A lightweight C++ math library for vectors and matrices, designed for game hacking and real-time applications.

MATHESIS

Lightweight C++ math library for game hacking, provides vector and matrix types (2D, 3D, 4D) with common operations like dot, cross, normalization, distance, lerp, and more. Designed to be header-only, minimal, and memory-friendly for direct use with game engines or memory manipulation.

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Features

This library is header-only and depends only on <cmath>, <ostream>, and <algorithm>. It is fully C++17-ready (using std::clamp), but can be adapted for earlier standards by replacing it with min/max. The API is consistent across vector2, vector3, vector4, and a simple matrix type.

Vectors

All vector types come with constructors for zero-initialization or component-wise initialization. Arithmetic is supported in a natural way: you can add, subtract, multiply, or divide vectors element-wise, and scale them with floats on either side (vec * s or s * vec). Compound assignments like +=, -=, *=, and /= are also provided, along with unary negation.

Equality and inequality are defined as exact float comparisons (you can swap in an epsilon check if you need fuzzy math). Each vector supports dot() products, and cross() is available as well: in 3D it returns another vector, while in 2D it gives a scalar representing the signed area. You also get length(), length_squared(), normalized() (copy), and normalize() (in-place).

For convenience, utility methods like distance(), lerp(), and clamp() are included, along with operator<< for easy printing.

Matrix

The matrix type is a very simple struct:

struct matrix
{
    float mvp_matrix[16];
};

It’s just a contiguous 16-float array, which makes it trivial to upload to a GPU or pass into graphics APIs. The struct can easily be extended with identity, perspective, transform builders, or with matrix * vector / matrix * matrix operations.

Example

vector3 a{1,2,3}, b{4,5,6};
auto c = a + b;                 // (5,7,9)
auto h = a * b;                 // Hadamard: (4,10,18)
float d = a.dot(b);             // 32
auto x = a.cross(b);            // (-3,6,-3)
auto n = a.normalized();        // unit-length copy

Tip: For float equality, consider replacing == with an epsilon-based comparison to avoid precision pitfalls.

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