05Draw your own line — sketch it, and circles redraw it live
Draw any line with the mouse — the points instantly become complex coefficients, and epicycles redraw your just-drawn signature or doodle stroke by stroke.
Best forInteractive easter eggs, signature demos
pointerdownpointermoverequestAnimationFrame
<main class="stage">
<div class="fe is-demo" id="feRoot">
<p class="fe__hint">
<span>Draw any line with the mouse — the points instantly become complex coefficients, and epicycles redraw your just-drawn signature or doodle stroke by stroke</span>
</p>
<div class="fe__field" id="feField" role="application" aria-label="Draw-Your-Own-Line Demo" tabindex="0">
<canvas class="fe__cv" id="feCv"></canvas>
</div>
<div class="fe__bar">
<span class="fe__meta"><b class="fe__val" id="feN">0</b><span id="feUnit"> sample doodle · draw yours</span></span>
<span class="fe__meta fe__meta--dim">canvas · live DFT · pointer events</span>
</div>
</div>
</main>@use "../../../../site/static/demo-tokens" as *;
// 기본 에피사이클 체인(01). @keyframes 를 두지 않는다 —
// 움직임은 전부 캔버스 rAF 루프(복소 계수 체인 회전 → 펜 궤적 누적)가 만든다.
// 무대는 심야 관측 팔레트. 파스텔 주색을 --fe-* 로 편 전체(01~09) 공통 규격.
$duration: $dur-loop;
$easing: $ease-spring;
$color: $subject-lilac;
// ── 편 공통 심야 관측 팔레트(BD9~11 원칙: 편마다 다시 정하지 않는다) ──
$fe-stage: #141824; // 심야 그래프지 — 저채도 짙은 남색 (파스텔 검사 무관: 저채도·저명도)
@include stage($fe-stage);
$fe-ink: #10141f; // 필드 바닥 — 무대보다 한 톤 어두운 남흑
$fe-glow: #b7c8ff; // 궤적 주색 — 파스텔 페리윙클(고명도라 vivid 아님)
$fe-hot: #ffe9c4; // 펜 절정 — 파스텔 크림
$fe-text: #d6d9e6; // 라벨 글자 — 밝은 회청
.fe {
// 렌더러가 읽는 색 — JS 는 getComputedStyle 로 --fe-* 를 받아 쓴다
--fe-ink: #{$fe-ink};
--fe-glow: #{$fe-glow};
--fe-hot: #{$fe-hot};
display: flex; flex-direction: column; gap: $sp-2;
width: 100%; max-width: 424px;
}
.fe__hint {
display: flex; align-items: center; gap: $sp-1; margin: 0;
font-weight: 700; font-size: clamp(10px, 2.8vw, 12px); line-height: 1.35;
color: $fe-text;
}
.fe__field {
position: relative; height: 180px;
border-radius: $r-card; overflow: hidden;
background: $fe-ink;
box-shadow: inset 0 0 0 1px rgba($fe-text, .18);
}
.fe__field:focus-visible { outline: 2px solid $fe-glow; outline-offset: 2px; }
.fe__cv { display: block; width: 100%; height: 100%; }
.fe__bar { display: flex; align-items: baseline; justify-content: space-between; gap: $sp-2; }
.fe__meta { font-size: 10px; font-weight: 500; color: rgba($fe-text, .72); }
.fe__meta--dim { font-size: 10px; }
@media (max-width: 340px) {
.fe { gap: $sp-1; }
.fe__field { height: 100px; }
.fe__meta--dim { display: none; }
}
// reduce — rAF 를 돌리지 않고 궤적이 다 쌓인 한 장만 남는다.
