GA-FuL Project Structure

🇩🇪 Deutsche Version

Table of Contents

  1. Overview
  2. Main Modules
  3. Directory Structure
  4. Dependencies
  5. Build Configuration

Overview

The GA-FuL project is divided into several modules, each providing specific functionalities. The structure follows the layered design of the library.

GeometricAlgebraFulcrumLib/
├── GeometricAlgebraFulcrumLib/          # Main folder with all modules
│   ├── GeometricAlgebraFulcrumLib.Algebra/
│   ├── GeometricAlgebraFulcrumLib.Modeling/
│   ├── GeometricAlgebraFulcrumLib.MetaProgramming/
│   ├── GeometricAlgebraFulcrumLib.Utilities.*/
│   ├── GeometricAlgebraFulcrumLib.Applications/
│   ├── GeometricAlgebraFulcrumLib.Mathematica/
│   ├── GeometricAlgebraFulcrumLib.Matlab/
│   └── ...
├── GeometricAlgebraFulcrumLib.Documentation/
├── GeometricAlgebraFulcrumLib.Visualizations/
├── docs/                                 # This documentation
├── assets/
├── README.adoc
└── LICENSE

Main Modules

Core Modules (Algebra Layer)

1. GeometricAlgebraFulcrumLib.Algebra

Purpose: Core algebra implementation

Main Components:

  • GeometricAlgebra/: GA operations and multivectors
    • Basis/: Basis blades and index sets
    • Dense/: Optimized dense implementation
    • Extended/: Extended GA (XGa)
    • Restricted/: Restricted GA (RGa)
  • ComplexAlgebra/: Complex numbers
  • LinearAlgebra/: Vectors, matrices, tensors
  • Scalars/: Scalar processors
  • GeometricFrequency/: Spectral analysis

Dependencies:

  • MathNet.Numerics
  • PeterO.Numbers
  • AngouriMath
  • NumpyDotNet

Important Classes:

GeometricAlgebra/
├── XGaProcessor<T>              # Main GA processor
├── XGaMultivector<T>            # Multivector
├── XGaKVector<T>                # k-vector
├── XGaBasisBlade               # Basis blade
├── XGaMetric                   # Metric definition
└── Composers/
    └── XGaMultivectorComposer<T>  # Multivector builder

2. GeometricAlgebraFulcrumLib.Utilities.Structures

Purpose: Basic data structures

Main Components:

  • IndexSets/: IIndexSet implementations
  • Dictionaries/: Optimized dictionary implementations
  • Collections/: Specialized collections
  • BitManipulation/: Bit operations for efficient index sets

Important Classes:

IndexSets/
├── IIndexSet                    # Interface
├── EmptyIndexSet               # Empty set
├── SingleIndexSet              # One element
├── UInt64IndexSet              # For dimension < 64
├── DenseIndexSet               # Dense array
└── SparseIndexSet              # Sparse hash set

3. GeometricAlgebraFulcrumLib.Utilities.Text

Purpose: Text and LaTeX generation

Main Components:

  • Text/: Formatted text generation
  • LaTeX/: LaTeX code composition
  • Parametric/: Template-based text generation
  • Files/: File and folder hierarchy creation

4. GeometricAlgebraFulcrumLib.Utilities.Code

Purpose: Code generation utilities

Main Components:

  • SyntaxTree/: Abstract Syntax Trees (AST)
  • Languages/: Language-specific code generators
  • Expressions/: Expression representations

5. GeometricAlgebraFulcrumLib.Utilities.Web

Purpose: Web graphics utilities

Main Components:

  • Svg/: SVG generation
  • Html/: HTML generation
  • JavaScript/: JavaScript code generation
  • BabylonJs/: Babylon.js integration

Modeling Modules

6. GeometricAlgebraFulcrumLib.Modeling

Purpose: Geometric modeling

Main Components:

