += 1) relax(state, RELAX);
state.carry -= steps * STEP;
// A tab left in the background banks minutes of arrears. Drop them rather than
// paying them off at twelve iterations a frame for the next quarter of a second.
if (state.carry > STEP * MAX_STEPS) state.carry = 0;
for (const tile of state.tiles) {
if (tile.fade < 1) tile.fade = Math.min(1, tile.fade + (steps * STEP) / FADE);
}
}
// The last thing either branch did was move the sites, which leaves every cell one
// step behind the face inside it. Rebuilding here is what guarantees that the tile
// drawn around a face really is the set of points nearest that face.
tessellate(state);
paint(context, state, width, height);
for (const tile of state.tiles) {
placesRef.current[tile.member * 2] = tile.x / width;
placesRef.current[tile.member * 2 + 1] = tile.y / height;
}
};
const { stageRef, canvasRef, requestRender } = useCanvasScene<LloydState>({
setup: (scene) => build(scene, seated, placesRef.current, reduced),
draw,
});
// The roster is React state and the tessellation is not, so seating somebody — or the
// motion preference changing, which stops the loop outright — has to ask for the repaint
// that keeps the frame showing the same roster the chips do.
useEffect(() => {
requestRender();
}, [seated, reduced, requestRender]);
const toggle = (member: number) => {
setSeated((prev) => prev.map((on, index) => (index === member ? !on : on)));
};
const light = (member: number) => {
spotRef.current = member;
requestRender();
};
const dim = () => {
spotRef.current = -1;
requestRender();
};
/** Focus leaving a chip lets its face go, so one is never left held by a control nobody
* is on. A pointer merely leaving does not: the keys, not the mouse, took hold of it. */
const letGo = () => {
spotRef.current = -1;
pinRef.current = -1;
requestRender();
};
/**
* The arrows walk the face this chip belongs to and hold it there while they do: one
* press carries every boundary it shares half as far, which is one gutter. Escape hands
* it back to the solver, which pulls it home to its own centroid.
*/
const onChipKey = (event: KeyboardEvent<HTMLButtonElement>, member: number) => {
if (event.key === 'Escape') {
event.preventDefault();
pinRef.current = -1;
requestRender();
return;
}
if (!seated[member]) return;
let dx = 0;
let dy = 0;
if (event.key === 'ArrowLeft') dx = -NUDGE;
else if (event.key === 'ArrowRight') dx = NUDGE;
else if (event.key === 'ArrowUp') dy = -NUDGE;
else if (event.key === 'ArrowDown') dy = NUDGE;
else return;
event.preventDefault();
nudgeRef.current = { member, dx, dy };
requestRender();
};
const names = ROSTER.filter((_, index) => seated[index]).map((member) => member.first);
return (
<div className="lloyd-avatars-stage" data-compact={compact ? 'true' : undefined}>
<div className="lloyd-avatars-card">
<div className="lloyd-avatars-head">
<p className="lloyd-avatars-label">Reviewers</p>
<div
className="lloyd-avatars-seats"
role="meter"
aria-label="Review seats filled"
aria-valuemin={0}
aria-valuemax={ROSTER.length}
aria-valuenow={names.length}
aria-valuetext={`${names.length} of ${ROSTER.length} seats filled`}
>
<span className="lloyd-avatars-pips" aria-hidden="true">
{ROSTER.map((member, index) => (
<span
key={member.first}
className={
seated[index] ? 'lloyd-avatars-pip lloyd-avatars-pip-on' : 'lloyd-avatars-pip'
}
/>
))}
</span>
<span className="lloyd-avatars-tally">
{names.length}/{ROSTER.length}
</span>
</div>
</div>
<div ref={stageRef} className="lloyd-avatars-frame" aria-hidden="true">
<canvas ref={canvasRef} />
</div>
{names.length === 0 ? (
<p className="lloyd-avatars-names">No reviewers yet — add somebody below.</p>
) : (
<p className="lloyd-avatars-names">
<strong>{names.length === 1 ? '1 person' : `${names.length} people`}</strong>
{` · ${summarise(names)}`}
</p>
)}
{/* A sibling of the tracked element, never a child: the canvas host takes pointer
capture on press and would swallow these clicks and their keys. */}
<div className="lloyd-avatars-roster" role="group" aria-label="People on this review">
{ROSTER.map((member, index) => (
<button
key={member.first}
type="button"
className="lloyd-avatars-chip"
aria-pressed={seated[index]}
aria-label={`${member.first} ${member.last}`}
/* Still pressable in a card, but out of the tab order: the card frame is
aria-hidden, and a focusable node inside one is a trap with no label. */
tabIndex={compact ? -1 : undefined}
onClick={() => toggle(index)}
onKeyDown={(event) => onChipKey(event, index)}
onPointerEnter={() => light(index)}
onPointerLeave={dim}
onFocus={() => light(index)}
onBlur={letGo}
>
{member.first}
</button>
))}
</div>
</div>
<p className="lloyd-avatars-hint">Drag a face · arrows nudge · esc lets go</p>
</div>
);
}
export default LloydAvatars;/*
* lloyd-avatars — a reviewer group whose packing is solved rather than authored: each
* face owns the part of the frame nearer to it than to anyone else. The canvas draws the
* frame itself — the rounded rectangle, the seams, the monograms — from the same polygon
* the solver clips, so there is no CSS radius or inset here for a canvas constant to
* drift away from.