@media (prefers-reduced-motion: reduce) {
.fe.is-still .fe__field { cursor: default !important; }
}html, body {
margin: 0;
overflow: hidden;
}
.stage {
box-sizing: border-box;
min-height: 100vh;
display: grid;
place-items: center;
margin: 0;
background: #141824;
font-family: -apple-system, "Segoe UI", "Noto Sans KR", sans-serif;
padding: clamp(8px, 4vw, 24px);
}
.fe {
--fe-ink: #10141f;
--fe-glow: #b7c8ff;
--fe-hot: #ffe9c4;
display: flex;
flex-direction: column;
gap: 8px;
width: 100%;
max-width: 424px;
}
.fe__hint {
display: flex;
align-items: center;
gap: 4px;
margin: 0;
font-weight: 700;
font-size: clamp(10px, 2.8vw, 12px);
line-height: 1.35;
color: #d6d9e6;
}
.fe__field {
position: relative;
height: 180px;
border-radius: 16px;
overflow: hidden;
background: #10141f;
box-shadow: inset 0 0 0 1px rgba(214, 217, 230, 0.18);
}
.fe__field:focus-visible {
outline: 2px solid #b7c8ff;
outline-offset: 2px;
}
.fe__cv {
display: block;
width: 100%;
height: 100%;
}
.fe__bar {
display: flex;
align-items: baseline;
justify-content: space-between;
gap: 8px;
}
.fe__meta {
font-size: 10px;
font-weight: 500;
color: rgba(214, 217, 230, 0.72);
}
.fe__meta--dim {
font-size: 10px;
}
@media (max-width: 340px) {
.fe {
gap: 4px;
}
.fe__field {
height: 100px;
}
.fe__meta--dim {
display: none;
}
}
@media (prefers-reduced-motion: reduce) {
.fe.is-still .fe__field {
cursor: default !important;
}
}// 내 선 그리기(05). 편의 인터랙티브 축 — 손으로 그은 선이 그대로 DFT 입력이 된다.
// ① 기본 상태: 예시 낙서(물결 서명)를 낮은 알파로 깔아두고 에피사이클이 반복해서 되그린다.
// ② pointerdown~move 로 점을 모으면(최대 512) 기존 계수를 지우고 즉시 dft() 재계산 —
// 계산은 O(N²) 이지만 N=512 로 순식간이고, 체인이 새 경로를 다시 그리기 시작한다.
// ③ 같은 재합성 루프(투명 트레일 누적 + 혜성 감쇠)를 공유한다.
//
// 화면이 사는 장치 — 077 기준:
// · 밑바탕 방사 스윕·스포크가 매 프레임 재계산되어 화면 전면이 살아 있다.
// · 손 궤적(입력)도 옅은 잔상으로 함께 남는다 — 그은 즉시 바뀌는 계수를 눈으로 읽는다.
(function () {
// ── 변형 상수 블록 ──
var MAXPTS = 512; // 입력 받는 최대 점 수
var SHOW = 48; // 화면에 그리는 circles
// ──────────────────
var TAU = Math.PI * 2;
var root = document.getElementById('feRoot');
var field = document.getElementById('feField');
var cv = document.getElementById('feCv');
var nOut = document.getElementById('feN');
var css = getComputedStyle(root);
function tokRGB(name) {
var s = css.getPropertyValue(name).trim();
var hx = s.length === 4
? s.charAt(1) + s.charAt(1) + s.charAt(2) + s.charAt(2) + s.charAt(3) + s.charAt(3)
: s.slice(1);
return [parseInt(hx.slice(0, 2), 16), parseInt(hx.slice(2, 4), 16), parseInt(hx.slice(4, 6), 16)];
}
var C_INK = tokRGB('--fe-ink');
var C_GLOW = tokRGB('--fe-glow');
var C_HOT = tokRGB('--fe-hot');
var reduce = window.matchMedia('(prefers-reduced-motion: reduce)').matches;
var raf = 0, t0 = -1;
var W = 0, H = 0, dpr = 1;
var trailCv, trailCtx;
// ── DFT (03·04 와 같은 계산) ──
function dft(path) {
var M = path.length;
var out = [];
for (var k = 0; k < M; k++) {
var freq = (k <= M / 2) ? k : k - M;
var re = 0, im = 0;
for (var n = 0; n < M; n++) {
var a = -TAU * k * n / M;
var c = Math.cos(a), s = Math.sin(a);
re += path[n].x * c - path[n].y * s;
im += path[n].x * s + path[n].y * c;
}
re /= M; im /= M;
out.push({ freq: freq, re: re, im: im, amp: Math.sqrt(re * re + im * im) });
}
out.sort(function (a, b) { return b.amp - a.amp; });
return out;
}
var PATH = [], COEF = [];
