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  1. PS C:\Users\me> ollama run nemotron-3-nano:mxfp4_moe
  2. >>> Create a trippy, color-changing, spinning 3d wireframe “small sphere inside a thick donut inside another thick donut inside a big sphere”. The objects shouldn't overlap. All objects must be made of wireframe material. Objects must spin in the x and y axes in real time, some clockwise, some anti-clockwise at varying speeds. Each object's rotation speed should bein sync with its colors, speeding up and down like a sine wave. The scene should scale dynamically based on screen dimensions. Use HTML/CSS/Three JS.
  3. Thinking...
  4. We need to provide an implementation description or code snippets for an HTML/CSS/JavaScript using Three.js that creates this structure: small sphere -> thick donut (torus) inside another thick
  5. donut -> big sphere, all wireframe, no overlapping? But they cannot overlap physically; but can be nested visually perhaps with different radii. Use color-changing basedon some hue cycling per
  6. object like sinusoidal color changes synchronized with rotation speeds via sine wave.
  7.  
  8. Objects spin in x and y axes at varying speeds, clockwise/anticlockwise. Rotation speed varies over time as a sine wave, causing speed up/slow down. Need dynamic scalingbased on screen
  9. dimensions; perhaps using window resize event to adjust camera or scaling factor? Use orthographic? Probably perspective camera with field of view etc., but we can also scale the scene uniformly
  10. based on aspect ratio.
  11.  
  12. We need to deliver code that actually works: full HTML file including three.js CDN, a script that sets up scene, creates a big sphere (wireframe geometry), then two torus shapes nested (maybe
  13. offset?). They cannot overlap; perhaps one is inside another by having smaller radius but placed at center? Actually they said "small sphere inside a thick donut inside another thick donin’ t...".
  14. Could be concentric: small sphere inscribed within donut's hole, then that donut inside larger torus etc.
  15.  
  16. Better to arrange like:
  17.  
  18. - Large sphere with certain radius (outer bounding)
  19. - Inside it we have two donuts one after the other? Actually "thick donut" likely means a thick-walled torus with tube thickness maybe 0.5 and major radius bigger but not overlapping with outer
  20. sphere; they'd be placed centered.
  21.  
  22. But to show nesting without overlap, we can make them separate objects sharing same center at (0,0,0) but varying radii ensures they don't intersect geometry? Actually if radii differ enough, the
  23. wireframe shapes will occupy different distances from origin. That is fine: small sphere radius r_small, torus major radius r1 > r_small + thickness maybe; second torus larger major radius etc.
  24.  
  25. But we need "small sphere inside a thick donut" meaning the sphere is placed within the hole of the first donut. The sphere could be at center too? Actually if the donutis centered on origin, its
  26. hole goes through center; you can put sphere also at center but will intersect geometry at the donut's central void; but they said objects shouldn't overlap physically. So we need to offset one
  27. from the other maybe.
  28.  
  29. Simplify: We'll create three nested shapes each sharing same center but with distinct radii and thickness such that they are visually inside each other.
  30.  
  31. For example:
  32.  
  33. - Outer sphere radius = 10 units.
  34. - Middle thick torus (donut) major radius = 8, tube radius = 2 => so the donut surface goes from 6 to 10 in radial distance; but small sphere radius must be less than inner radius of donut which
  35. is 6? Actually inner radius=major-radius - tubeRadius = 8-2=6. So if we put a sphere radius <6 inside, that would not intersect the torus geometry. That's okay.
  36.  
  37. - Inner torus (thicker) major radius maybe 5? But then its inner radius might be smaller; but also must contain the donut? The "inside another thick donut". Actually description ambiguous: small
  38. sphere -> thick donut inside another thick donut inside a big sphere. Means layers: Starting from outer, there is big sphere (outermost), inside it is two nested donuts of thickness like onion? Or
  39. more like: Outer sphere encloses everything; then inside that we have a thick torus (first), and inside the hole of that torus sits another thicker donut maybe smaller but offset? But they said
  40. "inside a thick donut inside another thick donut". Maybe they mean: small sphere is inside first donut, which itself is placed inside a second donut, which then fits within big sphere. That seems
  41. like three nested layers, each with increasing size outward.
  42.  
  43. Better interpret as concentric shapes:
  44.  
  45. 1. Big sphere (outermost)
  46. 2. Thick donut (middle layer) maybe bigger radius but still inside sphere.
  47. 3. Another thick donut but smaller? Actually description "small sphere inside a thick donut inside another thick donut inside a big sphere". So order from innermost outward: small sphere -> first
  48. thick donut contains it, then that first thick donut is itself placed within second thicker donut (i.e., outer donut surrounds inner donut). Then outermost is big sphereenclosing the whole thing.
  49.  
  50. Thus we get nested layers like Russian dolls but with shape differences. So we can implement:
  51.  
  52. - innermost: small sphere radius = 1
  53. - middle torus #1: major radius = 3, tube radius = 0.8 (some thickness)
  54. - outer torus #2: major radius = 5, tube radius = 1.2 maybe.
  55.  
  56. Outermost big sphere must be larger radius than everything else to fully enclose them. We'll set its radius=7 or something.
  57.  
  58. But they said "another thick donut inside a big sphere" meaning that outermost shape is the big sphere; there are two toruses nested between small sphere and sphere. So we can place central axis
  59. aligned at origin, so the shapes share center; but then inner surfaces might intersect? The small sphere will be located at center; its radius must be less than inner radius of middle donut
  60. (distance to donut's hole). That is okay.
  61.  
  62. Thus objects won't overlap geometry if radii defined appropriately.
  63.  
  64. Implementation: Using Three.js wireframe geometry lines. Use MeshBasicMaterial with color that changes over time based on some hue or RGB modulation using sine wave.
  65.  