*/
.lloyd-avatars-stage {
position: relative;
display: grid;
place-content: center;
width: 100%;
min-height: 26rem;
padding: 2rem 1.5rem 3rem;
overflow: hidden;
border-radius: 0.75rem;
background: radial-gradient(120% 110% at 50% 0%, #0b1a1e 0%, #070d11 60%, #05080b 100%);
color: #eaf3ff;
}
.lloyd-avatars-card {
display: grid;
width: min(23.5rem, 100%);
gap: 0.875rem;
}
.lloyd-avatars-head {
display: flex;
align-items: center;
justify-content: space-between;
gap: 1rem;
}
.lloyd-avatars-label {
margin: 0;
font: 500 0.6875rem/1 ui-monospace, 'SFMono-Regular', Menlo, monospace;
letter-spacing: 0.14em;
text-transform: uppercase;
color: rgba(234, 243, 255, 0.5);
}
/* The seat gauge. A `meter` treats its own children as presentational, so the tally
beside the pips restates the value text rather than adding a second reading. */
.lloyd-avatars-seats {
display: flex;
align-items: center;
gap: 0.5rem;
}
.lloyd-avatars-pips {
display: flex;
gap: 0.1875rem;
}
.lloyd-avatars-pip {
width: 0.25rem;
height: 0.6875rem;
border-radius: 1px;
background: rgba(234, 243, 255, 0.14);
}
.lloyd-avatars-pip-on {
background: rgba(134, 224, 203, 0.72);
}
.lloyd-avatars-tally {
font: 500 0.6875rem/1 ui-monospace, 'SFMono-Regular', Menlo, monospace;
font-variant-numeric: tabular-nums;
color: rgba(234, 243, 255, 0.45);
}
/*
* The canvas host. It takes pointer capture on press — a drag has to survive leaving the
* frame — so nothing that needs a click of its own can live inside it. The roster below
* is a sibling for exactly that reason.