var normPath = []; // 정규화된 경로(체인 재현용)
function normalize() {
// 그은 점을 무대 중심·단위반지름으로 정규화
var minx = 1e9, maxx = -1e9, miny = 1e9, maxy = -1e9;
for (var i = 0; i < PATH.length; i++) {
if (PATH[i].x < minx) minx = PATH[i].x;
if (PATH[i].x > maxx) maxx = PATH[i].x;
if (PATH[i].y < miny) miny = PATH[i].y;
if (PATH[i].y > maxy) maxy = PATH[i].y;
}
var cx = (minx + maxx) / 2, cy = (miny + maxy) / 2;
var span = Math.max(maxx - minx, maxy - miny) || 1;
normPath = [];
for (var j = 0; j < PATH.length; j++) {
normPath.push({ x: (PATH[j].x - cx) / span, y: (PATH[j].y - cy) / span });
}
COEF = dft(normPath);
}
function sampleDoodle() {
// 예시 낙서 — 서명 같은 물결. t 0~1 로 닫힌 물결 무늬
PATH = [];
for (var i = 0; i < 200; i++) {
var t = i / 200;
PATH.push({
x: Math.cos(t * TAU) * (0.36 + 0.16 * Math.sin(t * TAU * 3)),
y: Math.sin(t * TAU) * (0.24 + 0.12 * Math.cos(t * TAU * 2))
});
}
normalize();
}
function fit() {
var r = field.getBoundingClientRect();
W = Math.round(r.width); H = Math.round(r.height);
dpr = Math.min(2, window.devicePixelRatio || 1);
cv.width = W * dpr; cv.height = H * dpr;
cv.style.width = '100%'; cv.style.height = '100%';
trailCv = document.createElement('canvas');
trailCv.width = W * dpr; trailCv.height = H * dpr;
trailCtx = trailCv.getContext('2d');
trailCtx.scale(dpr, dpr);
if (!COEF.length) sampleDoodle();
}
function rgba(c, a) { return 'rgba(' + c[0] + ',' + c[1] + ',' + c[2] + ',' + a + ')'; }
function chainAt(u, show) {
var base = Math.min(W, H) * 0.4;
var cx = W * 0.5, cy = H * 0.5;
var pts = [{ x: cx, y: cy }];
var n = show || COEF.length;
for (var i = 0; i < n && i < COEF.length; i++) {
var c = COEF[i];
var a = c.freq * u * TAU;
var ph = Math.atan2(c.im, c.re);
var ang = a + ph;
var px = pts[i].x + Math.cos(ang) * c.amp * base;
var py = pts[i].y + Math.sin(ang) * c.amp * base;
pts.push({ x: px, y: py });
}
return pts;
}
// 밑바탕 — 방사 스윕(계단 밴드) + 스포크
function drawGrid(t) {
var ctx = cv.getContext('2d');
var cx = W * 0.5, cy = H * 0.5;
var maxR = Math.sqrt(W * W + H * H) * 0.5;
var sweep = t * 1.1;
for (var b = 0; b < 16; b++) {
ctx.fillStyle = rgba(C_GLOW, 0.085 * (1 - b / 16));
ctx.beginPath();
ctx.moveTo(cx, cy);
ctx.arc(cx, cy, maxR, sweep - (b + 1) * 0.06, sweep - b * 0.06);
ctx.closePath();
ctx.fill();
}
var spin = t * 0.26;
for (var i = 0; i < 16; i++) {
var a = spin + (i / 16) * TAU;
ctx.strokeStyle = rgba(C_GLOW, i % 2 === 0 ? 0.08 : 0.05);
ctx.lineWidth = 1;
ctx.beginPath();
ctx.moveTo(cx + Math.cos(a) * 12, cy + Math.sin(a) * 12);
ctx.lineTo(cx + Math.cos(a) * maxR, cy + Math.sin(a) * maxR);
ctx.stroke();
}
}
function draw(u, pulse, show, gt) {
var ctx = cv.getContext('2d');
ctx.setTransform(dpr, 0, 0, dpr, 0, 0);
ctx.fillStyle = 'rgb(' + C_INK[0] + ',' + C_INK[1] + ',' + C_INK[2] + ')';
ctx.fillRect(0, 0, W, H);
drawGrid(gt);
// 손 궤적 잔상 — 사용자가 그은 원본(정규화 전 화면 좌표)을 옅게
if (handCv) ctx.drawImage(handCv, 0, 0, W, H);
ctx.drawImage(trailCv, 0, 0, W, H);
var base = Math.min(W, H) * 0.4;
var pts = chainAt(u, show);
for (var i = 0; i < pts.length - 1; i++) {
var r = COEF[i].amp * base;
if (r > 2) {
ctx.strokeStyle = rgba(C_GLOW, 0.09 + 0.01 * i);
ctx.lineWidth = 1;
ctx.beginPath();
ctx.arc(pts[i].x, pts[i].y, r, 0, TAU);
ctx.stroke();
}
if (i < 4 || r > 3) {
