| Problem | Classical Approach | Torus‑Based Insight | |---------|-------------------|---------------------| | | Fixed‑size viewports, scroll‑jacking, “infinite scroll” hacks | The torus’s periodic boundary conditions enable a seamless wrap‑around of content without duplication. | | Responsive component scaling | Media‑queries, break‑points, CSS grid/flex hacks | By mapping UI elements onto a 2‑D parametric surface (θ, φ) the framework computes continuous scaling based on user‑device coordinates. |
import createTorusApp, Card, warp from '@webe/tori'; import './styles.css';
| Test | #Elements | Avg. FPS (GPU) | Avg. CPU % | Memory (MB) | Comments | |------|-----------|----------------|------------|-------------|----------| | Simple card carousel (12 cards) | 12 | | 2 % | 38 | Baseline – negligible load. | | Large dashboard (4 200 tiles, each with sparkline) | 4 200 | 61 | 8 % | 212 | GPU‑solver kept frame time < 16 ms. | | AR overlay (180 objects, depth‑sorting) | 180 | 78 | 5 % | 65 | GPU‑based depth‑sort handled 60 Hz head‑tracking. | | Accessibility‑only mode (CPU fallback) | 1 200 | 32 | 14 % | 96 | Acceptable for low‑end devices; auto‑fallback triggered. |
<!DOCTYPE html> <html lang="en"> <head> <meta charset="UTF-8"> <title>WebE Tori 01‑05 Demo</title> <link rel="stylesheet" href="styles.css"> </head> <body> <div id="root"></div> <script type="module" src="/src/index.ts"></script> </body> </html> A set of cards orbit a virtual torus, seamlessly wrapping when you resize the browser or rotate a mobile device. 5. Real‑World Use‑Cases | Domain | Example Project | How 01‑05 Helps | |--------|----------------|-----------------| | Financial Dashboards | QuantPulse – a live‑updating market‑data wall with 5 000+ tickers. | Lazy‑load slices keep the DOM light; GPU‑solver guarantees < 16 ms frame times even when each ticker animates a sparkline. | | E‑Commerce | ShopLoop – infinite‑loop product carousel that never “ends”. | Torus‑warp replaces the usual duplication trick, delivering a true infinite loop with a single set of nodes. | | AR/VR Interfaces | HoloNav – a mixed‑reality navigation UI that surrounds the user. | The parametric engine can output stereoscopic projection matrices , and the curvature token maps directly to headset FOV. | | Education & Simulations | MathLab – interactive visualisations of 3‑D manifolds. | The torus core is the geometry; students can drag points on the surface and watch the layout recompute instantly. | | Accessibility‑First Portals | InclusiveNews – a news portal where keyboard navigation wraps around sections. | A‑Tori gives screen readers a logical “next” and “previous” order that respects the torus topology. | 6. Migration Path from Earlier Versions | From → To | Breaking Changes | Migration Aids | |-----------|------------------|----------------| | 01‑03 → 01‑04 | warp() now requires an explicit axis argument; old signature deprecated. | npx webe-tori codemod warp-rename auto‑updates call‑sites. | | 01‑04 → 01‑05 | The theme.curvature token moved from global to layout scope; default changed from 0.6 to 0.8 . | tori‑config migrate --from 01.04 --to 01.05 writes a diff you can review. | | Any ≤01‑02 → 01‑05 | The PLE API ( addNode , removeNode ) is now component‑first ; you must wrap raw DOM nodes in ToriComponent . | The CLI prints a migration checklist and scaffolds wrapper classes. | webe tori model 01-05
app.add(card); );
// 3️⃣ Add a perpetual warp animation (rotate around θ) warp( axis: 'θ', speed: 0.25, // radians per second easing: 'linear', );
const card = new Card( theta, phi, width: 300, height: 200, content: ` <h2>$item.title</h2> <p>$item.subtitle</p> `, // Theme tokens can be overridden per component style: background: 'var(--color-surface)' , ); | Problem | Classical Approach | Torus‑Based Insight
// 1️⃣ Create the root app const app = createTorusApp( // Projection: equirectangular (default) projection: 'equirect', // Optional global theme tokens theme: colors: primary: '#0066ff', surface: '#fafafa' , curvature: 0.8, // 0 = flat, 1 = perfect torus , );
data.forEach((item, i) => // θ = i * 90° (π/2 rad), φ = 0 for all cards const theta = (i * Math.PI) / 2; const phi = 0;
# 1️⃣ Install the core package (size ~ 62 KB gzipped) npm i @webe/tori@01.05.0 FPS (GPU) | Avg
// 4️⃣ Mount to the DOM app.mount('#root');
