City-Lifeline-Cockpit/.scratch/cockpit-real-data-wayfinding/research/fit-pin-bezier.mjs

// 一次性探针（票 47）：母版下半收尖的三次贝塞尔拟合。
// 假设：轮廓在帽圆某切点处离开圆，以一条三次贝塞尔到达尖端；对切点角度扫描取最优。
// 输出 bbox 坐标系（x-67, y-19）的 path 参数，直接嵌进 markerOverlay.js。
import { readFileSync } from 'node:fs'
import { inflateSync } from 'node:zlib'

function decodePng(path) {
    const buf = readFileSync(path)
    let pos = 8
    const idat = []
    let width = 0, height = 0, colorType = 0, trns = null
    while (pos < buf.length) {
        const len = buf.readUInt32BE(pos)
        const type = buf.toString('ascii', pos + 4, pos + 8)
        const data = buf.subarray(pos + 8, pos + 8 + len)
        if (type === 'IHDR') { width = data.readUInt32BE(0); height = data.readUInt32BE(4); colorType = data[9] }
        else if (type === 'tRNS') trns = Buffer.from(data)
        else if (type === 'IDAT') idat.push(data)
        else if (type === 'IEND') break
        pos += 12 + len
    }
    const channels = colorType === 6 ? 4 : colorType === 2 ? 3 : 1
    const stride = width * channels
    const raw = inflateSync(Buffer.concat(idat))
    const img = Buffer.alloc(height * stride)
    for (let y = 0; y < height; y++) {
        const filter = raw[y * (stride + 1)]
        const row = raw.subarray(y * (stride + 1) + 1, (y + 1) * stride)
        const prev = y > 0 ? img.subarray((y - 1) * stride, y * stride) : null
        const out = img.subarray(y * stride, (y + 1) * stride)
        for (let x = 0; x < stride; x++) {
            const a = x >= channels ? out[x - channels] : 0
            const b = prev ? prev[x] : 0
            const c = prev && x >= channels ? prev[x - channels] : 0
            let v = row[x]
            if (filter === 1) v += a
            else if (filter === 2) v += b
            else if (filter === 3) v += (a + b) >> 1
            else if (filter === 4) {
                const p = a + b - c
                const pa = Math.abs(p - a), pb = Math.abs(p - b), pc = Math.abs(p - c)
                v += pa <= pb && pa <= pc ? a : pb <= pc ? b : c
            }
            out[x] = v & 0xff
        }
    }
    const alphaAt = (x, y) => {
        if (colorType === 6) return img[y * stride + x * 4 + 3]
        const idx = img[y * stride + x]
        if (trns && idx < trns.length) return trns[idx]
        return 255
    }
    return { width, height, alphaAt }
}

// bbox 坐标系（绝对像素减 (67,19)）：帽圆 (188.5,189) r189；尖端 (188.5,474)
const CAP = { cx: 188.5, cy: 189, r: 189 }
const TIP = { x: 188.5, y: 474 }

const src = decodePng(process.argv[2] || 'public/cockpit/assets/icons/T_MarkPoint_WhiteFull.png')
// 左缘采样：每行第一个不透明点（bbox 坐标）
function leftEdge(yAbs) {
    for (let x = 67; x <= 444; x++) if (src.alphaAt(x, yAbs) > 8) return x - 67
    return null
}
const pts = []
for (let yAbs = 380; yAbs <= 492; yAbs += 2) {
    const x = leftEdge(yAbs)
    if (x != null) pts.push({ x, y: yAbs - 19 })
}
console.log(`左缘采样 ${pts.length} 点（y ${pts[0].y}..${pts[pts.length - 1].y}）`)
console.log(pts.map((p) => `(${p.x.toFixed(1)},${p.y.toFixed(1)})`).join(' '))

