// ============================================================
// test_four_dim_polytopes.js - 四维空间实验室数学块校验
// 从 public/tools/thought_lab/labs/four_dim_space/index.html 抽取
// POLYTOPE_MATH_BEGIN/END 之间的纯数学代码执行校验，保证测试对象 = 上线代码。
// 校验：5 个凸正多胞体的顶点数/边数（严格已知值）、外接半径全等、
//       旋转保范、投影 w=0 时缩放为 1、偶排列数 = 12。
// 运行：node dev_test_scripts/unit/test_four_dim_polytopes.js
// ============================================================
'use strict'
const fs = require('fs')
const path = require('path')
const vm = require('vm')

const HTML = path.resolve(__dirname, '..', '..', 'public', 'tools', 'thought_lab', 'labs', 'four_dim_space', 'index.html')
const src = fs.readFileSync(HTML, 'utf8')
const m = src.match(/\/\/ ==== POLYTOPE_MATH_BEGIN ====\n([\s\S]*?)\/\/ ==== POLYTOPE_MATH_END ====/)
if (!m) { console.error('FAIL - 未找到 POLYTOPE_MATH 标记块'); process.exit(1) }

const api = vm.runInNewContext(m[1] + `
;({ POLYTOPES, edgesByMinDist, rotate4, project4to3, project3to2, evenPerms4, perms4, PHI })
`)

let pass = 0, fail = 0
const check = (name, cond) => {
  if (cond) { pass++; console.log('PASS -', name) }
  else { fail++; console.log('FAIL -', name) }
}

const norm = v => Math.sqrt(v.reduce((s, x) => s + x * x, 0))

// 排列数
check('4 元素全排列 = 24', api.perms4.length === 24)
check('偶排列 = 12', api.evenPerms4.length === 12)

// 各多胞体：顶点数 / 边数 / 外接半径全等
for (const key of Object.keys(api.POLYTOPES)) {
  const P = api.POLYTOPES[key]
  const verts = P.verts()
  const edges = api.edgesByMinDist(verts)
  check(`${key} 顶点数 = ${P.expect.v}`, verts.length === P.expect.v)
  check(`${key} 边数 = ${P.expect.e}`, edges.length === P.expect.e)
  const rs = verts.map(norm)
  const rMin = Math.min(...rs), rMax = Math.max(...rs)
  check(`${key} 外接半径全等（${rMin.toFixed(6)}）`, rMax - rMin < 1e-9)
}

// 600-胞体最小边长应 = 1/φ（单位外接半径）
{
  const verts = api.POLYTOPES.p600.verts()
  let min = Infinity
  for (let i = 0; i < verts.length; i++)
    for (let j = i + 1; j < verts.length; j++) {
      let s = 0
      for (let k = 0; k < 4; k++) { const d = verts[i][k] - verts[j][k]; s += d * d }
      min = Math.min(min, s)
    }
  check('600-胞体边长 = 1/φ', Math.abs(Math.sqrt(min) - 1 / api.PHI) < 1e-9)
}

// 旋转保范：六个平面各转 0.7 rad
{
  const v = [1, 2, 3, 4]
  const planes = [[0, 1], [0, 2], [1, 2], [0, 3], [1, 3], [2, 3]]
  let ok = true
  for (const [i, j] of planes) {
    const q = api.rotate4(v, i, j, 0.7)
    if (Math.abs(norm(q) - norm(v)) > 1e-12) ok = false
  }
  check('六平面旋转均保范', ok)
}

// 投影：w=0 时 4D→3D 缩放为 1；w>0 放大
{
  const a = api.project4to3([1, 1, 1, 0], 3)
  const b = api.project4to3([1, 1, 1, 0.9], 3)
  check('project4to3 w=0 缩放=1', Math.abs(a[0] - 1) < 1e-12)
  check('project4to3 w>0 放大', b[0] > 1)
  const c = api.project3to2([1, 1, 0], 6)
  check('project3to2 z=0 缩放=1', Math.abs(c[0] - 1) < 1e-12)
}

console.log(fail === 0 ? `ALL PASS (${pass})` : `FAILED: ${fail} / ${pass + fail}`)
process.exit(fail === 0 ? 0 : 1)