  66. Rotation speed: each mesh can have separate axis rotation speeds; we can set initial direction (clockwise vs anticlockwise) and apply varying angular velocity modulated by sin(time). We'll update
  67. in animate loop: rotation.x += baseSpeedX * Math.sin(time); similarly for y and z maybe just x,y as requested. Use sign of sinusoid to change direction over time? Sin wave amplitude could modify
  68. speed magnitude, maybe also have separate offset to keep positive? Actually we can compute angular velocity = baseAngularVelocity + amplitude * Math.sin(time) etc.
  69.  
  70. Goal: Colors should be in sync with rotation speed "speeding up/down like a sine wave".
  71.  
  72. Thus color changes (e.g., hue) based on sin wave similarly; each mesh maybe different frequency or offset for varied effect.
  73.  
  74. Responsive scaling: Use window.innerWidth and innerHeight to compute aspect ratio; perhaps scale factor = min(width, height)/some reference size. Could apply uniform scaling to scene using
  75. camera.position? Or simply adjust renderer.setSize and then set a scaling multiplier on geometry positions (like multiply coordinates by factor). Simpler: use responsivecanvas via resize event
  76. adjusting camera's aspect but not scaling. However requirement says "scale dynamically based on screen dimensions". That could be interpreted as the whole objects scale proportionally with
  77. viewport size; perhaps we can compute an overall scale factor based on the smaller dimension to keep them fitting nicely, and update positions accordingly (e.g., multiply all object radii by ratio
  78. of current width/height). Or just let canvas fill window.
  79.  
  80. We'll implement scaling: In animate loop compute scale = Math.min(window.innerWidth, window.innerHeight) / 500; then apply a uniform scaling transform to entire scene using scenescale variable
  81. that updates on resize and before rendering we set mesh.geometry.translate? Not efficient; easier is to set camera's zoom or adjust perspective but maintain geometry.
  82.  
  83. Alternatively we can update the renderer size and set CSS to be responsive; maybe they want objects resizing relative to window, like if window larger, objects become bigger. We'll simply update a
  84. global variable `scaleFactor` = Math.min(window.innerWidth, window.innerHeight) / BASE_SIZE (e.g., 500). Then apply this scale factor uniformly on object positions using
  85. `object.scale.set(scaleFactor, scaleFactor, scaleFactor)`. Or create a parent group and set its scale.
  86.  
  87. Thus the entire scene will expand or shrink accordingly; we also need to keep geometry's intrinsic size unaffected by scaling of coordinates (i.e., underlying geometry remain same but apply
  88. scaling transform). That can be done easily: after creating each mesh, store them in a container group `objectsGroup` for scaling operations. On resize, recompute scaleFactor and set
  89. objectsGroup.scale.set(scaleFactor,...). This changes the world-space positions but also speeds up rotation? It might affect perceived speeds? Rotations unaffected.
  90.  
  91. Better approach: Instead of scaling objects after creation, maybe we want to use CSS scaling or just adjust camera size; but they'd likely accept scaling based on screendimensions by adjusting
  92. renderer's pixel ratio and canvas. However they explicitly ask "Objects must spin in the x and y axes ... scene should scale dynamically based on screen dimensions." Means as window is resized,
  93. objects must change their apparent size accordingly (maybe to maintain proportion). We'll implement responsive scaling using `window.addEventListener('resize',...)` where we recompute bounding box
  94. and re-calc positions? Hmm.
  95.  
  96. Simplify: just update the renderer's pixel ratio and canvas size; not scale geometry. But perhaps they want uniform overall scaling with screen dimensions: e.g., width/height of viewport
  97. determines some scaling factor for all distances from origin (like use `scale = Math.min(window.innerWidth, window.innerHeight) / 800`). We'll compute base radius of bigsphere relative to that;
  98. then set geometry radii accordingly. However in our current approach we define absolute sizes independent of screen size; they'd remain static when resize occurs.
  99.  
  100. Thus maybe easiest: On each resize, recalc `scaleFactor` and multiply all positions after creation? But we can't store positions easily because geometry points are defined once.
  101.  
  102. Simplify further: Use OrbitControls not needed. Provide a container group with scale set to scale factor computed from `Math.min(window.innerWidth,window.innerHeight) / 500`. Update this each
  103. resize event. This will enlarge or shrink entire scene's size relative to canvas; the objects remain at same geometry (but scaling factor applied). Rotation speed unaffected.
  104.  
  105. Thus we can satisfy requirement: "scene should scale dynamically based on screen dimensions". That's likely acceptable.
  106.  
  107. Now code structure:
  108.  
  109. HTML with script loading three.js from CDN, and then our script.
  110.  
  111. Will need:
  112.  
  113. - scene, camera (perspective), renderer.
  114. - controls? Not needed but orbit maybe to view all angles; but not required.
  115. - We'll add a simple ambient light perhaps for shading lines? Wireframe material may be unaffected by lights; can use `MeshBasicMaterial`.
  116.  
  117. Implementation Steps in JS:
  118.  
  119. 1. Setup three.js canvas, responsive resizing.
  120.  
  121. ```js
  122. const scene = new THREE.Scene();
  123. const camera = new THREE.PerspectiveCamera(60, window.innerWidth / window.innerHeight, 0.1, 1000);
  124. camera.position.set(0, 2, 7); // positioned to see all objects
  125.  
  126. const renderer = new THREE.WebGLRenderer({ antialias:true });
  127. renderer.setSize(window.innerWidth, window.innerHeight);
  128. document.body.appendChild(renderer.domElement);
  129.  
  130. function onResize() {
  131. const width = window.innerWidth;
  132. const height = window.innerHeight;
  133. renderer.setSize(width,height);
  134. camera.aspect = width/height;
  135. camera.updateProjectionMatrix();
  136. }
  137. window.addEventListener('resize', onResize);
  138.  
  139. // optional: scaling group
  140. const root = new THREE.Group();
  141. scene.add(root);
  142. ```
  143.  
  144. 2. Define radii and geometry:
  145.  
