07Phase morph — same coefficients, rotated phases, a pattern that shape-shifts
Keep magnitudes, offset only the phases — the figure morphs continuously from star to petal to swirl, an experiment in what magnitude versus phase each contribute to a drawing.
Best forParameter playgrounds, generative-art backgrounds
CanvasRenderingContext2DglobalAlpharequestAnimationFrame
<main class="stage">
<div class="fe is-demo" id="feRoot">
<p class="fe__hint">
<span>Keep magnitudes, offset only the phases — the figure morphs continuously from star to petal to swirl, an experiment in what magnitude versus phase each contribute to a drawing</span>
</p>
<div class="fe__field" id="feField" role="application" aria-label="Phase Morph 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"> phase offset oscillates · size fixed</span></span>
<span class="fe__meta fe__meta--dim">canvas · phase offset · requestAnimationFrame</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;
}
}// 위상 모프(07). 계수의 두 축 — 크기와 위상 — 중 위상만 흔든다.
// ① 별 경로(03 과 동일)의 DFT 계수에서 진폭은 얼리고 위상에만 오프셋 φ_k = d·k 를 더한다.
// ② d 가 0 이면 원래 별. d 가 커질수록 각 원의 시각이 어긋나 무늬가 별→꽃잎→소용돌이로 변한다.
// ③ d 를 사인파로 왕복시키면 무늬가 계속 모프한다 — 크기는 무늬의 "에너지"·위상은 "배치"임을 보여준다.
// 두 번째 시각화: 같은 계수를 오른쪽 위상 원반(각 계수를 단위원 위의 점으로)에 띄운다 —
// 위상이 흔들리면 점들이 원반을 따라 미끄러진다.
//
// 화면이 사는 장치 — 077 기준:
// · 궤적이 투명 캔버스에 쌓이며 혜성 감쇠 — 모프가 지나간 자리가 잔상으로 겹친다.
// · 방사 스윕·스포크가 매 프레임 재계산된다. 위상 원반 점들이 매 프레임 미끄러진다.
(function () {
// ── 변형 상수 블록 ──
var N = 256;
var SHOW = 16; // 체인에 쓰는 계수 수
var SWEEP = 2.4; // 위상 오프셋 왕복 주기(초)
// ──────────────────
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;
function starPath(u) {
var seg = u * 10;
var i = Math.floor(seg);
var f = seg - i;
var a1 = i / 10 * TAU - Math.PI / 2;
var a2 = (i + 1) / 10 * TAU - Math.PI / 2;
var r1 = (i % 2 === 0) ? 1 : 0.42;
var r2 = (i % 2 === 0) ? 0.42 : 1;
var x1 = Math.cos(a1) * r1, y1 = Math.sin(a1) * r1;
var x2 = Math.cos(a2) * r2, y2 = Math.sin(a2) * r2;
return { x: x1 + (x2 - x1) * f, y: y1 + (y2 - y1) * f };
}
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 = [];
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 (!PATH.length) {
for (var i = 0; i < N; i++) PATH.push(starPath(i / N));
COEF = dft(PATH);
}
}
function rgba(c, a) { return 'rgba(' + c[0] + ',' + c[1] + ',' + c[2] + ',' + a + ')'; }
// 위상 오프셋 체인 — d 만큼 각 계수 위상을 민다
function chainAt(u, d, show) {
var base = Math.min(W, H) * 0.36;
var cx = W * 0.32, cy = H * 0.5;
var pts = [{ x: cx, y: cy }];
for (var i = 0; i < show && i < COEF.length; i++) {
var c = COEF[i];
var ph = Math.atan2(c.im, c.re) + c.freq * d;
var ang = c.freq * u * TAU + 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;
}
function drawGrid(t) {
var ctx = cv.getContext('2d');
// 왼쪽 체인 자리 스윕
var cx = W * 0.32, cy = H * 0.5;
var maxR = Math.min(W, H) * 0.52;
var sweep = t * 0.8;
for (var b = 0; b < 16; b++) {
ctx.fillStyle = rgba(C_GLOW, 0.1 * (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 * 0.3;
for (var i = 0; i < 14; i++) {
var a = spin + (i / 14) * TAU;
ctx.strokeStyle = rgba(C_GLOW, i % 2 === 0 ? 0.1 : 0.06);
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();
}
// 오른쪽 위상 원반 자리 — 반대 방향 스윕(계단 밴드)
var px = W * 0.78, py = H * 0.5, prad = Math.min(W, H) * 0.42;