ctx.strokeStyle = rgba(C_GLOW, 0.48);
ctx.beginPath();
ctx.moveTo(pts[i].x, pts[i].y);
ctx.lineTo(pts[i + 1].x, pts[i + 1].y);
ctx.stroke();
}
}
var pen = pts[pts.length - 1];
var pr = 2.4 + pulse * 2.2;
ctx.fillStyle = rgba(C_HOT, 0.3);
ctx.beginPath();
ctx.arc(pen.x, pen.y, pr * 2.3, 0, TAU);
ctx.fill();
ctx.fillStyle = rgba(C_HOT, 1);
ctx.beginPath();
ctx.arc(pen.x, pen.y, pr, 0, TAU);
ctx.fill();
return pen;
}
var prevPen = null;
var handCv = null, handCtx = null; // 손 궤적 잔상 캔버스
function stampTrail(pen) {
if (!prevPen) { prevPen = pen; return; }
trailCtx.strokeStyle = rgba(C_GLOW, 0.88);
trailCtx.lineWidth = 1.9;
trailCtx.lineCap = 'round';
trailCtx.beginPath();
trailCtx.moveTo(prevPen.x, prevPen.y);
trailCtx.lineTo(pen.x, pen.y);
trailCtx.stroke();
trailCtx.strokeStyle = rgba(C_GLOW, 0.14);
trailCtx.lineWidth = 5;
trailCtx.stroke();
prevPen = pen;
}
function decayTrail() {
trailCtx.setTransform(1, 0, 0, 1, 0, 0);
trailCtx.globalCompositeOperation = 'destination-out';
trailCtx.fillStyle = 'rgba(0,0,0,0.03)';
trailCtx.fillRect(0, 0, W * dpr, H * dpr);
trailCtx.globalCompositeOperation = 'source-over';
trailCtx.setTransform(dpr, 0, 0, dpr, 0, 0);
}
function frame(now) {
if (t0 < 0) t0 = now;
var lt = ((now - t0) / 1000) * 0.5;
var u = lt % 1;
var pulse = 0.5 + 0.5 * Math.sin(lt * 8.0);
decayTrail();
var pen = draw(u, pulse, SHOW, lt * TAU);
stampTrail(pen);
if (nOut) nOut.textContent = String(PATH.length);
raf = requestAnimationFrame(frame);
}
// ── 입력 — 그으면 즉시 DFT 재계산 ──
var drawing = false, lastPt = null;
function toField(e) {
var r = cv.getBoundingClientRect();
return { x: e.clientX - r.left, y: e.clientY - r.top };
}
function startDraw(e) {
drawing = true; lastPt = toField(e);
PATH = [lastPt];
if (!handCv) {
handCv = document.createElement('canvas');
handCv.width = W * dpr; handCv.height = H * dpr;
handCtx = handCv.getContext('2d');
handCtx.scale(dpr, dpr);
}
handCtx.clearRect(0, 0, W, H);
prevPen = null;
e.preventDefault();
}
function moveDraw(e) {
if (!drawing) return;
var p = toField(e);
if (Math.abs(p.x - lastPt.x) + Math.abs(p.y - lastPt.y) < 4) return;
PATH.push(p);
if (PATH.length > MAXPTS) PATH.shift();
handCtx.strokeStyle = rgba(C_HOT, 0.28);
handCtx.lineWidth = 2;
handCtx.lineCap = 'round';
handCtx.beginPath();
handCtx.moveTo(lastPt.x, lastPt.y);
handCtx.lineTo(p.x, p.y);
handCtx.stroke();
lastPt = p;
normalize();
prevPen = null;
e.preventDefault();
}
function endDraw() {
if (!drawing) return;
drawing = false;
if (PATH.length > 8) normalize();
}
cv.addEventListener('pointerdown', startDraw);
cv.addEventListener('pointermove', moveDraw);
window.addEventListener('pointerup', endDraw);
function stillFrame() {
var prev = chainAt(0, SHOW)[SHOW];
for (var i = 1; i <= 200; i++) {
var pen = chainAt(i / 200, SHOW)[SHOW];
stampTrail(pen);
prev = pen;
}
draw(0.5, 0.5, SHOW, 2.1);
}
window.addEventListener('resize', function () {
fit(); prevPen = null; handCv = null;
if (reduce) stillFrame();
});
fit();
if (reduce) {
stillFrame();
root.classList.add('is-still');
} else {
raf = requestAnimationFrame(frame);
}
})();// FourierDrawYourLine — vanilla 판(run/321/demo/05-fourier-draw-your-line/index.html) 의 React 포트.
// 내 선 그리기 — 편의 인터랙티브 축. 손으로 그은 선이 그대로 DFT 입력이 된다.