  • Geometry/: Geometric objects
    • CGa/: Conformal Geometric Algebra
    • PGa/: Projective Geometric Algebra
    • Euclidean/: Euclidean geometry
  • Graphics/: Graphics primitives
  • Calculus/: Geometric calculus (in development)

Important Classes:

Geometry/
└── CGa/
    ├── CGaGeometricSpace5D<T>      # 5D CGA for 3D geometry
    ├── CGaGeometricSpace4D<T>      # 4D CGA for 2D geometry
    └── Encoding/
        ├── EncodeIpnsRound         # IPNS round objects
        ├── EncodeOpnsFlat          # OPNS flat objects
        └── Decode                  # Decoding

Metaprogramming Modules

7. GeometricAlgebraFulcrumLib.MetaProgramming

Purpose: Code generation and optimization

Main Components:

  • Context/: Meta context
  • Expressions/: Meta expressions
  • Composers/: Code composers
  • Optimizers/: Code optimizers
  • Applications/: Application examples

Important Classes:

MetaProgramming/
├── MetaContext                  # Main context
├── IMetaExpression              # Expression interface
├── MetaExpressionComposer       # Expression builder
├── CodeComposer                 # Code generator
└── Optimizers/
    ├── ConstantPropagation
    ├── CommonSubexpressionElimination
    └── GeneticProgramming

Integration Modules

8. GeometricAlgebraFulcrumLib.Mathematica

Purpose: Wolfram Mathematica integration

Main Components:

  • Processors/: Mathematica scalar processor
  • Expressions/: Mathematica expression wrapper
  • Utilities/: Helper functions

Dependencies:

  • Wolfram.NETLink

9. GeometricAlgebraFulcrumLib.Matlab

Purpose: MATLAB integration and toolbox

Main Components:

  • GA-FuL MATLAB Toolbox/: Complete MATLAB toolbox
  • Processors/: MATLAB scalar processor
  • CodeGeneration/: MATLAB code generation

Features:

  • MATLAB function generation
  • GA operations in MATLAB
  • Visualization

Application Modules

10. GeometricAlgebraFulcrumLib.Applications

Purpose: General application examples

Main Components:

  • Various application examples for GA-FuL
  • Demos and tutorials

11. GeometricAlgebraFulcrumLib.Applications.Symbolic

Purpose: Symbolic applications

Main Components:

  • Symbolic GA computations
  • Mathematica-based applications

12. GeometricAlgebraFulcrumLib.Samples.Generations

Purpose: Code generation examples

Main Components:

  • Code generation samples
  • Template examples

Additional Modules

13. GeometricAlgebraFulcrumLib.MonoGame

Purpose: MonoGame integration for games and graphics

14. GeometricAlgebraFulcrumLib.Stride

Purpose: Stride Game Engine integration

15. GeometricAlgebraFulcrumLib.Optimization

Purpose: Optimization algorithms

16. GeometricAlgebraFulcrumLib.Benchmarks

Purpose: Performance benchmarks

Tools:

  • BenchmarkDotNet
  • Performance tests

17. GeometricAlgebraFulcrumLib.UnitTests

Purpose: Unit tests

Framework:

  • xUnit or NUnit

Directory Structure

Typical Module Structure

GeometricAlgebraFulcrumLib.ModuleName/
├── GeometricAlgebraFulcrumLib.ModuleName.csproj
├── Namespace1/
│   ├── Class1.cs
│   ├── Class2.cs
│   └── Subfolder/
│       └── Class3.cs
├── Namespace2/
│   └── ...
└── Properties/
    └── AssemblyInfo.cs (optional)

Example: Algebra Module

GeometricAlgebraFulcrumLib.Algebra/
├── GeometricAlgebraFulcrumLib.Algebra.csproj
├── Scalars/
│   ├── IScalarProcessor.cs
│   ├── ScalarProcessorOfFloat64.cs
│   ├── ScalarProcessorOfFloat32.cs
│   └── ...
├── GeometricAlgebra/
│   ├── Basis/
│   │   ├── IIndexSet.cs
│   │   ├── XGaBasisBlade.cs
│   │   └── ...
│   ├── Extended/
│   │   ├── XGaProcessor.cs
│   │   ├── XGaMultivector.cs
│   │   ├── XGaKVector.cs
│   │   └── Composers/
│   │       └── XGaMultivectorComposer.cs
│   └── Restricted/
│       ├── RGaProcessor.cs
│       └── ...
├── LinearAlgebra/
│   ├── Vectors/
│   ├── Matrices/
│   └── Tensors/
└── ComplexAlgebra/
    └── ...