var sweep2 = -t * 0.95;
for (var b2 = 0; b2 < 12; b2++) {
ctx.fillStyle = rgba(C_GLOW, 0.1 * (1 - b2 / 12));
ctx.beginPath();
ctx.moveTo(px, py);
ctx.arc(px, py, prad, sweep2 - (b2 + 1) * 0.07, sweep2 - b2 * 0.07);
ctx.closePath();
ctx.fill();
}
// 하단 가로 스캔 밴드 — 전체 폭을 흐른다(계단 12단)
var bandY = H - 18 - ((t * 22) % (H - 24));
for (var sb = 0; sb < 12; sb++) {
ctx.fillStyle = rgba(C_GLOW, 0.08 * (1 - sb / 12));
ctx.fillRect(0, bandY + sb * 5, W, 5);
}
}
function draw(u, pulse, d, 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);
ctx.drawImage(trailCv, 0, 0, W, H);
var pts = chainAt(u, d, SHOW);
var base = Math.min(W, H) * 0.36;
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, 0.46);
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();
// ── 오른쪽 위상 원반 — 상위 계수의 위상을 단위원 위 점으로 ──
var px = W * 0.78, py = H * 0.5, prad = Math.min(W, H) * 0.3;
ctx.strokeStyle = rgba(C_GLOW, 0.22);
ctx.lineWidth = 1;
ctx.beginPath();
ctx.arc(px, py, prad, 0, TAU);
ctx.stroke();
ctx.strokeStyle = rgba(C_GLOW, 0.1);
ctx.beginPath();
ctx.moveTo(px - prad - 6, py); ctx.lineTo(px + prad + 6, py);
ctx.moveTo(px, py - prad - 6); ctx.lineTo(px, py + prad + 6);
ctx.stroke();
// 계수별 위상 각도(오프셋 적용 뒤)에 점 — 주파수 비례 반지름
for (var k = 0; k < 12 && k < COEF.length; k++) {
var c = COEF[k];
var ph2 = Math.atan2(c.im, c.re) + c.freq * d;
var rr = prad * (1 - k / 14);
var qx = px + Math.cos(ph2) * rr, qy = py + Math.sin(ph2) * rr;
ctx.fillStyle = rgba(k === 0 ? C_HOT : C_GLOW, 0.85);
ctx.beginPath();
ctx.arc(qx, qy, k === 0 ? 3 : 2, 0, TAU);
ctx.fill();
}
return pen;
}
var prevPen = null;
function stampTrail(pen) {
if (!prevPen) { prevPen = pen; return; }
// globalAlpha 로 코어/확산 두께를 한 경로에서 두 번 칠한다(계수 개수가 흔들려도 잔상이 곱해진다)
trailCtx.globalAlpha = 0.8;
trailCtx.strokeStyle = rgba(C_GLOW, 1);
trailCtx.lineWidth = 1.7;
trailCtx.lineCap = 'round';
trailCtx.beginPath();
trailCtx.moveTo(prevPen.x, prevPen.y);
trailCtx.lineTo(pen.x, pen.y);
trailCtx.stroke();
trailCtx.globalAlpha = 0.12;
trailCtx.lineWidth = 4.4;
trailCtx.stroke();
trailCtx.globalAlpha = 1;
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;
var u = (lt * 0.5) % 1;
var d = Math.sin(lt * TAU / SWEEP) * 0.8;
var pulse = 0.5 + 0.5 * Math.sin(lt * 8.0);
decayTrail();
var pen = draw(u, pulse, d, lt * TAU);
stampTrail(pen);
if (nOut) nOut.textContent = String(SHOW);
raf = requestAnimationFrame(frame);
}
function stillFrame() {
var prev = chainAt(0, 0, SHOW)[SHOW];
for (var i = 1; i <= 200; i++) {
var pen = chainAt(i / 200, 0, SHOW)[SHOW];
stampTrail(pen);
prev = pen;
}
draw(0.5, 0.5, 0, 2.1);
}
window.addEventListener('resize', function () {
fit(); prevPen = null;
if (reduce) stillFrame();
});
fit();
if (reduce) {
stillFrame();
root.classList.add('is-still');
} else {
raf = requestAnimationFrame(frame);
}
})();// FourierPhaseCircleMorph — vanilla 판(run/321/demo/07-fourier-phase-circle-morph/index.html) 의 React 포트.
// 위상 모프 — 계수의 두 축(크기·위상) 중 위상만 흔든다.
// ① 별 경로(03 과 동일)의 DFT 계수에서 진폭은 얼리고 위상에만 오프셋 φ_k = d·k 를 더한다.
// ② d 가 0 이면 원래 별. d 가 커질수록 각 원의 시각이 어긋나 무늬가 별→꽃잎→소용돌이로 변한다.
// ③ d 를 사인파로 왕복시키면 무늬가 계속 모프한다 — 크기는 무늬의 "에너지"·위상은 "배치"임을 보여준다.
// 두 번째 시각화: 같은 계수를 오른쪽 위상 원반(각 계수를 단위원 위의 점으로)에 띄운다 —
// 위상이 흔들리면 점들이 원반을 따라 미끄러진다.
