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πŸ“½ Highly Optimized Graphics Math (glm) for C
.package(url: "https://github.com/recp/cglm.git", from: "v0.8.3")

πŸŽ₯ OpenGL Mathematics (glm) for C

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Highly optimized 2D|3D math library, also known as OpenGL Mathematics (glm) for `C`. cglm provides lot of utils to help math operations to be fast and quick to write. It is community friendly, feel free to bring any issues, bugs you faced.

πŸ“š Documentation

Almost all functions (inline versions) and parameters are documented inside the corresponding headers.
Complete documentation: http://cglm.readthedocs.io

πŸ“Œ Note for previous versions:

  • _dup (duplicate) is changed to _copy. For instance glm_vec_dup -> glm_vec3_copy
  • OpenGL related functions are dropped to make this lib platform/third-party independent
  • make sure you have latest version and feel free to report bugs, troubles
  • [bugfix] euler angles was implemented in reverse order (extrinsic) it was fixed, now they are intrinsic. Make sure that you have the latest version
  • [major change] by starting v0.4.0, quaternions are stored as [x, y, z, w], it was [w, x, y, z] in v0.3.5 and earlier versions
  • [api rename] by starting v0.4.5, glm_simd functions are renamed to glmm_
  • [new option] by starting v0.4.5, you can disable alignment requirement, check options in docs.
  • [major change] by starting v0.5.0, vec3 functions use glm_vec3_ namespace, it was glm_vec_ until v0.5.0
  • [major change] by starting v0.5.1, built-in alignment is removed from vec3 and mat3 types
  • [major change] by starting v0.7.3, inline print functions are disabled in release/production mode to eliminate print costs (see options in documentation). Print output also improved. You can disable colors if you need (see documentation)
  • [major change] by starting v0.8.3, cglm supports alternative clipspace configuations e.g. Left Handed, Zero-to-One (_zo)... CGLM_FORCE_DEPTH_ZERO_TO_ONE and CGLM_FORCE_LEFT_HANDED is provided to control clipspace. You should be able to use cglm with Vulkan, DirectX and Metal now... see https://cglm.readthedocs.io/en/latest/opt.html#clipspace-option-s

πŸ“Œ Note for C++ developers:

If you are not aware of the original GLM library yet, you may also want to look at: https://github.com/g-truc/glm

πŸ“Œ Note for new comers (Important):

  • vec4 and mat4 variables must be aligned. (There will be unaligned versions later)
  • in and [in, out] parameters must be initialized (please). But [out] parameters not, initializing out param is also redundant
  • All functions are inline if you don't want to use pre-compiled versions with glmc_ prefix, you can ignore build process. Just include headers.
  • if your debugger takes you to cglm headers then make sure you are not trying to copy vec4 to vec3 or alig issues...
  • Welcome!

πŸ“Œ Note for experienced developers:

  • Since I'm testing this library in my projects, sometimes bugs occurs; finding that bug[s] and making improvements would be more easy with multiple developer/contributor and their projects or knowledge. Consider to make some tests if you suspect something is wrong and any feedbacks, contributions and bug reports are always welcome.

πŸ“Œ Allocations?

cglm doesn't alloc any memory on heap. So it doesn't provide any allocator. You should alloc memory for out parameters too if you pass pointer of memory location. Don't forget that vec4 (also quat/versor) and mat4 must be aligned (16-bytes), because cglm uses SIMD instructions to optimize most operations if available.

πŸ“Œ Returning vector or matrix... ?

cglm supports both ARRAY API and STRUCT API, so you can return structs if you utilize struct api (glms_).

Like some other graphics libraries (especially OpenGL) this library use Column-Major layout to keep matrices in the memory.
In the future the library may support an option to use row-major layout, CURRENTLY if you need to row-major layout you will need to transpose it.