// 三次贝塞尔最小二乘（P0/P3 固定，求 P1/P2；弦长参数化）
function fitBezier(p0, p3, samples) {
    const cum = [0]
    for (let i = 1; i < samples.length; i++) {
        cum.push(cum[i - 1] + Math.hypot(samples[i].x - samples[i - 1].x, samples[i].y - samples[i - 1].y))
    }
    const total = cum[cum.length - 1] || 1
    const ts = samples.map((_, i) => 0.5 - 0.5 * Math.cos(Math.PI * (cum[i] / total))) // 余弦参数化，端点加密
    const n = samples.length
    // 残差最小化：对每个样本 i，B(t_i) ≈ sample_i；B 对 P1,P2 线性 → 2×2 正规方程
    let a11 = 0, a12 = 0, a22 = 0, b1x = 0, b1y = 0, b2x = 0, b2y = 0
    const coef = (t) => {
        const mt = 1 - t
        return { p0: mt * mt * mt, p1: 3 * mt * mt * t, p2: 3 * mt * t * t, p3: t * t * t }
    }
    for (let i = 0; i < n; i++) {
        const c = coef(ts[i])
        const r1 = c.p1, r2 = c.p2
        a11 += r1 * r1; a12 += r1 * r2; a22 += r2 * r2
        b1x += r1 * (samples[i].x - c.p0 * p0.x - c.p3 * p3.x)
        b1y += r1 * (samples[i].y - c.p0 * p0.y - c.p3 * p3.y)
        b2x += r2 * (samples[i].x - c.p0 * p0.x - c.p3 * p3.x)
        b2y += r2 * (samples[i].y - c.p0 * p0.y - c.p3 * p3.y)
    }
    const det = a11 * a22 - a12 * a12
    const c1x = (b1x * a22 - b2x * a12) / det
    const c1y = (b1y * a22 - b2y * a12) / det
    const c2x = (b2x * a11 - b1x * a12) / det
    const c2y = (b2y * a11 - b1y * a12) / det
    const p1 = { x: c1x, y: c1y }, p2 = { x: c2x, y: c2y }
    let maxRes = 0
    for (let i = 0; i < n; i++) {
        const c = coef(ts[i])
        const bx = c.p0 * p0.x + c.p1 * p1.x + c.p2 * p2.x + c.p3 * TIP.x
        const by = c.p0 * p0.y + c.p1 * p1.y + c.p2 * p2.y + c.p3 * TIP.y
        maxRes = Math.max(maxRes, Math.hypot(bx - samples[i].x, by - samples[i].y))
    }
    return { p1, p2, maxRes }
}

