Simple header-only mathematics library

Description

A collection of mathematical classes and functions I use. The library is mainly a learning tool.

The library contains:

• 2d/3d/4d float vector classes and a 4d float matrix class: vec2, vec3, vec4, mat4x4
• templated 2d vector class tvec2<T>
• planes and lines: plane, line<T> (with specializations for 3d and 4d lines line3, line4) and create_line for obtaining a line through two points
• special matrices, e.g. for projections, translation, scaling and rotation: namespace matrices
• convenient names for fixed-point types from the compositional numeric library (fixed_t for 15.16 signed fixed-point, fixed_24_8_t for signed 23.8 fixed-point and fixed_28_4_t for signed 27.4 fixed-point) and some utility functions (integral_part, round, to_float and truncate_unchecked)
• fixed-point 2d vector class using the compositional numeric library: vec2_fixed
• a fixed-point representation of the (closed) unit interval [0,1]: fixed_32_t
• linear interpolation for general types (lerp), clamp vector components to unit interval (clamp_to_unit_interval), number truncation (truncate_unchecked, only for positive numbers).

Dependencies

By default, the main library header ml/all.h will also include some C++ math headers, some boost math headers and parts of the compositional numeric library (CNL). This behavior can be disabled by defining ML_NO_DEPS before including all.h, and a fine-grain control is provided by the switches ML_NO_CPP, ML_NO_BOOST, ML_NO_CNL.

The tests rely on the Boost.Test framework.

Setup

As a header-only library, just include all.h (note that CNL 1.1.2 needs a C++17 compatible tool chain, and the master branch needs a C++20 compatible tool chain).

By default, SSE versions of the functions and classes are used. Set ML_NO_SIMD to use non-SSE versions. Set ML_INCLUDE_SIMD to include both SSE and non-SSE versions of vec4 and mat4x4 (the SSE versions are found in the namespace simd). Currently the library uses up to SSE 4.1.

The library defines functions to access vector components similar to swizzle notation. This may increase build times and binary sizes and can be disabled by defining ML_NO_SWIZZLE before including all.h.

To build the tests, first run ./scripts/pre-build.sh from the root folder, which creates the build directory structure and downloads CNL, release 1.1.2. Then run ./scripts/build.sh from the root folder. The tests are written into the bin-directory.

Tested on Linux, GCC 10.2 (with C++17 enabled), CMake 3.19.6.

References and other libraries

• Compositional Numeric Library
• glm
• DirectXMath