Tesseract

1"use client"
2 
3import * as React from "react"
4import { useFrame } from "@react-three/fiber"
5import * as THREE from "three"
6 
7import {
8  SceneContainer,
9  type SceneContainerProps,
10} from "@/components/threecn/scene-container"
11import {
12  useShadcnTheme,
13  type ThemeMode,
14} from "@/components/hooks/use-shadcn-theme"
15 
16/** The 16 corners of a unit hypercube: every sign combination of (±1,±1,±1,±1). */
17const VERTS4: [number, number, number, number][] = Array.from(
18  { length: 16 },
19  (_, i) => [i & 1 ? 1 : -1, i & 2 ? 1 : -1, i & 4 ? 1 : -1, i & 8 ? 1 : -1]
20)
21 
22/** The 32 edges connect corners that differ in exactly one coordinate. */
23const EDGES: [number, number][] = []
24for (let i = 0; i < 16; i++) {
25  for (let b = 0; b < 4; b++) {
26    const j = i | (1 << b)
27    if (j !== i) EDGES.push([i, j])
28  }
29}
30 
31/** Distance of the virtual 4D "camera" used for the w-perspective projection. */
32const K = 3
33/** Shrinks the projection so the swelling outer cell stays in frame. */
34const BASE_SCALE = 0.62
35const UP = new THREE.Vector3(0, 1, 0)
36 
37/**
38 * Per-frame scratch for each corner's normalized 4D depth. Written in full,
39 * then read, inside a single frame callback — safe to share at module level.
40 */
41const depths = new Float32Array(VERTS4.length)
42 
43function Hypercube({
44  size,
45  speed,
46  thickness,
47  theme,
48}: {
49  size: number
50  speed: number
51  thickness: number
52  theme: ThemeMode
53}) {
54  const { primaryColor, accentColor } = useShadcnTheme(theme)
55  const groupRef = React.useRef<THREE.Group>(null)
56  const nodesRef = React.useRef<THREE.InstancedMesh>(null)
57  const strutsRef = React.useRef<THREE.InstancedMesh>(null)
58  const dummy = React.useMemo(() => new THREE.Object3D(), [])
59  const tmpColor = React.useMemo(() => new THREE.Color(), [])
60  const tmpDir = React.useMemo(() => new THREE.Vector3(), [])
61  const points = React.useMemo(() => VERTS4.map(() => new THREE.Vector3()), [])
62 
63  useFrame(({ clock }) => {
64    const nodes = nodesRef.current
65    const struts = strutsRef.current
66    const group = groupRef.current
67    if (!nodes || !struts || !group) return
68    const t = clock.getElapsedTime() * speed
69    group.rotation.y = t * 0.16
70    group.rotation.x = 0.32 + Math.sin(t * 0.2) * 0.12
71 
72    // Double rotation in two orthogonal 4D planes (XW and YZ) — the classic
73    // tesseract motion where the inner cell turns itself inside out.
74    const ca = Math.cos(t * 0.55)
75    const sa = Math.sin(t * 0.55)
76    const cb = Math.cos(t * 0.38)
77    const sb = Math.sin(t * 0.38)
78 
79// … truncated