// 切点扫描：P0 在帽圆左半（θ 自 +x 轴、y 向下；左下段 θ∈95°..140°：x<188.5 且 y>189）
let best = null
for (let deg = 95; deg <= 140; deg += 1) {
    const rad = (deg * Math.PI) / 180
    const p0 = { x: CAP.cx + CAP.r * Math.cos(rad), y: CAP.cy + CAP.r * Math.sin(rad) }
    if (p0.y < 300) continue
    // 路径方向 = 沿圆逆时针（屏幕系：顶→左→下），θ 递减方向的切向 = (sinθ, −cosθ)
    const tan = { x: Math.sin(rad), y: -Math.cos(rad) }
    // 样本 = 切点下方 3px 起的左缘点
    const samples = pts.filter((p) => p.y >= p0.y + 3 && p.x <= CAP.cx)
    if (samples.length < 6) continue
    // P1 = p0 + k·tan（G1 方向固定，长度 k 粗扫）
    for (let k = 10; k <= 160; k += 5) {
        const p1 = { x: p0.x + tan.x * k, y: p0.y + tan.y * k }
        const r = fitBezierG1(p0, p1, samples)
        if (!best || r.maxRes < best.maxRes) best = { deg, k, p0, p1, p2: r.p2, maxRes: r.maxRes }
    }
}
function fitBezierG1(p0, p1, samples) {
    // 固定 P0,P1,P3，求 P2（线性）
    const cum = [0]
    for (let i = 1; i < samples.length; i++) cum.push(cum[i - 1] + Math.hypot(samples[i].x - samples[i - 1].x, samples[i].y - samples[i - 1].y))
    const total = cum[cum.length - 1] || 1
    const ts = samples.map((_, i) => cum[i] / total)
    let aa = 0, ab = 0, bb = 0
    const sx = [], sy = []
    for (let i = 0; i < samples.length; i++) {
        const t = ts[i], mt = 1 - t
        const c0 = mt * mt * mt, c1 = 3 * mt * mt * t, c2 = 3 * mt * t * t, c3 = t * t * t
        aa += c2 * c2; ab += c2 * c3; bb += c3 * c3
        sx.push(samples[i].x - c0 * p0.x - c1 * p1.x)
        sy.push(samples[i].y - c0 * p0.y - c1 * p1.y)
    }
    // 最小化 Σ|c2·P2 + c3·TIP - s|²；未知 P2 二维，正规方程含 c3·TIP 交叉项
    let a2t = 0, s2x = 0, s2y = 0, ttx = 0, tty = 0
    for (let i = 0; i < samples.length; i++) {
        const t = ts[i], mt = 1 - t
        const c2 = 3 * mt * t * t, c3 = t * t * t
        a2t += c2 * c3; ttx += c3 * c3 * TIP.x; tty += c3 * c3 * TIP.y
        s2x += c2 * sx[i]; s2y += c2 * sy[i]
    }
    // aa·P2 + a2t·TIP = Sx（分量式）→ P2 = (Sx - a2t·TIP.x)/aa
    const p2 = { x: (s2x - a2t * TIP.x) / aa, y: (s2y - a2t * TIP.y) / aa }
    let maxRes = 0
    for (let i = 0; i < samples.length; i++) {
        const t = ts[i], mt = 1 - t
        const c0 = mt * mt * mt, c1 = 3 * mt * mt * t, c2 = 3 * mt * t * t, c3 = t * t * t
        const bx = c0 * p0.x + c1 * p1.x + c2 * p2.x + c3 * TIP.x
        const by = c0 * p0.y + c1 * p1.y + c2 * p2.y + c3 * TIP.y
        maxRes = Math.max(maxRes, Math.hypot(bx - samples[i].x, by - samples[i].y))
    }
    return { p2, maxRes }
}
if (!best) { console.log('无有效拟合'); process.exit(1) }
console.log(`\n最优：切点角 ${best.deg}° → P0(${best.p0.x.toFixed(1)}, ${best.p0.y.toFixed(1)})，k=${best.k}`)
console.log(`P1(${best.p1.x.toFixed(1)}, ${best.p1.y.toFixed(1)}) P2(${best.p2.x.toFixed(1)}, ${best.p2.y.toFixed(1)}) → TIP(188.5,474)`)
console.log(`最大残差 ${best.maxRes.toFixed(2)}px`)
// 完整闭合路径（bbox 空间，viewBox 外扩 40 同 billboard 裁剪窗）：
// 顶点起，左弧（视觉逆时针 = sweep 0）到切点 → 贝塞尔到尖端 → 镜像贝塞尔（反放：控制点 P2',P1'）到右切点 → 右弧回顶。
console.log(`\npath: M188.5 0 A189 189 0 0 0 ${best.p0.x.toFixed(1)} ${best.p0.y.toFixed(1)} C${best.p1.x.toFixed(1)} ${best.p1.y.toFixed(1)} ${best.p2.x.toFixed(1)} ${best.p2.y.toFixed(1)} 188.5 474 C${(377 - best.p2.x).toFixed(1)} ${best.p2.y.toFixed(1)} ${(377 - best.p1.x).toFixed(1)} ${best.p1.y.toFixed(1)} ${(377 - best.p0.x).toFixed(1)} ${best.p0.y.toFixed(1)} A189 189 0 0 0 188.5 0 Z`)