  146. ```js
  147. // parameters
  148. const smallSphereRadius = 1;
  149. const sphereSmallGeo = new THREE.SphereGeometry(smallSphereRadius, 32, 32);
  150. // color later
  151.  
  152. // thick donut #1 (inner donut)
  153. const innerDonutMajorRadius = 3; // distance from origin to tube center
  154. const innerDonutMinorRadius = 0.8; // thickness of pipe
  155. const innerDonutGeo = new THREE.TorusKnotGeometry(innerDonutMajorRadius, innerDonutMinorRadius, 100, 20);
  156. // Actually we want standard torus geometry: new THREE.TorusGeometry(majorRadius, minorRadius, segments);
  157. ```
  158.  
  159. Wait "thick donut" perhaps refer to a torus tube with thickness; but we can use `THREE.TorusGeometry`.
  160.  
  161. Let's define:
  162.  
  163. ```js
  164. const innerDonutGeo = new THREE.TorusGeometry(innerDonutMajorRadius, innerDonutMinorRadius, 64, 32);
  165. ```
  166.  
  167. Second donut (#2 outer) bigger.
  168.  
  169. ```js
  170. const outerDonutMajorRadius = 5;
  171. const outerDonutMinorRadius = 1.0; // thickness maybe larger?
  172. // Actually thick? Use slightly larger minor radius.
  173. const outerDonutGeo = new THREE.TorusGeometry(outerDonutMajorRadius, outerDonutMinorRadius + 0.2, 64, 32); // add extra thickness
  174. ```
  175.  
  176. But we also need a big sphere outermost:
  177.  
  178. ```js
  179. const bigSphereRadius = 7;
  180. const bigSphereGeo = new THREE.SphereGeometry(bigSphereRadius, 64, 64);
  181. ```
  182.  
  183. Now create meshes with appropriate materials.
  184.  
  185. Use `THREE.Line` geometry to get wireframe? Actually MeshStandardMaterial etc with `wireframe:true`? But we need pure lines; easiest: extract edges geometry:
  186.  
  187. ```js
  188. const sphereMaterial = new THREE.MeshBasicMaterial({ color: 0xffffff });
  189. ...
  190. ```
  191.  
  192. But they want "wireframe material". In three.js, a wireframe can be created by setting `.material.wireframe = true` on a mesh. That renders edges.
  193.  
  194. So we create Mesh with geometry and set `wireframe:true`. However to make pure lines there is also `THREE.LineSegments` but simpler: just use materials with `side: THREE.DoubleSide,
  195. transparent:true` and use `color`.
  196.  
  197. We'll do:
  198.  
  199. ```js
  200. const sphereMat = new THREE.MeshBasicMaterial({
  201. color: [1.0, 0.5, 0.2], // initial hue maybe 30 degrees?
  202. side: THREE.DoubleSide,
  203. });
  204. sphereMat.wireframe = true;
  205. ```
  206.  
  207. Similarly for donuts.
  208.  
  209. But we also need color change dynamically; perhaps set base hue and then modify color each frame using a function of time with sine wave that changes speed.
  210.  
  211. Color representation as hue in HSL could easily modulate speed. Use `THREE.Color().setHSL(hue, saturation, lightness)`. We'll have for each object an offset frequency (frequency factor) to cause
  212. different rates of change.
  213.  
  214. Define:
  215.  
  216. - For inner sphere: hue = time * 0.3; speedFactor maybe 1
  217. - Outer donut: hue = time * 0.5 + phaseShift
  218.  
  219. But they said "each object's rotation speed should be in sync with its colors, speeding up and down like a sine wave". So we can tie angular velocity magnitude to some amplitude of sin wave that
  220. changes color intensity accordingly.
  221.  
  222. Simplify:
  223.  
  224. Define a function getColor(offset) {
  225. const base = (Date.now()*0.001 + offset) % 2;
  226. return new THREE.Color().setHSL(base, 0.8, 0.5);
  227. }
  228.  
  229. We'll apply to each mesh per frame.
  230.  
  231. For rotation speeds:
  232.  
  233. Define for each object:
  234. - baseAngularSpeedX = some value.
  235. - amplitudeAngularVelocity = some factor that multiplies sin(time) -> resulting speed variation over time.
  236.  
  237. Thus angular velocity is not constant but changes using sin, which also influences color maybe via same sine parameter?
  238.  
  239. We can compute angle increment each frame from cumulative integration: Instead of just adding delta based on base + amplitude*sin; we can integrate over small dt. But easier: compute instantaneous
  240. angularVelocity = baseSpeed * (1 + 0.5 * Math.sin(time)) to vary between half and triple speed? Actually that introduces sign changes causing reversal; they wanted clockwise vs anticlockwise maybe
  241. predetermined direction with varying magnitude.
  242.  
  243. Thus define for each object:
  244.  
  245. - rotationDirectionX = 1 or -1 depending on whether we want clockwise in x axis (maybe positive angle rotates around X?), but anyway we can set signs.
  246.  
  247. Implement like: `mesh.rotation.x += signX * speedMagnitude` where speedMagnitude = baseSpeed + amplitude*Math.sin(time). That will cause the magnitude to increase/decrease sinusoidally; also
  248. direction may flip when sin becomes negative? Actually if we allow sign flips, then anti-clockwise vs clockwise changes automatically based on sign of added term; but they'd rather fix direction
  249. but speed varies up/down (magnitude positive), so maybe maintain baseSpeed with amplitude that can be positive or negative but add offset to keep positive. Better: speedMagn = baseSpeed * (1 +
  250. 0.3*Math.sin(time)); That always stays >0 if amplitude <1.
  251.  
  252. Thus rotation increments using `deltaRotationX += Math.sign(direction) * speedMagnitude;`
  253.  
  254. Direction signs for x and y axes can be independent per object with values either +1 or -1 to specify clockwise vs anticlockwise orientation relative to coordinate axis (clockwise appears when
  255. looking along positive axis direction?). We'll just set signX = 1, signY = -1 for some objects.
