Apunts

An interactive computing and academic platform engineered for computer science and applied mathematics at UPC-FIB. Built for responsiveness, algorithmic rigor, and real-time collaboration.

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Architectural Highlights

• Deterministic DAG Engine (Roadmap)
  Topological curriculum navigation governed by an acyclic graph invariant. Cycle detection runs in $\mathcal{O}(V + E)$ time via zero-allocation queue traversals, cascading prerequisite states deterministically across academic terms.

• Greedy Interval Partitioning (Gantt)
  Sub-millisecond timeline layout powered by a binary Min-Heap priority queue. Guarantees $\mathcal{O}(N \log K)$ track scheduling and continuous 60/120 FPS rendering without layout thrashing.

• Reactive AST Pipeline (Markdown)
  Nine-pass unified syntax compilation with lazy visualizer isolation. Directives, KaTeX mathematical typesetting, and WebGL contexts execute under isolated error boundaries with zero runtime jank.

• Realtime Collaborative Canvas
  Multiplayer vector drawing and presence tracking backed by Firebase Realtime Database. Cursors are throttled at 20 FPS with requestAnimationFrame batching to ensure fluid co-presence with minimal network overhead.

• Disjoint-Set Comment Architecture
  One-level threaded tree reconstruction operating in $\mathcal{O}(N)$ amortized time with true path compression and cycle-guarded root discovery.

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System Overview

Layer	Technologies
Interface	React 19, TypeScript, Tailwind CSS v4, Framer Motion
Graphics & Math	Three.js, React Three Fiber, Mafs, KaTeX, React Force Graph (D3)
State & Flow	React Flow (@xyflow/react), Zustand (useShallow), Native Context
Content Pipeline	@content-collections (Zod), Remark / Rehype, CodeMirror
Realtime & Cloud	Firebase (Auth, Firestore, RTDB), Cloudflare R2, Vercel Serverless

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Getting Started

Prerequisites

• Node.js 20+
• npm 10+

Quickstart

# Clone the repository
git clone https://github.com/CreatorSaWiX/apunts-pro2.git
cd apunts-pro2

# Install dependencies
npm install

# Start development server
npm run dev

Production Build

# Compile and verify type integrity
npm run build

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Engineering Standards

• Strict Type Invariants: Zero compilation errors under tsc -b.
• Fault Isolation: Sandboxed error boundaries prevent sub-component failures from bubbling to root views.
• Allocation Economy: Cache-first data structures (Set, Map, Min-Heap) prioritized over repeated array allocations in performance-critical loops.

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License

MIT © CreatorSaWiX