Dependencies

Dependency Graph

┌─────────────────────────────────────┐
│   Applications, Samples, Tests      │
└────────────┬────────────────────────┘
             │
┌────────────▼────────────────────────┐
│  MetaProgramming, Mathematica       │
└────────────┬────────────────────────┘
             │
┌────────────▼────────────────────────┐
│         Modeling                    │
└────────────┬────────────────────────┘
             │
┌────────────▼────────────────────────┐
│         Algebra                     │
└────────────┬────────────────────────┘
             │
┌────────────▼────────────────────────┐
│      Utilities (Text, Code,         │
│      Structures, Web)               │
└─────────────────────────────────────┘

NuGet Packages

Algebra Module:

<PackageReference Include="AngouriMath" Version="1.3.0" />
<PackageReference Include="MathNet.Numerics" Version="5.0.0" />
<PackageReference Include="PeterO.Numbers" Version="1.8.2" />
<PackageReference Include="NumpyDotNet" Version="0.9.87.2" />
<PackageReference Include="OxyPlot.Core" Version="2.2.0" />
<PackageReference Include="SixLabors.ImageSharp" Version="3.1.10" />
<PackageReference Include="EPPlus" Version="8.0.7" />
<PackageReference Include="Dew.Math" Version="6.2.3" />

Mathematica Module:

<Reference Include="Wolfram.NETLink" />

Build Configuration

.NET Configuration

All projects use:

<PropertyGroup>
    <TargetFramework>net8.0</TargetFramework>
    <LangVersion>latest</LangVersion>
    <Nullable>enable</Nullable>
    <ImplicitUsings>enable</ImplicitUsings>
</PropertyGroup>

Build Commands

Build entire solution:

cd GeometricAlgebraFulcrumLib
dotnet build GeometricAlgebraFulcrumLib.sln

Build specific project:

cd GeometricAlgebraFulcrumLib/GeometricAlgebraFulcrumLib.Algebra
dotnet build

Run tests:

cd GeometricAlgebraFulcrumLib/GeometricAlgebraFulcrumLib.UnitTests
dotnet test

Release build:

dotnet build -c Release

Naming Conventions

Assembly Names

Format: GeometricAlgebraFulcrumLib.<ModuleName>

Examples:

  • GeometricAlgebraFulcrumLib.Algebra
  • GeometricAlgebraFulcrumLib.Modeling
  • GeometricAlgebraFulcrumLib.MetaProgramming

Namespace Conventions

Format: GeometricAlgebraFulcrumLib.<ModuleName>.<SubNamespace>

Examples:

  • GeometricAlgebraFulcrumLib.Algebra.Scalars
  • GeometricAlgebraFulcrumLib.Algebra.GeometricAlgebra.Basis
  • GeometricAlgebraFulcrumLib.Modeling.Geometry.CGa

Class Prefixes

Prefix Meaning Example
XGa Extended GA XGaProcessor<T>
RGa Restricted GA RGaProcessor<T>
CGa Conformal GA CGaGeometricSpace5D<T>
PGa Projective GA PGaGeometricSpace<T>
Float64 64-bit float optimized RGaFloat64Multivector

Summary

The GA-FuL project structure:

✓ Modular: Clear separation of responsibilities ✓ Layered: From Utilities to Applications ✓ Extensible: Easy to add new modules ✓ Well organized: Consistent naming conventions ✓ Documented: Clear structure and dependencies

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