ComplexFieldGeometry: Complete Architectural & Conceptual Map (Updated)

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1. Overview

ComplexFieldGeometry is a real‑time, browser‑based visualization framework that builds and animates a grid of points connected by edges, enriched with scalar, vector, and tensor fields. It leverages:

• Three.js for 3D rendering
• dat.GUI for interactive parameter tuning
• Webpack/Babel for ES6+ module bundling and compatibility

Core Goals

• Modularity — Separate geometry computation, state management, visualization controls, and app bootstrap
• Extensibility — Support arbitrary fields, tensor visualizations, custom differential operators
• Performance — Spatial bucketing, incremental updates, debounced rendering, minimal GC pressure
• Interactivity — Real-time user control, animation toggles, scalar/vector/tensor visualizations

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2. High-Level Project Structure

src/
├── index.html              ← HTML entrypoint
├── index.js                ← App bootstrap & render loop
├── complex-field-geometry.js ← Geometry engine (vertices, edges, fields)
├── field-manager.js        ← Field abstraction layer (scalar, vector, tensor fields)
├── visualization.js        ← dat.GUI setup + visualization helpers
├── state-store.js          ← Centralized parameter store + flags
├── logger.js               ← Timestamped logger (init, update hooks)

build/
├── .babelrc                ← ES6+ transpilation
├── webpack.config.js       ← Module bundling, dev server
├── package.json            ← Scripts, dependencies
└── package-lock.json       ← Resolved deps tree

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3. Core Modules & Classes

3.1 Tensor

• Purpose: N‑dimensional numerical array with fast access via strides
• Members:
  • dimensions: number[]
  • data: Float32Array
  • strides: number[]
• Methods:
  • .getValue(...indices)
  • .setValue(value, ...indices)

3.2 EnhancedVertex

Encapsulates geometry, visual mesh, field data, and user-defined functions.

• Properties:

  • id: number
  • position: THREE.Vector3
  • vector: THREE.Vector3
  • tensor: Tensor | null
  • functions: Map<string, Function>
  • properties: Map<string, any>
  • mesh: THREE.Mesh

• Methods:

  • .setVector(x, y, z)
  • .setTensor(dimensions, data)
  • .addFunction(name, fn) / .evaluateFunction(name, args)
  • .setProperty(name, value) / .getProperty(name)
  • .updateVisual(material)

3.3 Edge

Undirected connection with geometric and field data.

• Properties:

  • from, to: EnhancedVertex
  • distance: number
  • properties: Map<string, any>
  • line: THREE.Line

• Methods:

  • .updateDistance()
  • .setProperty(name, value) / .getProperty(name)
  • .updateVisual(material)

3.4 ComplexFieldGeometry

Main class managing all geometry, stateful fields, and rendering groups.

• Properties:
  • vertices: EnhancedVertex[]
  • edges: Edge[]
  • mesh: THREE.Group
  • fields: Map<string, Map<vertexId, value>>
  • geometryCache: SphereGeometry, LineMaterial, etc.
  • vertexMap, adjacencyMap
  • nextVertexId

Lifecycle Methods:

• createBaseGeometry(stateStore)
• disposeGeometry()
• createFields()
• update(stateStore)
• updateFields()

Differential Operators:

• computeDifferentialField(name, derivationFn)
• computeGradient(fieldName, newFieldName)
• (planned) computeCurl, computeLaplacian, computeDivergence

Visualization:

• visualizeScalarField(name) → color mapping (HSL)
• visualizeVectorField(name) → arrow glyphs
• visualizeTensorComponent() → tensor entry/determinant visualized
• animateVertices() → centralized animation hook (debounced) ✅ COMPLETED

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4. FieldManager

Abstraction layer for managing scalar/vector/tensor fields:

• Stores per-field metadata: domain, color mapping, normalization
• Delegates to ComplexFieldGeometry to apply visuals
• Plans for legend rendering & field selector UI components

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5. GUI & User Interactions (visualization.js)

Powered by dat.GUI with folders:

• Grid: gridSize, spacing
• Visual: pointSize, pointColor, lineColor
• Metrics: maxDistance, dimensionality
• Fields: selector, compute buttons
• Animation: enableAnimation, timeSlice, etc.
• Tensor: entry selector (0,0…det)

Callbacks:

• Changes set stateStore.needsUpdate = true
• Compute buttons trigger field updates
• Debounced GUI sync to minimize excessive update calls

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6. Application Bootstrap & Runtime (index.js)

init()

• Sets up Logger, StateStore, Scene, Camera, Renderer, Controls, Clock
• Creates ComplexFieldGeometry → adds mesh → calls createBaseGeometry()
• Runs setupGUI() and adds event listeners

animate()

• requestAnimationFrame(animate)
• Handles camera damping, time updates
• If stateStore.needsUpdate, call geometry.update()
• If enableAnimation, call animateVertices()
• renderer.render()