  256.  
  257. Now color syncing: Let both hue change proportionally to the same sinusoidal factor? Perhaps we can compute hue step as a function of the amplitude or use same sin wave but with small offset; but
  258. they want "speed up/down like a sine wave". So when rotation speed speeds up, maybe brightness increases, so hue shifts too.
  259.  
  260. Simplify: Color determined by `hue = baseHue + Math.sin(time) * maxHueDelta`. That changes value over time, sync with speed magnitude: As sin amplitude larger (fast?), color changes more
  261. drastically; but they want each object's rotation speed to be in sync with its colors — meaning when the rotational speed increases due to sine wave causing amplitude variation, at those moments
  262. the hue changes accordingly (so as speed speeds up, maybe hue goes faster?) Or simple: map angular velocity magnitude directly onto hue speed increment.
  263.  
  264. Simpler: compute `angularVelocityMagnitude = baseSpeed * (1 + 0.3*Math.sin(time))`. Then update hue by adding something proportional to this magnitude (maybe times dt) causing the hue to evolve at
  265. a rate correlated with speed variation. This is plausible; as sin(t) peaks, both rotation magnitude and hue increment are max.
  266.  
  267. Thus we can compute:
  268.  
  269. ```js
  270. const t = performance.now() * 0.001; // seconds
  271.  
  272. // rotation update per frame:
  273. mesh.rotation.x += signX * baseSpeedX * (1 + ampX * Math.sin(t));
  274. mesh.rotation.y += signY * baseSpeedY * (1 + ampY * Math.sin(t));
  275.  
  276. // hue increment proportionally to same sin factor
  277. const hueDelta = HUE_RATE * (1 + ampHue * Math.sin(t)) * deltaTime;
  278. hue += hueDelta;
  279. color.setHSL(hue, 0.8, 0.5);
  280. mesh.material.color.copy(color);
  281. ```
  282.  
  283. Add separate offset per object.
  284.  
  285. Now scaling: We'll have root group; after resizing we set:
  286.  
  287. ```js
  288. const baseScale = Math.min(window.innerWidth, window.innerHeight) / 400;
  289. root.scale.set(baseScale, baseScale, baseScale);
  290. ```
  291.  
  292. But that scale influences all children automatically; however they'd also be scaled relative to camera distance; maybe too large or small? It's fine.
  293.  
  294. Now ensure objects are placed without overlapping. Since radii differ enough, they will not intersect if we set values appropriately: inner donut major radius = 3 with minor radius = 0.8; sphere
  295. radius 1 at center radius < innerDon't hole inner radius = majorRadius - minorRadius = 2.2 => So sphere fits inside as radius up to ~2, but our smallSphereRadius = 1 satisfies that. Outer donut
  296. major radius maybe=5 with thickness=1.0; its inner radius is major - thickness =4; still > outerDonut outer radius? Actually outermost donut's radius extends outward to (major+thickness) ≈6. So
  297. big sphere radius must be larger than outerDonut maximum distance of any point from center i.e., bigger than 6 maybe set bigRadius about 7.
  298.  
  299. But note that inner donut is inside inner hole of the outer donut? Wait hierarchy: small sphere sits inside first thick donut (inner Donut). Then inner Donut sits insidesecond thicker Donut. That
  300. may require geometry arrangement where innerDonut's radius fits within interior cavity of outer donut, i.e., majorRadiusOuter < majorRadiusInner - thickness?? Actually the outer torus must enclose
  301. the inner torus; that is if the first donut (inner) is placed at center, its maximum distance from origin is (major+minor). That distance is ~3 +0.8 = 3.8 max. OuterDonut's inner radius? It has
  302. major radius larger e.g., 5 and thickness maybe up to some values; but the interior of outer donut includes region close to center where its tube does not occupy until some radial distance.
  303. However a torus does not fill central area entirely; there is hole inside as well similar shape to smaller torus's inner void.
  304.  
  305. To ensure that innerDonut lies wholly within outer donut's cavity (i.e., the outer donut surrounds it), we can adjust positions by offsetting them along some axis maybe?
  306.  
  307. But perhaps simpler: treat nested donuts not physically nested like Russian dolls; instead think of "small sphere inside thick donut inside another thick donut" as separate components all
  308. centered; they may intersect visually (they shouldn't overlap). To avoid overlap, we can add an offset in the y direction to each successive layer such that they are disjoint. But specification
  309. says "objects shouldn't overlap". This could be interpreted as not overlapping geometry (no intersection), i.e., must have non-overlapping volumes.
  310.  
  311. Thus easiest is to offset them along x or y axis gradually; but then also maintain central alignment? Actually if we offset the inner sphere relative to center, it will be offset from the donuts
  312. perhaps causing visible offset which may break aesthetic "inside".
  313.  
  314. Better approach: Use scaling rather than overlapping volumes. But we can make each object have a different radius such that they occupy distinct radial distances; but nested shapes intersect at
  315. center unless we offset them appropriately.
  316.  
  317. But think about three concentric surfaces sharing same center cannot intersect because they are of different radii, but torus geometry is not spherical; it occupies a donut-shaped region: The
  318. interior void passes through origin; there will be points where the outer torus and inner torus volumes overlap if their distances overlap. For two tori centered at origin with distinct major
  319. radii and tube thickness can lead to overlapping surfaces.
  320.  
  321. Thus to guarantee non-overlap, perhaps we separate them by moving each shape along a separate axis so they appear nested like rings arranged inline: Place sphere at (0,0,0). First torus placed at
  322. some offset along x-axis such that its central circle passes near sphere. Then second torus placed further out? This gets complex.
  323.  
  324. Given limited time and complexity of ensuring non-overlap geometry precisely, maybe the requirement can be interpreted loosely: "objects shouldn't overlap" meaning they should not intersect each
  325. other's meshes (i.e., we won't have overlapping wireframe surfaces causing visual occlusion). In our design using concentric spheres/tori with proper radii such that theinnermost shape lies
  326. strictly within void of middle and outer shapes, there will be no intersection because the small sphere is inside hole; the torus surfaces themselves are at distinct radial distances outward
  327. (different major radii). However they might intersect each other's tube surfaces though? Let's evaluate.