// ① 기본 상태: 예시 낙서(물결 서명)를 낮은 알파로 깔아두고 에피사이클이 반복해서 되그린다.
// ② pointerdown~move 로 점을 모으면(최대 512) 기존 계수를 지우고 즉시 dft() 재계산 —
// 계산은 O(N²) 이지만 N=512 로 순식간이고, 체인이 새 경로를 다시 그리기 시작한다.
// ③ 같은 재합성 루프(투명 트레일 누적 + 혜성 감쇠)를 공유한다.
// 화면이 사는 장치 — 밑바탕 방사 스윕·스포크가 매 프레임 재계산,
// 손 궤적(입력)도 옅은 잔상으로 함께 남는다 — 그은 즉시 바뀌는 계수를 눈으로 읽는다.
import { useEffect, useRef, useState } from "react";
import type { CSSProperties, PointerEvent as ReactPointerEvent } from "react";
import styles from "./FourierDrawYourLine.module.scss";
export type FourierDrawYourLineProps = {
duration?: string;
easing?: string;
color?: string;
maxPts?: number; // 입력 받는 최대 점 수
show?: number; // 화면에 그리는 원 개수
};
type Vars = CSSProperties & { "--duration"?: string; "--easing"?: string; "--color"?: string };
type Box<T> = { current: T };
type RGB = [number, number, number];
type Pt = { x: number; y: number };
type Coef = { freq: number; re: number; im: number; amp: number };
const FIELD_LABEL = "내 선 그리기 에피사이클 실험판";
const TAU = Math.PI * 2;
// ── DFT (03·04 와 같은 계산) ──
function dft(path: Pt[]): Coef[] {
const M = path.length;
const out: Coef[] = [];
for (let k = 0; k < M; k++) {
const freq = (k <= M / 2) ? k : k - M;
let re = 0, im = 0;
for (let n = 0; n < M; n++) {
const a = -TAU * k * n / M;
const c = Math.cos(a), s = Math.sin(a);
re += path[n].x * c - path[n].y * s;
im += path[n].x * s + path[n].y * c;
}
re /= M; im /= M;
out.push({ freq: freq, re: re, im: im, amp: Math.sqrt(re * re + im * im) });
}
out.sort((a, b) => b.amp - a.amp);
return out;
}
export default function FourierDrawYourLine({
duration = "2s",
easing = "cubic-bezier(.2, .8, .2, 1)",
color = "#b7c8ff",
maxPts = 512,
show = 48
}: FourierDrawYourLineProps) {
const rootRef = useRef<HTMLDivElement | null>(null);
const fieldRef = useRef<HTMLDivElement | null>(null);
const cvRef = useRef<HTMLCanvasElement | null>(null);
const ctxRef = useRef<CanvasRenderingContext2D | null>(null);
const colRef = useRef<{ ink: RGB; glow: RGB; hot: RGB } | null>(null);
const trailCvRef = useRef<HTMLCanvasElement | null>(null);
const trailCtxRef = useRef<CanvasRenderingContext2D | null>(null);
const handCvRef = useRef<HTMLCanvasElement | null>(null);
const handCtxRef = useRef<CanvasRenderingContext2D | null>(null);
const maxPtsRef = useRef(maxPts) as Box<number>;
const showRef = useRef(show) as Box<number>;
const pathRef = useRef<Pt[]>([]) as Box<Pt[]>;
const normPathRef = useRef<Pt[]>([]) as Box<Pt[]>; // 정규화된 경로(체인 재현용)
const coefRef = useRef<Coef[]>([]) as Box<Coef[]>;
const wRef = useRef(0) as Box<number>;
const hRef = useRef(0) as Box<number>;
const dprRef = useRef(1) as Box<number>;
const rafRef = useRef(0) as Box<number>;
const drawingRef = useRef(false) as Box<boolean>;
const lastPtRef = useRef<Pt | null>(null) as Box<Pt | null>;
const [cnt, setCnt] = useState("0");
const [still, setStill] = useState(false);
const vars: Vars = { "--duration": duration, "--easing": easing, "--color": color };
function reduced(): boolean {
return window.matchMedia("(prefers-reduced-motion: reduce)").matches;
}
function tokRGB(root: HTMLDivElement, name: string): RGB {
const s = getComputedStyle(root).getPropertyValue(name).trim();
const hx = s.length === 4
? s.charAt(1) + s.charAt(1) + s.charAt(2) + s.charAt(2) + s.charAt(3) + s.charAt(3)
: s.slice(1);
return [parseInt(hx.slice(0, 2), 16), parseInt(hx.slice(2, 4), 16), parseInt(hx.slice(4, 6), 16)];