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7. Build Toolchain

• Webpack + Babel targeting modern browsers
• babel-loader, css-loader, asset modules
• DevServer with hot module reload
• Scripts:
  • npm run dev / npm start
  • npm run build

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8. Core Concepts & Optimizations

• Spatial Bucketing → O(N) neighbor search for efficient adjacency calculation
• Incremental Updates → separate flags for mesh rebuilds vs. field updates
• Debouncing → GUI updates & render triggers to prevent redundant operations
• Field Abstraction → scalar/vector/tensor fields as maps + metadata
• Animation → time-driven function modulation per vertex
• Tensor Visualization → component-specific & determinant coloring
• Logger → timestamped events for init, updates, and profiling

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9. High-Priority Performance Improvements ✅

9.1 Debouncing/Batching (COMPLETED)

Status: ✅ IMPLEMENTED

Implemented update debouncing to prevent redundant update() and createBaseGeometry() calls:

let updateQueued = false;
function scheduleUpdate() {
  if (!updateQueued) {
    updateQueued = true;
    requestAnimationFrame(() => {
      update();
      updateQueued = false;
    });
  }
}

Benefits:

• Eliminates multiple redundant updates per second
• Batches related parameter changes into single update calls
• Significantly reduces computational waste from repeated identical parameter changes

9.2 Material-Only Updates (IMPLEMENTED)

Status: ✅ IMPLEMENTED

Added intelligent update detection to skip geometry rebuild for material-only changes:

function update(params) {
  if (params.onlyAffectMaterial) {
    applyMaterialChanges(params);
    return;
  }
  createBaseGeometry();
}

Benefits:

• Color changes (pointColor, lineColor) no longer trigger full geometry rebuilds
• Vastly improved performance for visual-only parameter adjustments
• Cleaner separation between structural and aesthetic updates

9.3 Profiling Hooks for Heavy Computations (IMPLEMENTED)

Status: ✅ IMPLEMENTED

Added performance monitoring for gradient field computations and other heavy operations:

console.time("Gradient Field Computation");
computeGradientField();
console.timeEnd("Gradient Field Computation");

Benefits:

• Visibility into computation bottlenecks
• Performance tracking as grid size scales (100 → 169+ vertices)
• Foundation for future Web Worker optimization
• DevTools integration for main thread blocking detection

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10. Pending Issues & Further Improvements

Area	Description	Priority
Update Invalidation Granularity	Add per-feature flags: needsMeshRebuild, needsRecolorOnly, needsMaterialRefresh, etc.	Medium
Vector Field Rendering	Implement arrow glyphs via GPU instancing or line meshes	High
Shader-Based Color Mapping	Move scalar color mapping into fragment shader for performance	Medium
User Field Import	Support CSV/JSON loading to override sin/cos analytic defaults	Low
Unit Tests	Tensor ops, field computations, differential correctness tests	Medium
TensorVisualizer	Encapsulate component selection, normalization, legend	Medium
Web Worker Integration	Move heavy gradient computations off main thread	High
Volumetric 3D Support	Expand to full 3D lattices (x,y,z), 3D adjacency, slicing controls	Low

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11. Performance Profiling & Monitoring

Current Metrics

• Grid scaling: 100 → 169+ vertices successfully tested
• Gradient field computation time: monitored via console profiling
• Update frequency: reduced from multiple/second to batched updates

Monitoring Tools

• performance.now() timing logs
• Console.time/timeEnd for heavy computations
• DevTools markers for main thread analysis
• Update frequency tracking

Future Optimizations

• GPU Offloading: Shader-based computations, InstancedMesh
• Web Workers: Gradient and differential operator computations
• Memory Pooling: Reduce GC pressure in animation loops
• LOD System: Level-of-detail for large grids

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12. Completed Tasks ✅

Task	Status	Description
Duplicate animateVertices Refactor	✅ COMPLETED	Consolidated animation logic into geometry.animateVertices()
Debouncing/Batching Implementation	✅ COMPLETED	Implemented scheduleUpdate() with requestAnimationFrame batching
Material-Only Update Detection	✅ COMPLETED	Added onlyAffectMaterial check to skip geometry rebuilds
Profiling Hooks	✅ COMPLETED	Added performance monitoring for heavy computations

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13. Summary

ComplexFieldGeometry is a modular, extensible, and high-performance framework for real-time field visualization. Recent improvements have significantly enhanced performance through intelligent update batching, material-only change detection, and comprehensive profiling hooks.

The framework elegantly integrates mathematical structure (fields, tensors, differential operators), rendering architecture (Three.js, optimized geometry), and UI control (dat.GUI), making it suitable for:

• Scientific Visualization: Real-time field analysis and differential operator visualization
• Educational Tools: Interactive mathematical concept demonstration
• Simulation Frontends: High-performance data visualization for computational results

Continued development should focus on GPU acceleration, Web Worker integration for heavy computations, and expanding vector field visualization capabilities while maintaining the modular architecture that enables easy extension and customization.