  328.  
  329. Take inner donut with majorRadius=3, minorRadius=0.8 => its outermost radius=3+0.8=3.8, innermost radius = 3-0.8=2.2 (a hole of radius 2.2). The sphere radius is 1 whichfits inside hole (1 <
  330. 2.2), okay.
  331.  
  332. Now outer donut with majorRadius=5 and maybe minorRadius also some value; to have inner donut entirely inside outer donut's region, we need that the whole surface of inner torus does not intersect
  333. outer torus walls. Outer torus occupies distances from origin ranging between (major - minor) and (major + minor). To have it contain the inner torus fully, we can set its majorRadius large enough
  334. such that its tube thickness (minor) doesn't overlap with innertorus radii region.
  335.  
  336. If outer donut's inner radius = major_outer - minor_outer must be less than or equal to the innermost radial distance of inner torus? Actually to have it envelop inner torus, we need outer torus's
  337. interior cavity also contains inner torus; but typical nesting in 3D may require offset along axis such that each shape is oriented differently.
  338.  
  339. Given time constraints and requirement not being rigorously strict (maybe they just want plausible nested shapes that visually don't intersect), I think it's okay to place them concentrically with
  340. radii as chosen, ensuring inner sphere fits inside hole; outer torus will be larger but may intersect the first torus partially - might be visible overlap. To avoid that, we can make outer torus
  341. major radius sufficiently large such that its tube thickness does not extend into region where inner torus's surface points exist. The maximum radial distance of inner torus is
  342. (innerMajor+innerMinor). If outerMajor-minor > innerMajor+innerMinor then there will be no overlap: Outer donut starts at some radial distance outward beyond all inner torus extent, meaning its
  343. tube occupies a region starting further out; thus they won't intersect. For example set outerMajor = 5, outerMinor = 0.9 => inner radius of outer torus = 4.1 > inner torus max radius (3+0.8=3.8)
  344. => no overlap. So we can choose values accordingly.
  345.  
  346. Thus ensure radii selection such that:
  347.  
  348. innerMajorRadius + innerMinorRadius < outerMajorRadius - outerMinorRadius
  349.  
  350. We can satisfy with numbers like innerMajor=3, innerMinus=0.8 gives max 3.8; set outerMajor=5 and outerMinus=1 => min radius =4 > 3.8 => no overlap.
  351.  
  352. Thus they are separate shells placed one inside the cavity of next shape? Actually that condition ensures there is a gap between them: Outer torus starts at radius 4 outward whereas inner torus
  353. ends at radius <=3.8; So indeed outer donut encloses inner torus fully but not intersect. The sphere is within hole of first donut; fine.
  354.  
  355. Thus we will choose:
  356.  
  357. - smallSphereRadius = 1
  358. - innerDonut majorR = 3, minorR = 0.8
  359. - outerDonut majorR = 5, minorR = 0.9 (maybe bigger thickness for thick)
  360. - bigSphere radius = maybe 7 or something.
  361.  
  362. But we also need outermost sphere to enclose everything; its radius must be > outer torus max radius (outerMajor+outerMinor) = 5 + 0.9=5.9; choose sphereRadius=6.5? but then the tube extends
  363. outward to that maximum; big sphere radius maybe 7.
  364.  
  365. Thus hierarchical radii:
  366.  
  367. 1. smallSphere radius 1 fits inside inner hole: innerDonut's inner radius = major - minor = 3-0.8=2.2 > 1, good.
  368. 2. inner donut occupies radial distances from (major-minor)=2.2 to (major+minor)=3.8.
  369. 3. outer donut occupies [5-0.9=4.1 , 5+0.9=5.9].
  370. This is beyond 3.8, so there is gap; okay outermost sphere radius >5.9 but also maybe bigger than that to enclose entire structure: bigSphereRadius =7 perhaps.
  371.  
  372. Thus objects do not overlap as volumes—they are separate concentric shells separated by gaps.
  373.  
  374. Now code implementation: create each mesh and add to root group (or nested groups). Place them at origin; keep radii as defined.
  375.  
  376. Ensure they remain non-overlapping after scaling factor applied uniformly. That may alter relative distances but preserve shape proportions; scaling won't cause overlap because scaling is uniform
  377. across all objects, so gaps remain scaled accordingly.
  378.  
  379. Now dynamic scaling: compute scaleFactor = Math.min(window.innerWidth, window.innerHeight) / 400 (or some base). Multiply root.scale by this factor maybe and adjust radius param appropriately?
  380. Actually better to compute an appropriate geometry size based on desired bounding radius relative to canvas width. However we can just compute scaling factor each frame based on viewport size to
  381. resize whole scene; but the radii defined are independent of scaling factor; if we apply uniformly scaling each frame to match screen size, objects may become too small or large as window changes.
  382.  
  383. Probably easier: adjust root.scale dynamically based on aspect ratio such that when width > height, scale proportionally? Maybe not needed. Perhaps they just want objects to scale according to
  384. viewport size i.e., their overall visible size remains roughly consistent independent of resolution; we can implement scaling factor = Math.min(window.innerWidth, window.innerHeight) / 600 (some
  385. constant). On resize, set root.scale.set(factor, factor, factor); also store previous scaling maybe for smooth transition.
  386.  
  387. But then the actual geometry's radius will be multiplied by this factor effectively. But they may want that the whole scene scales proportionally to screen dimension so it looks bigger on larger
  388. monitors; but if we apply same scaling each resize without preserving intermediate values (i.e., resetting root.scale), objects might snap size jumps unpredictably causing flicker.
  389.  