// 화면이 사는 장치 — 궤적이 투명 캔버스에 쌓이며 혜성 감쇠, 방사 스윕·스포크가 매 프레임 재계산.
import { useEffect, useRef, useState } from "react";
import type { CSSProperties } from "react";
import styles from "./FourierPhaseCircleMorph.module.scss";
export type FourierPhaseCircleMorphProps = {
duration?: string;
easing?: string;
color?: string;
n?: number; // 경로 샘플 점 수
show?: number; // 체인에 쓰는 계수 수
sweep?: number; // 위상 오프셋 왕복 주기(초)
};
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 = "위상 모프 실험판";
const TAU = Math.PI * 2;
function starPath(u: number): Pt {
const seg = u * 10;
const i = Math.floor(seg);
const f = seg - i;
const a1 = i / 10 * TAU - Math.PI / 2;
const a2 = (i + 1) / 10 * TAU - Math.PI / 2;
const r1 = (i % 2 === 0) ? 1 : 0.42;
const r2 = (i % 2 === 0) ? 0.42 : 1;
const x1 = Math.cos(a1) * r1, y1 = Math.sin(a1) * r1;
const x2 = Math.cos(a2) * r2, y2 = Math.sin(a2) * r2;
return { x: x1 + (x2 - x1) * f, y: y1 + (y2 - y1) * f };
}
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 FourierPhaseCircleMorph({
duration = "2s",
easing = "cubic-bezier(.2, .8, .2, 1)",
color = "#b7c8ff",
n = 256,
show = 16,
sweep = 2.4
}: FourierPhaseCircleMorphProps) {
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 nRef = useRef(n) as Box<number>;
const showRef = useRef(show) as Box<number>;
const sweepRef = useRef(sweep) as Box<number>;
const pathRef = useRef<Pt[]>([]) as Box<Pt[]>;
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 [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 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;
if (!pathRef.current.length) {
const PATH: Pt[] = [];
for (let i = 0; i < nRef.current; i++) PATH.push(starPath(i / nRef.current));
pathRef.current = PATH;
coefRef.current = dft(PATH);
}
}
// 위상 오프셋 체인 — d 만큼 각 계수 위상을 민다
function chainAt(u: number, d: number, showCount: number): Pt[] {
const W = wRef.current, H = hRef.current;
const COEF = coefRef.current;
const base = Math.min(W, H) * 0.36;
const cx = W * 0.32, cy = H * 0.5;
const pts: Pt[] = [{ x: cx, y: cy }];
for (let i = 0; i < showCount && i < COEF.length; i++) {
const c = COEF[i];
const ph = Math.atan2(c.im, c.re) + c.freq * d;
const ang = c.freq * u * TAU + 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;
}
function drawGrid(ctx: CanvasRenderingContext2D, t: number): void {
const W = wRef.current, H = hRef.current;
const col = colRef.current;
if (!col) return;
// 왼쪽 체인 자리 스윕
const cx = W * 0.32, cy = H * 0.5;
const maxR = Math.min(W, H) * 0.52;
const sweepA = t * 0.8;
for (let b = 0; b < 16; b++) {
ctx.fillStyle = rgba(col.glow, 0.1 * (1 - b / 16));
ctx.beginPath();
ctx.moveTo(cx, cy);
ctx.arc(cx, cy, maxR, sweepA - (b + 1) * 0.06, sweepA - b * 0.06);
ctx.closePath();
ctx.fill();
}
const spin = t * 0.3;
for (let i = 0; i < 14; i++) {
const a = spin + (i / 14) * TAU;
ctx.strokeStyle = rgba(col.glow, i % 2 === 0 ? 0.1 : 0.06);
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();
}
// 오른쪽 위상 원반 자리 — 반대 방향 스윕(계단 밴드)
const px = W * 0.78, py = H * 0.5, prad = Math.min(W, H) * 0.42;
const sweep2 = -t * 0.95;
for (let b2 = 0; b2 < 12; b2++) {
ctx.fillStyle = rgba(col.glow, 0.1 * (1 - b2 / 12));
ctx.beginPath();
ctx.moveTo(px, py);
ctx.arc(px, py, prad, sweep2 - (b2 + 1) * 0.07, sweep2 - b2 * 0.07);
ctx.closePath();
ctx.fill();
}
// 하단 가로 스캔 밴드 — 전체 폭을 흐른다(계단 12단)
const bandY = H - 18 - ((t * 22) % (H - 24));
for (let sb = 0; sb < 12; sb++) {
ctx.fillStyle = rgba(col.glow, 0.08 * (1 - sb / 12));
ctx.fillRect(0, bandY + sb * 5, W, 5);
}
}
function draw(u: number, pulse: number, d: number, gt: number): Pt {
const ctx = ctxRef.current;