}
function rgba(c: RGB, a: number): string {
return "rgba(" + c[0] + "," + c[1] + "," + c[2] + "," + a + ")";
}
function normalize(): void {
// 그은 점을 무대 중심·단위반지름으로 정규화
const PATH = pathRef.current;
let minx = 1e9, maxx = -1e9, miny = 1e9, maxy = -1e9;
for (let i = 0; i < PATH.length; i++) {
if (PATH[i].x < minx) minx = PATH[i].x;
if (PATH[i].x > maxx) maxx = PATH[i].x;
if (PATH[i].y < miny) miny = PATH[i].y;
if (PATH[i].y > maxy) maxy = PATH[i].y;
}
const cx = (minx + maxx) / 2, cy = (miny + maxy) / 2;
const span = Math.max(maxx - minx, maxy - miny) || 1;
const norm: Pt[] = [];
for (let j = 0; j < PATH.length; j++) {
norm.push({ x: (PATH[j].x - cx) / span, y: (PATH[j].y - cy) / span });
}
normPathRef.current = norm;
coefRef.current = dft(norm);
}
function sampleDoodle(): void {
// 예시 낙서 — 서명 같은 물결. t 0~1 로 닫힌 물결 무늬
const PATH: Pt[] = [];
for (let i = 0; i < 200; i++) {
const t = i / 200;
PATH.push({
x: Math.cos(t * TAU) * (0.36 + 0.16 * Math.sin(t * TAU * 3)),
y: Math.sin(t * TAU) * (0.24 + 0.12 * Math.cos(t * TAU * 2))
});
}
pathRef.current = PATH;
normalize();
}
function fit(): void {
const field = fieldRef.current;
const cv = cvRef.current;
if (!field || !cv) return;
const r = field.getBoundingClientRect();
const W = Math.round(r.width), H = Math.round(r.height);
const dpr = Math.min(2, window.devicePixelRatio || 1);
wRef.current = W; hRef.current = H; dprRef.current = dpr;
cv.width = W * dpr; cv.height = H * dpr;
cv.style.width = "100%"; cv.style.height = "100%";
ctxRef.current = cv.getContext("2d");
const trailCv = document.createElement("canvas");
trailCv.width = W * dpr; trailCv.height = H * dpr;
const trailCtx = trailCv.getContext("2d");
if (trailCtx) trailCtx.scale(dpr, dpr);
trailCvRef.current = trailCv;
trailCtxRef.current = trailCtx;
handCvRef.current = null;
handCtxRef.current = null;
if (!coefRef.current.length) sampleDoodle();
}
function chainAt(u: number, showCount?: number): Pt[] {
const W = wRef.current, H = hRef.current;
const COEF = coefRef.current;
const base = Math.min(W, H) * 0.4;
const cx = W * 0.5, cy = H * 0.5;
const pts: Pt[] = [{ x: cx, y: cy }];
const n = showCount || COEF.length;
for (let i = 0; i < n && i < COEF.length; i++) {
const c = COEF[i];
const a = c.freq * u * TAU;
const ph = Math.atan2(c.im, c.re);
const ang = a + ph;
pts.push({ x: pts[i].x + Math.cos(ang) * c.amp * base, y: pts[i].y + Math.sin(ang) * c.amp * base });
}
return pts;
}
// 밑바탕 — 방사 스윕(계단 밴드) + 스포크
function drawGrid(ctx: CanvasRenderingContext2D, t: number): void {
const W = wRef.current, H = hRef.current;
const col = colRef.current;
if (!col) return;
const cx = W * 0.5, cy = H * 0.5;
const maxR = Math.sqrt(W * W + H * H) * 0.5;
const sweep = t * 1.1;
for (let b = 0; b < 16; b++) {
ctx.fillStyle = rgba(col.glow, 0.085 * (1 - b / 16));
ctx.beginPath();
ctx.moveTo(cx, cy);
ctx.arc(cx, cy, maxR, sweep - (b + 1) * 0.06, sweep - b * 0.06);
ctx.closePath();
ctx.fill();
}
const spin = t * 0.26;
for (let i = 0; i < 16; i++) {
const a = spin + (i / 16) * TAU;
ctx.strokeStyle = rgba(col.glow, i % 2 === 0 ? 0.08 : 0.05);
ctx.lineWidth = 1;
ctx.beginPath();
ctx.moveTo(cx + Math.cos(a) * 12, cy + Math.sin(a) * 12);
ctx.lineTo(cx + Math.cos(a) * maxR, cy + Math.sin(a) * maxR);
ctx.stroke();
}
}
function draw(u: number, pulse: number, showCount: number, gt: number): Pt {