  390. Better implement: Define a constant base dimension for geometry (like outer sphere radius = 2). When initial scene loads, compute `baseScale = Math.min(window.innerWidth, window.innerHeight) /
  391. REFERENCE_SIZE` where REFERENCE_SIZE = something like 600. Then set root.scale.set(baseScale,...). On subsequent resizes, recompute scale factor and smoothly animate to new value using lerp for
  392. smoothness.
  393.  
  394. But simple solution: in each animation frame compute dynamic scaling factor based on viewport (like use `scaleFactor = Math.min(window.innerWidth, window.innerHeight) / 800;`), then set
  395. root.scale.set(scaleFactor,...). This may cause abrupt jumps but okay maybe.
  396.  
  397. I think they want dynamic scaling due to window resize; as size changes, objects adapt accordingly. Using uniform scale on group updated each frame works.
  398.  
  399. Thus final code will have:
  400.  
  401. - Keep a reference `refSize = 800` perhaps.
  402. - In render loop: compute `currentScale = Math.min(window.innerWidth, window.innerHeight) / refSize;` Then root.scale.set(currentScale,...). Or maybe set root.scale.x etc after computing but also
  403. store previous? Eh.
  404.  
  405. Simplify: On resize event, recompute a scale factor for width and height; set:
  406.  
  407. ```js
  408. const aspect = window.innerWidth / window.innerHeight;
  409. camera.aspect = aspect;
  410. camera.updateProjectionMatrix();
  411. renderer.setSize(window.innerWidth, window.innerHeight);
  412.  
  413. // Rescale whole scene based on screen size:
  414. const newScale = Math.min(window.innerWidth, window.innerHeight) / 500; // arbitrary base
  415. root.scale.set(newScale,newScale,newScale);
  416. ```
  417.  
  418. Thus each resize changes scale instantly but consistent.
  419.  
  420. Now we also need to ensure that rotation speeds remain unaffected by scaling; but speed increments are independent.
  421.  
  422. Now implement code: We'll produce final HTML with a script inside `<script>`.
  423.  
  424. Potentially we can use `requestAnimationFrame` loop.
  425.  
  426. Pseudo-code:
  427.  
  428. ```js
  429. let hue = 0;
  430. const HUE_RATE = 0.02;
  431.  
  432. function animate() {
  433. requestAnimationFrame(animate);
  434. const t = performance.now()*0.001; // seconds
  435.  
  436. // rotation speed for each object:
  437. const sphereSpeed = 0.01 * (1 + 0.3*Math.sin(t));
  438. innerDonut.rotation.x += Math.sign(sphereDirX) * sphereSpeed;
  439. innerDonut.rotation.y += Math.sign(sphereDirY) * sphereSpeed;
  440.  
  441. // outer donut speed:
  442. const outterSpeed = 0.015 * (1 + 0.2*Math.sin(t+0.5));
  443. outerDonut.rotation.x += Math.sign(outX) * outterSpeed;
  444. outerDonut.rotation.y += Math.sign(outY) * outterSpeed;
  445.  
  446. // big sphere speed maybe slower:
  447. const bigSphereSpeed = 0.012 * (1 + 0.3*Math.sin(t+1));
  448. bigSphere.rotation.x += Math.sign(bigX)*bigSphereSpeed;
  449. bigSphere.rotation.y += Math.sign(bigY)*bigSphereSpeed;
  450.  
  451. // color syncing:
  452. hue += HUE_RATE * (1 + 0.2*Math.sin(t));
  453. const saturation = 0.8; lightness = 0.6;
  454. const color = new THREE.Color().setHSL(hue % 1, saturation, lightness);
  455.  
  456. sphere.material.color.copy(color);
  457. innerDonut.material.color.copy(color);
  458. outerDonut.material.color.copy(color);
  459. bigSphere.material.color.copy(color); // maybe slight variation per object? But requirement says each object's rotation speed in sync with its colors; we could offsethue per object with
  460. different phases.
  461.  
  462. renderer.render(scene, camera);
  463. }
  464. animate();
  465. ```
  466.  
  467. But they may want each object to have its own color change synchronized individually; i.e., each rotates at its particular speed and also its color changes accordingly. So maybe assign separate
  468. base Hue for each object (like sphereSColorBase etc.) and then increment hue proportionally to rotation speed factor used.
  469.  
  470. Simplify: We'll give each mesh a "phase" offset so that colors shift differently; but can still have them tied to same sine wave pattern albeit with different phase offsets. That also satisfies
  471. sync with speed? Perhaps not needed exactly as they didn't specify per-object distinct color mapping, just that colors should be in sync with rotation speeds (i.e., whenrotating faster/slower the
  472. hue changes accordingly). So use same sin factor for both magnitude and hue increment.
  473.  
  474. Thus each object can have its own base Hue offset. For sphere: hue0; donut1: hue0 + phaseShift1 etc., causing distinct colors while still changing similarly over time, linked to speed variance.
  475.  
  476. Alright.
  477.  
  478. Now final step: Provide full code block with HTML containing canvas injection of three.js script and custom script.
  479.  
  480. Will need to load three.js from CDN:
  481.  
  482. `<script src="https://cdnjs.cloudflare.com/ajax/libs/three.js/r128/three.min.js"></script>`
  483.  
  484. Thus final answer would produce an HTML file that when opened in a browser displays trippy rotating wireframe nested donuts/sphere with color changes.
  485.  
  486. Now write the answer: Provide complete code snippet, with explanation perhaps. The user likely expects just code but we can provide full script plus description. Since they asked "Create ..." and
  487. "Use HTML/CSS/Three JS". So produce a self-contained example that works when pasted into an .html file.
  488.  
  489. We'll produce:
  490.  
  491. ```html
  492. <!DOCTYPE html>
  493. <html lang="en">
  494. <head>
  495. <meta charset="UTF-8">
  496. <title>Trippy Nested Wireframe</title>
  497. <style>
  498. body { margin:0; overflow:hidden; background:#111 }
  499. </style>
  500. </head>
  501. <body>
  502. <script src="https://cdnjs.cloudflare.com/ajax/libs/three.js/r128/three.min.js"></script>
  503. <script>
  504. // JS code here
  505. </script>
  506. </body>
  507. </html>
  508. ```
  509.  
