FixedMathSharp

A high-precision, deterministic fixed-point math library for .NET.
Ideal for simulations, games, and physics engines requiring reliable arithmetic without floating-point inaccuracies.

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🛠️ Key Features

• Deterministic Calculations: Perfect for simulations, multiplayer games, and physics engines.
• High Precision Arithmetic: Uses fixed-point math to eliminate floating-point inaccuracies.
• Comprehensive Vector Support: Includes 2D and 3D vector operations (Vector2d, Vector3d).
• Quaternion Rotations: Leverage FixedQuaternion for smooth rotations without gimbal lock.
• Matrix Operations: Supports transformations with Fixed4x4 and Fixed3x3 matrices.
• Bounding Shapes: Includes IBound structs BoundingBox, BoundingSphere, and BoundingArea for lightweight spatial calculations.
• Advanced Math Functions: Includes trigonometry and common math utilities.
• Unity Integration: Seamless interoperability with Unity using FixedMathSharp.Editor.

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🚀 Installation

Via NuGet:

dotnet add package FixedMathSharp

Testing Locally:

1. Build the package:

   dotnet pack --configuration Release

2. Create a local NuGet source and test it:

   mkdir ./LocalNuGet
   cp ./bin/Release/*.nupkg ./LocalNuGet/
   dotnet nuget add source ./LocalNuGet --name LocalNuGet
   dotnet add package FixedMathSharp --source ./LocalNuGet

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📖 Usage Examples

Basic Arithmetic with Fixed64:

Fixed64 a = new Fixed64(1.5);
Fixed64 b = new Fixed64(2.5);
Fixed64 result = a + b;
Console.WriteLine(result); // Output: 4.0

Vector Operations:

Vector3d v1 = new Vector3d(1, 2, 3);
Vector3d v2 = new Vector3d(4, 5, 6);
Fixed64 dotProduct = Vector3d.Dot(v1, v2);
Console.WriteLine(dotProduct); // Output: 32

Quaternion Rotation:

FixedQuaternion rotation = FixedQuaternion.FromAxisAngle(Vector3d.Up, FixedMath.PiOver2); // 90 degrees around Y-axis
Vector3d point = new Vector3d(1, 0, 0);
Vector3d rotatedPoint = rotation.Rotate(point);
Console.WriteLine(rotatedPoint); // Output: (0, 0, -1)

Matrix Transformations:

Fixed4x4 matrix = Fixed4x4.Identity;
Vector3d position = new Vector3d(1, 2, 3);
matrix.SetTransform(position, Vector3d.One, FixedQuaternion.Identity);
Console.WriteLine(matrix);

Bounding Shapes and Intersection

BoundingBox box = new BoundingBox(new Vector3d(0, 0, 0), new Vector3d(5, 5, 5));
BoundingSphere sphere = new BoundingSphere(new Vector3d(3, 3, 3), new Fixed64(1));
bool intersects = box.Intersects(sphere);
Console.WriteLine(intersects); // Output: True

Trigonometry Example:

Fixed64 angle = FixedMath.PiOver4; // 45 degrees
Fixed64 sinValue = FixedTrigonometry.Sin(angle);
Console.WriteLine(sinValue); // Output: ~0.707

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📦 Library Structure

• Fixed64 Struct: Represents fixed-point numbers for precise arithmetic.
• Vector2d and Vector3d Structs: Handle 2D and 3D vector operations.
• FixedQuaternion Struct: Provides rotation handling without gimbal lock, enabling smooth rotations and quaternion-based transformations.
• IBound Interface: Standard interface for bounding shapes BoundingBox, BoundingArea, and BoundingSphere, each offering intersection, containment, and projection logic.
• FixedMath Static Class: Provides common math functions.
• FixedTrigonometry Class: Offers trigonometric functions using fixed-point math.
• Fixed4x4 and Fixed3x3: Support matrix operations for transformations.
• FixedMathSharp.Editor: Extensions for seamless integration with Unity, including property drawers and type conversions.

Fixed64 Struct

Fixed64 is the core data type representing fixed-point numbers. It provides various mathematical operations, including addition, subtraction, multiplication, division, and more. The struct guarantees deterministic behavior by using integer-based arithmetic with a configurable SHIFT_AMOUNT.

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⚡ Performance Considerations

This library leverages inline methods and fixed-point arithmetic to ensure high precision without the pitfalls of floating-point numbers. It is optimized for deterministic behavior, making it ideal for physics engines, multiplayer simulations, and other time-sensitive applications.

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🧪 Testing and Validation

Unit tests are used extensively to validate the correctness of mathematical operations. Special fuzzy comparisons are employed where small precision discrepancies might occur, mimicking floating-point behavior.

To run the tests:

dotnet test --configuration Release

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🛠️ Compatibility

• .NET Framework: 4.7.1+
• Unity3D: Fully compatible with Unity using the FixedMathSharp.Editor extension.
• Platforms: Windows, Linux, macOS

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📄 License

This project is licensed under the MIT License - see the LICENSE file for details.

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👥 Contributors

• mrdav30 - Lead Developer
• Contributions are welcome! Feel free to submit pull requests or report issues.

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📧 Contact

For questions or support, reach out to mrdav30 via GitHub or open an issue in the repository.

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