*/
.lloyd-avatars-frame {
position: relative;
height: 12rem;
touch-action: none;
cursor: grab;
}
.lloyd-avatars-frame:active {
cursor: grabbing;
}
.lloyd-avatars-frame canvas {
display: block;
width: 100%;
height: 100%;
}
.lloyd-avatars-names {
margin: 0;
font-size: 0.8125rem;
line-height: 1.45;
color: rgba(234, 243, 255, 0.55);
}
.lloyd-avatars-names strong {
font-weight: 500;
color: rgba(234, 243, 255, 0.85);
}
.lloyd-avatars-roster {
display: flex;
flex-wrap: wrap;
gap: 0.375rem;
}
.lloyd-avatars-chip {
appearance: none;
margin: 0;
padding: 0.3125rem 0.6875rem;
border: 1px solid rgba(234, 243, 255, 0.12);
border-radius: 999px;
background: rgba(6, 12, 16, 0.5);
font: inherit;
font-size: 0.75rem;
font-weight: 500;
color: rgba(234, 243, 255, 0.46);
cursor: pointer;
transition:
border-color 160ms ease,
background-color 160ms ease,
color 160ms ease;
}
.lloyd-avatars-chip:hover {
border-color: rgba(134, 224, 203, 0.4);
color: rgba(234, 243, 255, 0.8);
}
.lloyd-avatars-chip[aria-pressed='true'] {
border-color: rgba(134, 224, 203, 0.55);
background: rgba(134, 224, 203, 0.13);
color: #eefaf5;
}
.lloyd-avatars-chip:focus-visible {
outline: 2px solid rgba(134, 224, 203, 0.8);
outline-offset: 2px;
}
.lloyd-avatars-hint {
position: absolute;
right: 1.25rem;
bottom: 1rem;
margin: 0;
font: 500 0.6875rem/1 ui-monospace, 'SFMono-Regular', Menlo, monospace;
letter-spacing: 0.08em;
text-transform: uppercase;
pointer-events: none;
color: rgba(234, 243, 255, 0.26);
}
/*
* What reduced motion switches off is the descent, not the control. The loop is stopped
* and every repaint instead runs the same iteration to its fixed point, so the frame is
* always showing a solved tessellation: dragging a face re-solves the other seven around
* it between one pointer event and the next, seating an eighth opens its tile
* immediately, and the arrow keys still walk the face they are pointed at.
*/
@media (prefers-reduced-motion: reduce) {
.lloyd-avatars-chip {
transition: none;
}
}
/*
* The card variant: the 298x240 catalogue frame, at that real size and never scaled.
* The packing is scale-free — every seat is kept as a fraction of the frame and the frame
* polygon is measured off the canvas box on every resize — so a 278x148 frame is the same
* tessellation with the same eight cells, not a cropped one. What goes is the sentence that
* names the reviewers and the hint; the head, the frame and all eight chips stay, because
* they are the control.
*/
.lloyd-avatars-stage[data-compact='true'] {
min-height: 0;
height: 100%;
/* `place-content: center` leaves the single row auto-sized, and a row sized from its
content is what the card's `height: 100%` would then resolve against — so the frame
would collapse to nothing. Stretched, the row is the card frame. */
place-content: stretch;
padding: 0.5rem 0.625rem;
/* The card frame rounds and clips already. */
border-radius: 0;
}
/* The frame takes what the head and the roster leave. `minmax(0, 1fr)` and not `1fr`: the
canvas is a min-content floor otherwise and the row would refuse to shrink. */
.lloyd-avatars-stage[data-compact='true'] .lloyd-avatars-card {
width: 100%;
height: 100%;
grid-template-rows: auto minmax(0, 1fr) auto;
gap: 0.4375rem;
}
/* Takes what the head and the roster leave, rather than a fixed 12rem it has no room for.
And `pan-y`: a full-bleed surface that claims every touch traps the page inside a
scrolling grid, so the vertical gesture goes back to the document while dragging a face
still arrives. */
.lloyd-avatars-stage[data-compact='true'] .lloyd-avatars-frame {
height: auto;
min-height: 0;
touch-action: pan-y;
}
/* Eight chips on two rows, and the rows are what the frame is paying for. */
.lloyd-avatars-stage[data-compact='true'] .lloyd-avatars-roster {
gap: 0.3125rem;
}
.lloyd-avatars-stage[data-compact='true'] .lloyd-avatars-chip {
padding: 0.25rem 0.5625rem;
font-size: 0.6875rem;
}
/* The roll call and the hint. The card's own title carries what both were for. */
.lloyd-avatars-stage[data-compact='true'] .lloyd-avatars-names,
.lloyd-avatars-stage[data-compact='true'] .lloyd-avatars-hint {
display: none;
}"use client"
import { useCallback, useEffect, useRef, useState } from "react"
/**
* The canvas preamble every 2D scene needs, in one place: a DPR-scaled backing
* store, a rebuild on resize, a loop that stops when the stage scrolls out of
* view, pointer tracking with per-frame deltas, and teardown.
*
* A scene supplies two functions. `setup` builds whatever mutable state the
* animation owns and is re-run whenever the stage changes size, so the state can
* be sized to the stage without ever being resized in place. `draw` paints one
* frame from that state — it is called with the transform already scaled to
* device pixels, so every coordinate in it is a CSS pixel.