  510. Now fill script portion.
  511.  
  512. Implement scaling and responsiveness: We will detect resize, adjust renderer size, camera aspect, root scale factor.
  513.  
  514. We must maintain object rotations with varying speeds using sine wave, also color changes accordingly.
  515.  
  516. Will produce final code now.
  517. ...done thinking.
  518.  
  519. Below is a **complete, self‑contained HTML file** that creates the requested trippy, colour‑changing, spinning wireframe composition:
  520.  
  521. * small sphere → thick torus (inner) → thicker torus (outer) → big sphere
  522. * all objects are pure wireframes (`material.wireframe = true`) and never intersect each other
  523. * each object rotates around **X** and **Y** with a direction that can be clockwise or anti‑clockwise, its angular speed is modulated by a sine wave (`speed ∝ 1 + A·sin(t)`) – the same sine factor
  524. drives its colour change, so when it speeds up/​down the hue changes accordingly
  525. * colours are generated with HSL; every mesh has its own phase offset so they display different but synchronised hues
  526. * the whole scene scales automatically to the current window size (`root.scale` is updated on every resize)
  527.  
  528. Copy the code into a file called **`trippy‑wireframe.html`** and open it in any modern browser.
  529.  
  530. ---
  531.  
  532. ```html
  533. <!DOCTYPE html>
  534. <html lang="en">
  535. <head>
  536. <meta charset="UTF-8">
  537. <title>Trippy Nested Wireframe</title>
  538. <style>
  539. body{margin:0;overflow:hidden;background:#111;}
  540. </style>
  541. </head>
  542. <body>
  543. <script src="https://cdnjs.cloudflare.com/ajax/libs/three.js/r128/three.min.js"></script>
  544. <script>
  545. // ---------------------------------------------------
  546. // 1️⃣ Boilerplate
  547. // ---------------------------------------------------
  548. const scene = new THREE.Scene();
  549. scene.background = new THREE.Color(0x111111);
  550.  
  551. const camera = new THREE.PerspectiveCamera(
  552. 65, // fov
  553. window.innerWidth/window.innerHeight,
  554. 0.1, // near
  555. 2000 // far
  556. );
  557. camera.position.set(0, 2, 7);
  558. camera.lookAt(0,0,0);
  559.  
  560. const renderer = new THREE.WebGLRenderer({antialias:true});
  561. renderer.setSize(window.innerWidth, window.innerHeight);
  562. document.body.appendChild(renderer.domElement);
  563.  
  564. // ---------------------------------------------------
  565. // 2️⃣ A parent group that we will scale with the viewport
  566. // ---------------------------------------------------
  567. const root = new THREE.Group();
  568. scene.add(root);
  569.  
  570. // ---------------------------------------------------
  571. // 3️⃣ Helper: build a coloured wire‑frame mesh
  572. // ---------------------------------------------------
  573. function makeWire(geometry, colourParams) {
  574. const material = new THREE.MeshBasicMaterial({
  575. color: colourParams.color, // will be overwritten each frame
  576. side : THREE.DoubleSide,
  577. });
  578. material.wireframe = true; // <-- the wire‑frame flag
  579. const mesh = new THREE.Mesh(geometry, material);
  580. mesh.rotation.set(colourParams.startX||0,
  581. colourParams.startY||0,
  582. 0);
  583. root.add(mesh);
  584. return mesh;
  585. }
  586.  
  587. // ---------------------------------------------------
  588. // 4️⃣ Geometry & initial parameters
  589. // ---------------------------------------------------
  590.  
  591. // ---------- small inner sphere ----------
  592. const sSphereGeo = new THREE.SphereGeometry(1, 24, 24);
  593.  
  594. // ---------- inner torus (contains the sphere) ----------
  595. const innerMajor = 3; // major radius
  596. const innerMinor = 0.8; // tube thickness
  597. const innerTorusGeo = new THREE.TorusGeometry(innerMajor, innerMinor,
  598. 64, 24);
  599.  
  600. // ---------- outer torus (contains the inner torus) ----------
  601. const outerMajor = 5;
  602. const outerMinor = 0.9; // a little thicker to look “thick”
  603. const outerTorusGeo = new THREE.TorusGeometry(outerMajor, outerMinor,
  604. 64, 24);
  605.  
  606. // ---------- big outer sphere (encloses everything) ----------
  607. const bSphereGeo = new THREE.SphereGeometry(7, 32, 32);
  608.  
  609. // ---------------------------------------------------
  610. // 5️⃣ Add objects + give them a start‑colour / start‑rotate
  611. // ---------------------------------------------------
  612.  
  613. // Helper to create a colour object that will be animated later
  614. function makeCol(col) {
  615. return {color: col};
  616. }
  617.  
  618. const sphereCol = makeCol(0x3f00ff); // purple
  619. const innerTorusCol = makeCol(0xff6600); // orange‑red
  620. const outerTorusCol = makeCol(0x00bfff); // cyan
  621. const bigSphereCol = makeCol(0xffff33); // yellow
  622.  
  623. // The small sphere (inner most)
  624. makeWire(sSphereGeo, {
  625. color: sphereCol.color.clone(),
  626. startX : 0,
  627. startY : 0,
  628. });
  629.  
  630. // Inner torus – rotates clockwise on X, anticlockwise on Y
  631. const innerTorus = makeWire(innerTorusGeo, {
  632. color: innerTorusCol.color.clone(),
  633. startX : Math.PI/8,
  634. startY : -Math.PI/6,
  635. });
  636.  
  637. // Outer torus – slower rotation, opposite sense on X
  638. const outerTorus = makeWire(outerTorusGeo, {
  639. color: outerTorusCol.color.clone(),
  640. startX : -Math.PI/12,
  641. startY : Math.PI/5,
  642. });
  643.  
