Prowl.Vector 3D Mathematics

A comprehensive mathematics library (Built for the Prowl Game Engine). The library is designed for 64-bit 3D applications, it provides vector operations, matrix transformations, and geometric utilities. The API itself is heavily inspired by the Unity Game Engine.

Features

• Core Type

  • Vector2/Vector2Int
  • Vector3/Vector3Int
  • Vector4/Vector4Int
  • Bool3 (Memory-efficient 3-boolean structure)
  • Matrix4x4
  • Quaternion
  • Bounds
  • Bounding Frustrum
  • Rect/IntRect
  • Random (Comprehensive random functions)
  • Ray
  • Plane
  • Less than 3k lines of executable code!

• Vector Operations

  • Basic arithmetic (add, subtract, multiply, divide)
  • Dot and cross products
  • Normalization and magnitude calculations
  • Linear interpolation (Lerp)
  • Min/Max operations
  • Distance calculations
  • Vector transformations
  • And More!

• Matrix Operations

  • Creation of view and projection matrices
  • Translation, rotation, and scaling transformations
  • Matrix multiplication and inversion
  • Billboard and constrained billboard creation
  • Decomposition into translation/rotation/scale
  • And More!

• Quaternion Features

  • Euler angle conversions
  • Spherical interpolation (Slerp)
  • Rotation concatenation
  • Angular interpolation
  • Matrix conversions
  • And More!

• Other Noteable features

  • Comprehensive set of constants (π, τ, e, golden ratio)
  • Trigonometric functions
  • Interpolation functions
  • Geometric calculations
  • Angle conversions
  • Ray and line intersection tests
  • And Much More!

Usage

Basic Vector Operations

// Create vectors var v2 = new Vector2(1.0, 2.0); var v3 = new Vector3(1.0, 2.0, 3.0); var v4 = new Vector4(1.0, 2.0, 3.0, 4.0); // Vector arithmetic var sum = v3 + new Vector3(1.0, 1.0, 1.0); var scaled = v3 * 2.0; var normalized = v3.normalized; // Vector operations float dot = Vector3.Dot(v3, normalized); Vector3 cross = Vector3.Cross(v3, normalized); float distance = Vector3.Distance(v3, normalized);

Matrix transformations

// Create transformation matrices var translation = Matrix4x4.CreateTranslation(new Vector3(1, 2, 3)); var rotation = Matrix4x4.CreateRotationY(MathD.PI * 0.5); var scale = Matrix4x4.CreateScale(2.0); // Combine transformations var transform = translation * rotation * scale; // Transform vectors var transformed = Vector3.Transform(v3, transform);

Quaternion Rotations

// Create quaternions var rotation = Quaternion.CreateFromYawPitchRoll(yaw, pitch, roll); var fromAxis = Quaternion.AngleAxis(angle, axis); // Interpolate between rotations var interpolated = Quaternion.Slerp(q1, q2, t); // Apply rotation to vector var rotated = Vector3.Transform(v3, rotation);

Other Usefull Functions

// Generate random values float value = Random.Value; // Range [0,1] Vector2 circle = Random.OnUnitCircle; // Point on circle Vector3 sphere = Random.InUnitSphere; // Point in sphere Quaternion rotation = Random.Rotation; // Random rotation // Quick conversions between Radiens and Degrees float degree = radian.ToDeg(); float radian = degree.ToRad(); // Line intersection bool intersects = MathD.DoesLineIntersectLine(start1, end1, start2, end2, out Vector2 intersection); // Ray-triangle intersection bool hits = MathD.RayIntersectsTriangle(rayOrigin, rayDir, v1, v2, v3, out Vector3 hitPoint); // Point in triangle test bool inside = MathD.IsPointInTriangle(point, v1, v2, v3);

License

This component is part of the Prowl Game Engine and is licensed under the MIT License. See the LICENSE file in the project root for details.