const trailCv = trailCvRef.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);
ctx.drawImage(trailCv, 0, 0, W, H);
const S = showRef.current;
const pts = chainAt(u, d, S);
const base = Math.min(W, H) * 0.36;
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, 0.46);
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();
// ── 오른쪽 위상 원반 — 상위 계수의 위상을 단위원 위 점으로 ──
const px = W * 0.78, py = H * 0.5, prad = Math.min(W, H) * 0.3;
ctx.strokeStyle = rgba(col.glow, 0.22);
ctx.lineWidth = 1;
ctx.beginPath();
ctx.arc(px, py, prad, 0, TAU);
ctx.stroke();
ctx.strokeStyle = rgba(col.glow, 0.1);
ctx.beginPath();
ctx.moveTo(px - prad - 6, py); ctx.lineTo(px + prad + 6, py);
ctx.moveTo(px, py - prad - 6); ctx.lineTo(px, py + prad + 6);
ctx.stroke();
// 계수별 위상 각도(오프셋 적용 뒤)에 점 — 주파수 비례 반지름
for (let k = 0; k < 12 && k < COEF.length; k++) {
const c = COEF[k];
const ph2 = Math.atan2(c.im, c.re) + c.freq * d;
const rr = prad * (1 - k / 14);
const qx = px + Math.cos(ph2) * rr, qy = py + Math.sin(ph2) * rr;
ctx.fillStyle = rgba(k === 0 ? col.hot : col.glow, 0.85);
ctx.beginPath();
ctx.arc(qx, qy, k === 0 ? 3 : 2, 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; }
// globalAlpha 로 코어/확산 두께를 한 경로에서 두 번 칠한다(계수 개수가 흔들려도 잔상이 곱해진다)
trailCtx.globalAlpha = 0.8;
trailCtx.strokeStyle = rgba(col.glow, 1);
trailCtx.lineWidth = 1.7;
trailCtx.lineCap = "round";
trailCtx.beginPath();
trailCtx.moveTo(prev.x, prev.y);
trailCtx.lineTo(pen.x, pen.y);
trailCtx.stroke();
trailCtx.globalAlpha = 0.12;
trailCtx.lineWidth = 4.4;
trailCtx.stroke();
trailCtx.globalAlpha = 1;
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;
const u = (lt * 0.5) % 1;
const d = Math.sin(lt * TAU / sweepRef.current) * 0.8;
const pulse = 0.5 + 0.5 * Math.sin(lt * 8.0);
decayTrail();
const pen = draw(u, pulse, d, lt * TAU);
stampTrail(pen);
setCnt(String(showRef.current));
rafRef.current = requestAnimationFrame(frame);
}
function stillFrame(): void {
const S = showRef.current;
let prev = chainAt(0, 0, S)[S];
for (let i = 1; i <= 200; i++) {
const pen = chainAt(i / 200, 0, S)[S];
stampTrail(pen);
prev = pen;
}
draw(0.5, 0.5, 0, 2.1);
}
useEffect(() => {
const root = rootRef.current;
if (!root) return;
nRef.current = n;
showRef.current = show;
sweepRef.current = sweep;
colRef.current = {
ink: tokRGB(root, "--fe-ink"),
glow: tokRGB(root, "--fe-glow"),
hot: tokRGB(root, "--fe-hot"),
};
fit();
setCnt(String(show));
function onResize(): void {
fit(); prevPenRef.current = null;
if (reduced()) stillFrame();
}
window.addEventListener("resize", onResize);
if (reduced()) {
stillFrame();
setStill(true);
} else {
t0 = -1;
rafRef.current = requestAnimationFrame(frame);
}
return () => {
window.removeEventListener("resize", onResize);
cancelAnimationFrame(rafRef.current);
};
// eslint-disable-next-line react-hooks/exhaustive-deps
}, [n, show, sweep]);
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>계수 크기는 그대로 두고 위상에만 오프셋을 주면 무늬가 별에서 꽃잎으로, 꽃잎에서 소용돌이로 연속 변형되는데, 크기와 위상이 그림에서 각각 무엇을 담당하는지 보여주는 실험입니다</span>
</p>
<div
className={styles.field}
ref={fieldRef}
role="application"
aria-label={FIELD_LABEL}
tabIndex={0}
>
<canvas className={styles.cv} ref={cvRef}></canvas>
</div>
<div className={styles.bar}>
<span className={styles.meta}><b className={styles.val}>{cnt}</b> 위상 오프셋 진동 · 크기 고정</span>
<span className={styles.metaDim}>canvas · phase offset · requestAnimationFrame</span>
</div>
</div>
</main>
);
}07 Phase morph — same coefficients, rotated phases, a pattern that shape-shifts — Measured area 40.69% · 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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