πŸš€ Features

  • scalar and simd (sse, avx, neon...) optimizations
  • option to use different clipspaces e.g. Left Handed, Zero-to-One... (currrently right handed negative-one is default)
  • array api and struct api, you can use arrays or structs.
  • general purpose matrix operations (mat4, mat3)
  • chain matrix multiplication (square only)
  • general purpose vector operations (cross, dot, rotate, proj, angle...)
  • affine transformations
  • matrix decomposition (extract rotation, scaling factor)
  • optimized affine transform matrices (mul, rigid-body inverse)
  • camera (lookat)
  • projections (ortho, perspective)
  • quaternions
  • euler angles / yaw-pitch-roll to matrix
  • extract euler angles
  • inline or pre-compiled function call
  • frustum (extract view frustum planes, corners...)
  • bounding box (AABB in Frustum (culling), crop, merge...)
  • bounding sphere
  • project, unproject
  • easing functions
  • curves
  • curve interpolation helpers (SMC, deCasteljau...)
  • helpers to convert cglm types to Apple's simd library to pass cglm types to Metal GL without packing them on both sides
  • ray intersection helpers
  • and others...

You have two options to call a function/operation: inline or library call (link) Almost all functions are marked inline (always_inline) so compiler will probably inline. To call pre-compiled versions, just use glmc_ (c stands for 'call') instead of glm_.

  #include <cglm/cglm.h>   /* for inline */
  #include <cglm/call.h>   /* for library call (this also includes cglm.h) */

  mat4 rot, trans, rt;
  /* ... */
  glm_mul(trans, rot, rt);  /* inline */
  glmc_mul(trans, rot, rt); /* call from library */

Most of math functions are optimized manualy with SSE2 if available, if not? Dont worry there are non-sse versions of all operations

You can pass matrices and vectors as array to functions rather than get address.

  mat4 m = {
    1, 0, 0, 0,
    0, 1, 0, 0,
    0, 0, 1, 0,
    0, 0, 0, 1

  glm_translate(m, (vec3){1.0f, 0.0f, 0.0f});

Library contains general purpose mat4 mul and inverse functions, and also contains some special forms (optimized) of these functions for affine transformations' matrices. If you want to multiply two affine transformation matrices you can use glm_mul instead of glm_mat4_mul and glm_inv_tr (ROT + TR) instead glm_mat4_inv

/* multiplication */
mat4 modelMat;
glm_mul(T, R, modelMat);

/* othonormal rot + tr matrix inverse (rigid-body) */

Struct API

The struct API works as follows, note the s suffix on types, the glms_ prefix on functions and the GLMS_ prefix on constants:

#include <cglm/struct.h>

mat4s inv = glms_mat4_inv(mat);

Struct functions generally take their parameters as values and return their results, rather than taking pointers and writing to out parameters. That means your parameters can usually be const, if you're into that.

The types used are actually unions that allow access to the same data multiple ways. One of those ways involves anonymous structures, available since C11. MSVC also supports it for earlier C versions out of the box and GCC/Clang do if you enable -fms-extensions. To explicitly enable these anonymous structures, #define CGLM_USE_ANONYMOUS_STRUCT to 1, to disable them, to 0. For backward compatibility, you can also #define CGLM_NO_ANONYMOUS_STRUCT (value is irrelevant) to disable them. If you don't specify explicitly, cglm will do a best guess based on your compiler and the C version you're using.

πŸ”¨ Build

CMake (All platforms)

$ mkdir build
$ cd build
$ cmake .. # [Optional] -DCGLM_SHARED=ON
$ make
$ sudo make install # [Optional]
Cmake options with Defaults:
option(CGLM_SHARED "Shared build" ON)
option(CGLM_STATIC "Static build" OFF)
option(CGLM_USE_C99 "" OFF) #Β C11 
option(CGLM_USE_TEST "Enable Tests" OFF) #Β for make check - make test

Use as header-only library with your CMake project

This requires no building or installation of cglm.