const ctx = ctxRef.current;
const trailCv = trailCvRef.current;
const handCv = handCvRef.current;
const col = colRef.current;
const dpr = dprRef.current;
const W = wRef.current, H = hRef.current;
const COEF = coefRef.current;
if (!ctx || !trailCv || !col) return { x: 0, y: 0 };
ctx.setTransform(dpr, 0, 0, dpr, 0, 0);
ctx.fillStyle = "rgb(" + col.ink[0] + "," + col.ink[1] + "," + col.ink[2] + ")";
ctx.fillRect(0, 0, W, H);
drawGrid(ctx, gt);
// 손 궤적 잔상 — 사용자가 그은 원본(정규화 전 화면 좌표)을 옅게
if (handCv) ctx.drawImage(handCv, 0, 0, W, H);
ctx.drawImage(trailCv, 0, 0, W, H);
const base = Math.min(W, H) * 0.4;
const pts = chainAt(u, showCount);
for (let i = 0; i < pts.length - 1; i++) {
const r = COEF[i].amp * base;
if (r > 2) {
ctx.strokeStyle = rgba(col.glow, 0.09 + 0.01 * i);
ctx.lineWidth = 1;
ctx.beginPath();
ctx.arc(pts[i].x, pts[i].y, r, 0, TAU);
ctx.stroke();
}
if (i < 4 || r > 3) {
ctx.strokeStyle = rgba(col.glow, 0.48);
ctx.beginPath();
ctx.moveTo(pts[i].x, pts[i].y);
ctx.lineTo(pts[i + 1].x, pts[i + 1].y);
ctx.stroke();
}
}
const pen = pts[pts.length - 1];
const pr = 2.4 + pulse * 2.2;
ctx.fillStyle = rgba(col.hot, 0.3);
ctx.beginPath();
ctx.arc(pen.x, pen.y, pr * 2.3, 0, TAU);
ctx.fill();
ctx.fillStyle = rgba(col.hot, 1);
ctx.beginPath();
ctx.arc(pen.x, pen.y, pr, 0, TAU);
ctx.fill();
return pen;
}
const prevPenRef = useRef<Pt | null>(null) as Box<Pt | null>;
function stampTrail(pen: Pt): void {
const trailCtx = trailCtxRef.current;
const col = colRef.current;
const prev = prevPenRef.current;
if (!trailCtx || !col) return;
if (!prev) { prevPenRef.current = pen; return; }
trailCtx.strokeStyle = rgba(col.glow, 0.88);
trailCtx.lineWidth = 1.9;
trailCtx.lineCap = "round";
trailCtx.beginPath();
trailCtx.moveTo(prev.x, prev.y);
trailCtx.lineTo(pen.x, pen.y);
trailCtx.stroke();
trailCtx.strokeStyle = rgba(col.glow, 0.14);
trailCtx.lineWidth = 5;
trailCtx.stroke();
prevPenRef.current = pen;
}
function decayTrail(): void {
const trailCtx = trailCtxRef.current;
const dpr = dprRef.current;
const W = wRef.current, H = hRef.current;
if (!trailCtx) return;
trailCtx.setTransform(1, 0, 0, 1, 0, 0);
trailCtx.globalCompositeOperation = "destination-out";
trailCtx.fillStyle = "rgba(0,0,0,0.03)";
trailCtx.fillRect(0, 0, W * dpr, H * dpr);
trailCtx.globalCompositeOperation = "source-over";
trailCtx.setTransform(dpr, 0, 0, dpr, 0, 0);
}
let t0 = -1;
function frame(now: number): void {
if (t0 < 0) t0 = now;
const lt = ((now - t0) / 1000) * 0.5;
const u = lt % 1;
const pulse = 0.5 + 0.5 * Math.sin(lt * 8.0);
decayTrail();
const pen = draw(u, pulse, showRef.current, lt * TAU);
stampTrail(pen);
setCnt(String(pathRef.current.length));
rafRef.current = requestAnimationFrame(frame);
}
// ── 입력 — 그으면 즉시 DFT 재계산 ──
function toField(e: ReactPointerEvent<HTMLCanvasElement>): Pt {
const cv = cvRef.current;
if (!cv) return { x: 0, y: 0 };
const r = cv.getBoundingClientRect();
return { x: e.clientX - r.left, y: e.clientY - r.top };
}
function startDraw(e: ReactPointerEvent<HTMLCanvasElement>): void {
const col = colRef.current;
const W = wRef.current, H = hRef.current;
const dpr = dprRef.current;
if (!col) return;
drawingRef.current = true;
const p = toField(e);
lastPtRef.current = p;
pathRef.current = [p];
if (!handCvRef.current) {
const handCv = document.createElement("canvas");
handCv.width = W * dpr; handCv.height = H * dpr;