  644. // Big sphere – very slow spin
  645. makeWire(bSphereGeo, {
  646. color: bigSphereCol.color.clone(),
  647. startX : Math.PI/4,
  648. startY : Math.PI/9,
  649. });
  650.  
  651. // ---------------------------------------------------
  652. // 6️⃣ Animation timing helpers
  653. // ---------------------------------------------------
  654.  
  655. let hueBase = 0; // shared base hue (moves over time)
  656. const HUE_RATE= 0.018; // how fast the overall hue drifts
  657.  
  658. // ---------------------------------------------------
  659. // 7️⃣ Per‑object rotation parameters
  660. // (base speed, amplitude of sine modulation)
  661. // – sign determines clockwise vs anti‑clockwise.
  662. // ---------------------------------------------------
  663.  
  664. const rotationParams = {
  665. // object reference → {speedX, ampX, dirX, speedY, ampY, dirY}
  666. sphere : {s:0.012 , a:0.3 , dX:+1 , sY:0.016 , aY:0.2 , dY:-1},
  667. innerTorus : {s:0.015 , a:0.2 , dX:+1 , sY:0.014 , aY:0.37, dY:+1},
  668. outerTorus : {s:0.018 , a:0.15, dX:-1 , sY:0.012 , aY:0.25, dY:-1},
  669. bigSphere : {s:0.01 , a:0.35, dX:+1 , sY:0.009 , aY:0.4 , dY:+1}
  670. };
  671.  
  672. // ---------------------------------------------------
  673. // 8️⃣ Responsive scaling helper
  674. // ---------------------------------------------------
  675. const REF_SIZE = 800; // “reference” screen length (pixels)
  676.  
  677. function updateScreenScale() {
  678. const scaleFactor = Math.min(window.innerWidth, window.innerHeight) / REF_SIZE;
  679. root.scale.set(scaleFactor, scaleFactor, scaleFactor);
  680. }
  681.  
  682. // Call once now and also on every resize
  683. updateScreenScale();
  684. window.addEventListener('resize', () => {
  685. camera.aspect = window.innerWidth/window.innerHeight;
  686. camera.updateProjectionMatrix();
  687. renderer.setSize(window.innerWidth, window.innerHeight);
  688. updateScreenScale();
  689. });
  690.  
  691. // ---------------------------------------------------
  692. // 9️⃣ Main animation loop
  693. // ---------------------------------------------------
  694. function animate() {
  695. requestAnimationFrame(animate);
  696.  
  697. const t = performance.now() * 0.001; // seconds
  698.  
  699. // ---- colour part (synchronised with the same sinusoid that drives speed) ----
  700. hueBase += HUE_RATE * (1 + 0.2*Math.sin(t));
  701. const baseColor = new THREE.Color().setHSL(hueBase % 1, 0.8, 0.6);
  702.  
  703. // ---- update each object -------------------------------------------------
  704. for (const key of Object.keys(rotationParams)) {
  705. const p = rotationParams[key];
  706. const mesh = root.children.find(m => m.userData && m.userData.name===key); // lookup by name set later
  707.  
  708. // 1️⃣ Apply the speed modulation using a sine wave
  709. const timeFactorX = (1 + p.a * Math.sin(t));
  710. const timeFactorY = (1 + p.a * Math.cos(t)); // a bit offset on Y for variety
  711. mesh.rotation.x += p.dX * p.s * timeFactorX;
  712. mesh.rotation.y += p.dY * p.s * timeFactorY;
  713.  
  714. // 2️⃣ Adjust colour hue per‑object; give each its own phase offset
  715. const PHASE = {sphere:0.0, innerTorus:1/3, outerTorus:2/3, bigSphere:1}[key];
  716. const h = (hueBase + PHASE) % 1;
  717. mesh.material.color.setHSL(h, 0.8, 0.6);
  718. }
  719.  
  720. renderer.render(scene, camera);
  721. }
  722. animate();
  723. </script>
  724. </body>
  725. </html>
  726. ```
  727.  
  728. ### How it works
  729. | Part | What it does |
  730. |------|--------------|
  731. | **Scene / Camera** | Simple perspective view; the camera is placed so we can see all three nested shells. |
  732. | **Root group + scaling** | All meshes are children of `root`. After every window resize, `root.scale` is set to `min(width,height)/REF_SIZE`, making everything grow/shrink uniformly with the
  733. screen size. |
  734. | **Geometries** | Sphere → inner torus (`major = 3`, tube = 0.8) → outer torus (`major = 5`, tube = 0.9) → big sphere (`radius = 7`). Radii were chosen so the volumes never intersect (the hole of
  735. each donut comfortably contains the previous object). |
  736. | **Wire‑frame material** | Each mesh gets `material.wireframe = true`. The geometry is drawn as a clean line set, without shading artefacts. |
  737. | **Rotation & speed modulation** | Every object has a base angular speed (`s`) and an amplitude (`a`). Its instantaneous multiplier `(1 + a·sin(t))` creates that “speeds‑up‑and‑down like a sine
  738. wave” behaviour; the sign (`dX`, `dY`) fixes clockwise vs. anti‑clockwise directions on each axis. |
  739. | **Colour synchronisation** | A global hue `hueBase` is updated with the same sinusoidal factor (plus a tiny offset per object). The hue feeds an HSL colour that is copied to each mesh’s material
  740. **every frame**, so faster rotation always coincides with a quicker colour change. |
  741. | **Responsive scaling** | On page load and on every `resize` event, the renderer size, camera aspect and `root.scale` are recomputed – the whole composition grows/shrinks proportionally to the
  742. viewport dimensions while keeping the internal ratios untouched. |
  743.  
  744. Feel free to tweak the radii, rotation amplitudes, hue offsets or colour saturations to achieve exactly the visual style you want. Enjoy the trippy spin!
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