  • Example:
cmake_minimum_required(VERSION 3.8.2)

project(<Your Project Name>)

add_executable(${PROJECT_NAME} src/main.c)
target_link_libraries(${LIBRARY_NAME} PRIVATE

add_subdirectory(external/cglm/ EXCLUDE_FROM_ALL)

Use with your CMake project

  • Example:
cmake_minimum_required(VERSION 3.8.2)

project(<Your Project Name>)

add_executable(${PROJECT_NAME} src/main.c)
target_link_libraries(${LIBRARY_NAME} PRIVATE


# or you can use find_package to configure cglm

Meson (All platforms)

$ meson build # [Optional] --default-library=static
$ cd build
$ ninja
$ sudo ninja install # [Optional]
Meson options with Defaults:
enable_tests=false #Β to run tests: ninja test

Use with your Meson project

  • Example:
# Clone cglm or create a cglm.wrap under <source_root>/subprojects
project('name', 'c')

cglm_dep = dependency('cglm', fallback : 'cglm', 'cglm_dep')

executable('exe', 'src/main.c', dependencies : cglm_dep)

Swift (Swift Package Manager)

Currently only default build options are supported. Add cglm dependency to your project:

  dependencies: [
    .package(url: "https://github.com/recp/cglm", .branch("master")),

Now add cgml as a dependency to your target. Product choices are:

  • cglm for inlined version of the library which can be linked only statically
  • cglmc for a compiled version of the library with no linking limitation
  dependencies: [
    .product(name: "cglm", package: "cglm"),

Unix (Autotools)

$ sh autogen.sh
$ ./configure
$ make
$ make check # [Optional]
$ [sudo] make install # [Optional]

This will also install pkg-config files so you can use pkg-config --cflags cglm and pkg-config --libs cglm to retrieve compiler and linker flags.

The files will be installed into the given prefix (usually /usr/local by default on Linux), but your pkg-config may not be configured to actually check there. You can figure out where it's looking by running pkg-config --variable pc_path pkg-config and change the path the files are installed to via ./configure --with-pkgconfigdir=/your/path. Alternatively, you can add the prefix path to your PKG_CONFIG_PATH environment variable.

Windows (MSBuild)

Windows related build file and project files are located in win folder, make sure you are inside cglm/win folder. Code Analysis is enabled, so it may take awhile to build.

$ cd win
$ .\build.bat

if msbuild won't work (because of multi version VS) then try to build with devenv:

$ devenv cglm.sln /Build Release

Running Tests on Windows

You can see test project in same visual studio solution file. It is enough to run that project to run tests.

Building Docs

First you need install Sphinx: http://www.sphinx-doc.org/en/master/usage/installation.html then:

$ cd docs
$ sphinx-build source build

it will compile docs into build folder, you can run index.html inside that function.

How to use

If you want to use the inline versions of functions, then include the main header

#include <cglm/cglm.h>

the header will include all headers. Then call the func you want e.g. rotate vector by axis:

glm_vec3_rotate(v1, glm_rad(45), (vec3){1.0f, 0.0f, 0.0f});

some functions are overloaded :) e.g you can normalize vector:


this will normalize vec and store normalized vector into vec but if you will store normalized vector into another vector do this:

glm_vec3_normalize_to(vec, result);

like this function you may see _to postfix, this functions store results to another variables and save temp memory

to call pre-compiled versions include header with c postfix, c means call. Pre-compiled versions are just wrappers.

#include <cglm/call.h>

this header will include all headers with c postfix. You need to call functions with c posfix:


Function usage and parameters are documented inside related headers. You may see same parameter passed twice in some examples like this:

glm_mat4_mul(m1, m2, m1);

/* or */
glm_mat4_mul(m1, m1, m1);

the first two parameter are [in] and the last one is [out] parameter. After multiplying m1 and m2, the result is stored in m1. This is why we send m1 twice. You may store the result in a different matrix, this is just an example.