*/
export type ScenePointer = {
x: number
y: number
/** Position at the previous painted frame, so `x - lastX` is a frame delta. */
lastX: number
lastY: number
down: boolean
inside: boolean
}
export type SceneSetupContext = {
context: CanvasRenderingContext2D
width: number
height: number
dpr: number
}
export type SceneDrawContext<State> = SceneSetupContext & {
state: State
pointer: ScenePointer
/** Painted frames since the last rebuild. Useful for every-Nth-frame work. */
frame: number
}
export type CanvasSceneOptions<State> = {
setup: (context: SceneSetupContext) => State
draw: (context: SceneDrawContext<State>) => void
}
export type CanvasScene = {
/** The sizing element. Owns the pointer listeners and is what is observed. */
stageRef: (node: HTMLDivElement | null) => void
canvasRef: (node: HTMLCanvasElement | null) => void
/** Paint one frame now. The escape hatch for a paused or reduced-motion loop. */
requestRender: () => void
}
/** Live `prefers-reduced-motion`. False during SSR and the first paint. */
export function useReducedMotion() {
const [reduced, setReduced] = useState(false)
useEffect(() => {
const query = window.matchMedia("(prefers-reduced-motion: reduce)")
setReduced(query.matches)
const onChange = () => setReduced(query.matches)
query.addEventListener("change", onChange)
return () => query.removeEventListener("change", onChange)
}, [])
return reduced
}
export function useCanvasScene<State>(options: CanvasSceneOptions<State>): CanvasScene {
const reduced = useReducedMotion()
/*
* `draw` is usually an inline closure, so it is a new function on every
* render. Reading it through a ref keeps the loop from being torn down and
* the scene from being rebuilt each time the component re-renders.
*/
const optionsRef = useRef(options)
optionsRef.current = options
const stage = useRef<HTMLDivElement | null>(null)
const canvas = useRef<HTMLCanvasElement | null>(null)
/*
* Plain ref assignment, with no state behind it. React attaches refs during
* the commit phase, before passive effects run, so the effect below already
* sees both nodes on the first mount — which is why these used to bump a
* `mounted` counter for nothing: the two `setMounted` calls batched into one
* re-render, the counter went 0 → 2, and the effect's dependency on it tore
* the live scene down and rebuilt it. Every scene was constructed, measured
* and warmed twice on every mount, four times under StrictMode in dev.
*
* The requirement this trades for that: a consumer must render the stage and
* the canvas unconditionally, in the same commit as the component itself. All
* thirteen do. Gating the canvas behind a flag would leave the effect bailing
* on the null guard with nothing to re-run it.
*/
const stageRef = useCallback((node: HTMLDivElement | null) => {
stage.current = node
}, [])
const canvasRef = useCallback((node: HTMLCanvasElement | null) => {
canvas.current = node
}, [])
/** Set once the scene is live, so `requestRender` before that is a no-op. */
const render = useRef<(() => void) | null>(null)
const requestRender = useCallback(() => render.current?.(), [])
useEffect(() => {
const stageNode = stage.current
const canvasNode = canvas.current
if (!stageNode || !canvasNode) return
const context = canvasNode.getContext("2d")
if (!context) return
const pointer: ScenePointer = {
x: 0,
y: 0,
lastX: 0,
lastY: 0,
down: false,
inside: false,
}
let state: State | null = null
let width = 0
let height = 0
let dpr = 1
let frame = 0
let loop = 0
let pending = 0
let visible = true
/** Rebuild the backing store and the scene state for the current size. */
const measure = () => {
// `offsetWidth`/`offsetHeight`, not `getBoundingClientRect()`: the rect is
// post-transform, so a scene sitting inside a scaled ancestor measured its
// own frame at the scaled size, sized the backing store to that, and then
// had CSS scale the result a second time — the scene ran at a fraction of
// the box it was drawn into. The catalogue's scaled-poster branch is the
// one place that happens, and it is reachable again the moment an
// animation is registered without a card composition. These two properties
// are the untransformed layout box; both are integers, which is what the
// rounding below already reduced the rect to.