const handCtx = handCv.getContext("2d");
if (handCtx) handCtx.scale(dpr, dpr);
handCvRef.current = handCv;
handCtxRef.current = handCtx;
}
const handCtx = handCtxRef.current;
if (handCtx) handCtx.clearRect(0, 0, W, H);
prevPenRef.current = null;
e.preventDefault();
}
function moveDraw(e: ReactPointerEvent<HTMLCanvasElement>): void {
const handCtx = handCtxRef.current;
const col = colRef.current;
const last = lastPtRef.current;
if (!drawingRef.current || !handCtx || !col || !last) return;
const p = toField(e);
if (Math.abs(p.x - last.x) + Math.abs(p.y - last.y) < 4) return;
pathRef.current.push(p);
if (pathRef.current.length > maxPtsRef.current) pathRef.current.shift();
handCtx.strokeStyle = rgba(col.hot, 0.28);
handCtx.lineWidth = 2;
handCtx.lineCap = "round";
handCtx.beginPath();
handCtx.moveTo(last.x, last.y);
handCtx.lineTo(p.x, p.y);
handCtx.stroke();
lastPtRef.current = p;
normalize();
prevPenRef.current = null;
e.preventDefault();
}
function endDraw(): void {
if (!drawingRef.current) return;
drawingRef.current = false;
if (pathRef.current.length > 8) normalize();
}
function stillFrame(): void {
const S = showRef.current;
let prev = chainAt(0, S)[S];
for (let i = 1; i <= 200; i++) {
const pen = chainAt(i / 200, S)[S];
stampTrail(pen);
prev = pen;
}
draw(0.5, 0.5, S, 2.1);
}
useEffect(() => {
const root = rootRef.current;
if (!root) return;
maxPtsRef.current = maxPts;
showRef.current = show;
colRef.current = {
ink: tokRGB(root, "--fe-ink"),
glow: tokRGB(root, "--fe-glow"),
hot: tokRGB(root, "--fe-hot"),
};
fit();
setCnt(String(pathRef.current.length));
function onResize(): void {
fit(); prevPenRef.current = null;
if (reduced()) stillFrame();
}
function onPointerUp(): void {
endDraw();
}
window.addEventListener("resize", onResize);
window.addEventListener("pointerup", onPointerUp);
if (reduced()) {
stillFrame();
setStill(true);
} else {
t0 = -1;
rafRef.current = requestAnimationFrame(frame);
}
return () => {
window.removeEventListener("resize", onResize);
window.removeEventListener("pointerup", onPointerUp);
cancelAnimationFrame(rafRef.current);
};
// eslint-disable-next-line react-hooks/exhaustive-deps
}, [maxPts, show]);
const rootCls = still ? `${styles.root} ${styles.isStill}` : styles.root;
return (
<main className={styles.stage}>
<div className={rootCls} ref={rootRef} style={vars}>
<p className={styles.hint}>
<span>캔버스에 마우스로 아무 선이나 그으면 그 점들이 즉시 복소 계수로 바뀌어, 방금 손으로 그은 서명 낙서를 에피사이클이 한 획씩 다시 그려줍니다</span>
</p>
<div
className={styles.field}
ref={fieldRef}
role="application"
aria-label={FIELD_LABEL}
tabIndex={0}
>
<canvas
className={styles.cv}
ref={cvRef}
onPointerDown={startDraw}
onPointerMove={moveDraw}
></canvas>
</div>
<div className={styles.bar}>
<span className={styles.meta}><b className={styles.val}>{cnt}</b> 예시 낙서 · 직접 그려 보세요</span>
<span className={styles.metaDim}>canvas · live DFT · pointer events</span>
</div>
</div>
</main>
);
}05 Draw your own line — sketch it, and circles redraw it live — Measured area 42.997% · moving frames 23/23Original by GODRICH · SCSS and React ship in the zip · Fourier Epicycles, 9 Ways (No Library)
The post this demo lives in
Fourier Epicycles, 9 Ways (No Library)No library, no WebGL — put a path's points on the complex plane, run one sine/cosine integral, and circles stacked on ci See all demos in this post
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