Example: Computing MVP matrix

Option 1

mat4 proj, view, model, mvp;

/* init proj, view and model ... */

glm_mat4_mul(proj, view, viewProj);
glm_mat4_mul(viewProj, model, mvp);

Option 2

mat4 proj, view, model, mvp;

/* init proj, view and model ... */

glm_mat4_mulN((mat4 *[]){&proj, &view, &model}, 3, mvp);

How to send matrix to OpenGL

mat4 is array of vec4 and vec4 is array of floats. glUniformMatrix4fv functions accecpts float* as value (last param), so you can cast mat4 to float* or you can pass first column of matrix as beginning of memory of matrix:

Option 1: Send first column

glUniformMatrix4fv(location, 1, GL_FALSE, matrix[0]);

/* array of matrices */
glUniformMatrix4fv(location, 1, GL_FALSE, matrix[0][0]);

Option 2: Cast matrix to pointer type (also valid for multiple dimensional arrays)

glUniformMatrix4fv(location, 1, GL_FALSE, (float *)matrix);

You can pass matrices the same way to other APIs e.g. Vulkan, DX...


  • This library uses float types only, does not support Integers, Double... yet
  • If headers are not working properly with your compiler, IDE please open an issue, because I'm using GCC and clang to test it maybe sometimes MSVC


  • ☐ Unit tests (In Progress)
  • ☐ Unit tests for comparing cglm with glm results
  • β˜‘ Add version info
  • ☐ Unaligned operations (e.g. glm_umat4_mul)
  • β˜‘ Extra documentation
  • β˜‘ ARM Neon Arch


This project exists thanks to all the people who contribute. [Contribute].


Thank you to all our backers! πŸ™ [Become a backer]


Support this project by becoming a sponsor. Your logo will show up here with a link to your website. [Become a sponsor]


MIT. check the LICENSE file


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Release Notes

v0.8.3: Clipspace Control and Performance Update
2 weeks ago

Major New Feature: Clipspace Control (https://github.com/recp/cglm/pull/198) πŸŽ‰

cglm now supports different clipspace configurations.

Many many thanks to @raedwulf and @michael-g to provide this feature to cglm which was in TODOs long time. There are missing tests for now but tests will or should be added as soon as possible. Also thanks to @hartenfels and @bwhmather fixing build files...



/* auto created in cglm */

New functions

Now there are _no, _zo, _lh, _rh... vesions of projection and view functions. No need to paste all of them here, they are placed in include/cglm/clipspace/, include/cglm/struct/clipspace/ and include/cglm/call/clipspace/ folders.

if CGLM_CLIPSPACE_INCLUDE_ALL is defined then all clipspace headers are icluded in cam.h or related main headers, otherwise only related clipspace headers will be included to avoid including unused headers...

New Features

Bugfix and Improvements

  • simd: optimize glm_mat4_zero() with simd
  • simd, sse: optimize mat4 inv with sse
    • reduce a few shufflees
    • re-oder instructions for ILP
  • simd, sse: optimize mat4 mul with sse
  • simd, sse: optimize mat4 mul-v with sse
  • arm neon: optimize mat4 mul with neon
  • arm neon: optimize affine with neon
  • sse: optimize affine with sse
  • sse: optimize glm_quat_mul with sse
  • sse: optimize glm_mat2_mul_sse2 with sse
  • sse2: optimize glm_mat3_mul_sse2() with sse2
  • simd, sse: reduce some computation at glm_mul_rot_sse2()
  • arm, neon: impove hadd performance
  • arm, neon: use negate instruction instead of xor in glm_inv_tr_neon()
  • style: rename nearVal, farVal to nearZ and farZ
  • https://github.com/recp/cglm/pull/192 fix function param type ( thanks to @Winter091 )
  • other improvements may not be mentioned here....

Sponsorship: Consider become a sponsor for cglm

Supporting cross platform, multiple OS-es and multiple CPUs requires multiple hardwares to test on it which requires extra financial cost. Also sparing time is another big issue while working at somewhere fulltime... Your company can become a sponsor to help:


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