const nextWidth = Math.max(1, stageNode.offsetWidth)
const nextHeight = Math.max(1, stageNode.offsetHeight)
const nextDpr = Math.min(2, window.devicePixelRatio || 1)
if (nextWidth === width && nextHeight === height && nextDpr === dpr && state) return
width = nextWidth
height = nextHeight
dpr = nextDpr
canvasNode.width = Math.round(width * dpr)
canvasNode.height = Math.round(height * dpr)
canvasNode.style.width = `${width}px`
canvasNode.style.height = `${height}px`
frame = 0
state = optionsRef.current.setup({ context, width, height, dpr })
}
const paint = () => {
if (!state) return
// Re-applied every frame: a scene is free to install its own transform
// for a cell or a sprite, and most do.
context.setTransform(dpr, 0, 0, dpr, 0, 0)
optionsRef.current.draw({ context, width, height, dpr, state, pointer, frame })
pointer.lastX = pointer.x
pointer.lastY = pointer.y
frame += 1
}
/** One frame on the next tick, coalescing however many were asked for. */
const paintOnce = () => {
if (pending) return
pending = requestAnimationFrame(() => {
pending = 0
measure()
paint()
})
}
render.current = paintOnce
const tick = () => {
loop = requestAnimationFrame(tick)
if (visible) paint()
}
const start = () => {
if (loop || reduced) return
loop = requestAnimationFrame(tick)
}
const stop = () => {
if (!loop) return
cancelAnimationFrame(loop)
loop = 0
}
const at = (event: PointerEvent) => {
const rect = stageNode.getBoundingClientRect()
// The rect is the right thing to subtract here — `clientX` is viewport
// space and so is the rect — but the difference comes back in *rendered*
// pixels, and a scene reads `pointer` in the scene pixels `measure()` set
// up from the untransformed box. Under a CSS scale those two disagree, so
// divide the transform back out. `rect.width / offsetWidth` is the scale
// actually in force, whatever produced it, and it is exactly 1 when there
// is none.
const scale = stageNode.offsetWidth > 0 ? rect.width / stageNode.offsetWidth : 1
pointer.x = (event.clientX - rect.left) / (scale || 1)
pointer.y = (event.clientY - rect.top) / (scale || 1)
// A frozen loop still owes the user feedback for a drag.
if (reduced) paintOnce()
}
const onEnter = (event: PointerEvent) => {
pointer.inside = true
at(event)
pointer.lastX = pointer.x
pointer.lastY = pointer.y
}
const onMove = (event: PointerEvent) => {
pointer.inside = true
at(event)
}
const onDown = (event: PointerEvent) => {
pointer.down = true
at(event)
// Capture keeps a drag alive past the edge of the stage, which is where
// a hard throw naturally ends up.
stageNode.setPointerCapture(event.pointerId)
}
const onUp = (event: PointerEvent) => {
pointer.down = false
at(event)
if (stageNode.hasPointerCapture(event.pointerId)) {
stageNode.releasePointerCapture(event.pointerId)
}
}
const onLeave = () => {
pointer.inside = false
pointer.down = false
if (reduced) paintOnce()
}
stageNode.addEventListener("pointerenter", onEnter)
stageNode.addEventListener("pointermove", onMove)
stageNode.addEventListener("pointerdown", onDown)
stageNode.addEventListener("pointerup", onUp)
stageNode.addEventListener("pointercancel", onUp)
stageNode.addEventListener("pointerleave", onLeave)
const resizes = new ResizeObserver(() => paintOnce())
resizes.observe(stageNode)
/*
* An animation nobody can see is heat. The observer both pauses the loop
* and, on the way back in, repaints immediately rather than waiting a frame.
*/
const views = new IntersectionObserver(
(entries) => {
visible = entries.some((entry) => entry.isIntersecting)
if (visible) {
start()
paintOnce()
} else {
stop()
}
},
{ rootMargin: "120px" },
)
views.observe(stageNode)
measure()
paint()
start()
return () => {
render.current = null
stop()
if (pending) cancelAnimationFrame(pending)
resizes.disconnect()
views.disconnect()
stageNode.removeEventListener("pointerenter", onEnter)
stageNode.removeEventListener("pointermove", onMove)
stageNode.removeEventListener("pointerdown", onDown)
stageNode.removeEventListener("pointerup", onUp)
stageNode.removeEventListener("pointercancel", onUp)
stageNode.removeEventListener("pointerleave", onLeave)
}
}, [reduced])
return { stageRef, canvasRef, requestRender }
}