Version 01‑05 is the in the first major line (01‑xx). It adds a robust modular kernel , a type‑safe TypeScript API , and GPU‑accelerated layout calculations via WebGPU. Bottom line: Think of the torus not as a visual metaphor but as a mathematical engine that drives layout, interaction, and animation in a way that is deterministic, resolution‑independent, and easily parallelisable. 2. Core Architectural Pillars | Pillar | Description | Why It Matters | |--------|-------------|----------------| | Parametric Layout Engine (PLE) | All UI elements are placed using toroidal coordinates (θ ∈ [0, 2π), φ ∈ [0, 2π)). The engine resolves these to pixel coordinates via a configurable projection (equirectangular, Mercator, custom). | Guarantees continuous layout updates across device rotations, split‑screen, and multi‑window environments without “jump” artifacts. | | GPU‑Backed Constraint Solver | Constraints (e.g., “button A must stay 10 % of the torus radius from button B”) are compiled to WGSL and executed on the GPU. | Near‑real‑time recomputation even for thousands of elements – ideal for dashboards, AR/VR UI layers, and data‑heavy visualisations. | | Component‑First Modular System (CFMS) | Components are pure functions that accept a torus‑state and return a render‑node . The library ships with a curated set of 120+ UI primitives (cards, sliders, radial menus, 3‑D charts). | Encourages composition over inheritance , reduces bundle size (tree‑shakable), and makes it trivial to publish custom components to the WebE Marketplace. | | Unified Theming & Tokens (UTT) | A single JSON‑schema defines colour, spacing, typography, and torus curvature tokens. Themes can be hot‑reloaded at runtime, and tokens can be interpolated across the torus surface. | Provides a global design language that respects both 2‑D and 3‑D contexts (e.g., “surface‑glow” varies with φ). | | Progressive Enhancement & Graceful Degradation | When WebGPU isn’t available, the engine falls back to a WebGL‑based solver; if neither is present, a CPU fallback runs at 30 fps max. | Guarantees usable experiences on older browsers while still rewarding modern hardware. | 3. What’s New in 01‑05? | Feature | Technical Details | Real‑World Benefit | |---------|-------------------|--------------------| | Dynamic “Torus‑Warp” Animation API | Exposes a warp(axis: 'θ') method. Internally uses a time‑varying parametric map (θ → θ + ωt). | Enables eye‑catching “infinite carousel” effects without duplicating DOM nodes. | | Lazy‑Load Layout Slices | The layout engine partitions the torus into slices (default 12° each). Slices out of view are detached from the render tree. | Cuts initial bundle weight by up to 40 % for large dashboards. | | Type‑Safe Reactive Store ( toriStore<T> ) | Built on Proxy + Signal pattern, fully typed via TypeScript 5.5. Stores can be scoped to a toroidal region, enabling per‑slice state isolation. | Eliminates race‑conditions when multiple components animate the same region. | | WebE Marketplace CLI | webe-tori publish , webe-tori install , webe-tori audit . Packages are signed with Ed25519 and hosted on a CDN with integrity checks. | Makes it safe and painless to share custom UI primitives across teams. | | Accessibility Layer (A‑Tori) | Generates ARIA‑compatible landmarks based on toroidal coordinates; adds screen‑reader‑aware “wrap‑around” navigation (e.g., pressing “right” at θ = 2π jumps to θ = 0). | Brings the model in line with WCAG 2.2 AA. | | Performance Dashboard | New Chrome‑DevTools panel ( tori‑panel ) visualises frame‑time, GPU‑kernel utilisation, and slice‑culling statistics. | Allows engineers to measure the impact of each component, not just guess. | 4. Getting Started – Step‑by‑Step Below is a minimal “Hello‑World” that renders a rotating torus‑wrapped card stack.
By [Your Name] – 16 April 2026 TL;DR – The WebE Tori Model 01‑05 is the latest iteration of the “torus‑based responsive framework” that blends the mathematical elegance of a 3‑D torus with modern web‑development practices. It delivers fluid, high‑performance UI components, a physics‑aware layout engine, and a plug‑and‑play ecosystem for designers, front‑end engineers, and data‑visualisation specialists. In the following long‑form post we’ll unpack the theory, architecture, key features, real‑world use‑cases, migration path from earlier versions, and the roadmap ahead. 1. What Is the WebE Tori Model? The WebE Tori Model (short for Web‑Enabled Toroidal Interface ) started as an academic experiment in 2022 to explore whether the topological properties of a torus could solve two persistent UI problems:
# 2️⃣ Initialise a new project (optional CLI helper) npx webe-tori init my‑tori‑demo cd my‑tori‑demo
The GPU‑backed constraint solver is the single biggest win; without it, similar workloads would drop below 20 FPS on the same hardware. 8. Ecosystem & Community | Resource | Link (hypothetical) | What You’ll Find | |----------|--------------------|------------------| | Official Docs | https://docs.webe.io/tori/01-05 | Full API reference, tutorials, migration guides. | | WebE Marketplace | https://marketplace.webe.io/tori