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GLM 1.0.0 Manual

0. Licenses
1. Getting started
1.1. Using global headers
1.2. Using separated headers
1.3. Using extension headers
1.4. Dependencies
1.5. Finding GLM with CMake
2. Preprocessor configurations
2.1. GLM_FORCE_MESSAGES: Platform auto detection and default configuration
2.2. GLM_FORCE_PLATFORM_UNKNOWN: Force GLM to no detect the build platform
2.3. GLM_FORCE_COMPILER_UNKNOWN: Force GLM to no detect the C++ compiler
2.4. GLM_FORCE_ARCH_UNKNOWN: Force GLM to no detect the build architecture
2.5. GLM_FORCE_CXX_UNKNOWN: Force GLM to no detect the C++ standard
2.6. GLM_FORCE_CXX**: C++ language detection
2.7. GLM_FORCE_EXPLICIT_CTOR: Requiring explicit conversions
2.8. GLM_FORCE_INLINE: Force inline
2.9. GLM_FORCE_ALIGNED_GENTYPES: Force GLM to enable aligned types
2.10. GLM_FORCE_DEFAULT_ALIGNED_GENTYPES: Force GLM to use aligned types by default
2.11. GLM_FORCE_INTRINSICS: Using SIMD optimizations
2.12. GLM_FORCE_PRECISION_**: Default precision
2.13. GLM_FORCE_SINGLE_ONLY: Removed explicit 64-bits floating point types
2.14. GLM_FORCE_SWIZZLE: Enable swizzle operators
2.15. GLM_FORCE_XYZW_ONLY: Only exposes x, y, z and w components
2.16. GLM_FORCE_LEFT_HANDED: Force left handed coordinate system
2.17. GLM_FORCE_DEPTH_ZERO_TO_ONE: Force the use of a clip space between 0 to 1
2.18. GLM_FORCE_SIZE_T_LENGTH: Vector and matrix static size type
2.19. GLM_FORCE_UNRESTRICTED_GENTYPE: Removing genType restriction
2.20. GLM_FORCE_SILENT_WARNINGS: Silent C++ warnings from language extensions
2.21. GLM_FORCE_QUAT_DATA_WXYZ: Force GLM to store quat data as w,x,y,z instead of x,y,z,w
3. Stable extensions
3.1. Scalar types
3.2. Scalar functions
3.3. Vector types
3.4. Vector types with precision qualifiers
3.5. Vector functions
3.6. Matrix types
3.7. Matrix types with precision qualifiers
3.8. Matrix functions
3.9. Quaternion types
3.10. Quaternion types with precision qualifiers
3.11. Quaternion functions
4. Recommended extensions
4.1. GLM_GTC_bitfield
4.2. GLM_GTC_color_space
4.3. GLM_GTC_constants
4.4. GLM_GTC_epsilon
4.5. GLM_GTC_integer
4.6. GLM_GTC_matrix_access
4.7. GLM_GTC_matrix_integer
4.8. GLM_GTC_matrix_inverse
4.9. GLM_GTC_matrix_transform
4.10. GLM_GTC_noise
4.11. GLM_GTC_packing
4.12. GLM_GTC_quaternion
4.13. GLM_GTC_random
4.14. GLM_GTC_reciprocal
4.15. GLM_GTC_round
4.16. GLM_GTC_type_alignment
4.17. GLM_GTC_type_precision
4.18. GLM_GTC_type_ptr
4.19. GLM_GTC_ulp
4.20. GLM_GTC_vec1
5. OpenGL interoperability
5.1. GLM Replacements for deprecated OpenGL functions
5.2. GLM Replacements for GLU functions
6. Known issues
6.1. Not function
6.2. Precision qualifiers support
7. FAQ
7.1 Why GLM follows GLSL specification and conventions?
7.2. Does GLM run GLSL programs?
7.3. Does a GLSL compiler build GLM codes?
7.4. Should I use ‘GTX’ extensions?
7.5. Where can I ask my questions?
7.6. Where can I find the documentation of extensions?
7.7. Should I use 'using namespace glm;'?
7.8. Is GLM fast?
7.9. When I build with Visual C++ with /w4 warning level, I have warnings...
7.10. Why some GLM functions can crash because of division by zero?
7.11. What unit for angles us used in GLM?
7.12. Windows headers cause build errors...
7.13. Constant expressions support
8. Code samples
8.1. Compute a triangle normal
8.2. Matrix transform
8.3. Vector types
8.4. Lighting
9. Contributing to GLM
9.1. Submitting bug reports
9.2. Contributing to GLM with pull request
9.3. Coding style
10. References
10.1. OpenGL specifications
10.2. External links
10.3. Projects using GLM
10.4. Tutorials using GLM
10.5. Equivalent for other languages
10.6. Alternatives to GLM
10.7. Acknowledgements

Licenses

The Happy Bunny License (Modified MIT License)

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

Restrictions: By making use of the Software for military purposes, you choose to make a Bunny unhappy.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

The MIT License

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

1. Getting started

1.1. Using global headers

GLM is a header-only library, and thus does not need to be compiled. We can use GLM's implementation of GLSL's mathematics functionality by including the <glm/glm.hpp> header:

#include <glm/glm.hpp>

To extend the feature set supported by GLM and keeping the library as close to GLSL as possible, new features are implemented as extensions that can be included through a separate header:

// Include all GLM core / GLSL features
#include <glm/glm.hpp> // vec2, vec3, mat4, radians

// Include all GLM extensions
#include <glm/ext.hpp> // perspective, translate, rotate

glm::mat4 transform(glm::vec2 const& Orientation, glm::vec3 const& Translate, glm::vec3 const& Up)
{
    glm::mat4 Proj = glm::perspective(glm::radians(45.f), 1.33f, 0.1f, 10.f);
    glm::mat4 ViewTranslate = glm::translate(glm::mat4(1.f), Translate);
    glm::mat4 ViewRotateX = glm::rotate(ViewTranslate, Orientation.y, Up);
    glm::mat4 View = glm::rotate(ViewRotateX, Orientation.x, Up);
    glm::mat4 Model = glm::mat4(1.0f);
    return Proj * View * Model;
}

Note: Including <glm/glm.hpp> and <glm/ext.hpp> is convenient but pull a lot of code which will significantly increase build time, particularly if these files are included in all source files. We may prefer to use the approaches describe in the two following sections to keep the project build fast.

1.2. Using separated headers

GLM relies on C++ templates heavily, and may significantly increase compilation times for projects that use it. Hence, user projects could only include the features they actually use. Following is the list of all the core features, based on GLSL specification, headers:

#include <glm/vec2.hpp>               // vec2, bvec2, dvec2, ivec2 and uvec2
#include <glm/vec3.hpp>               // vec3, bvec3, dvec3, ivec3 and uvec3
#include <glm/vec4.hpp>               // vec4, bvec4, dvec4, ivec4 and uvec4
#include <glm/mat2x2.hpp>             // mat2, dmat2
#include <glm/mat2x3.hpp>             // mat2x3, dmat2x3
#include <glm/mat2x4.hpp>             // mat2x4, dmat2x4
#include <glm/mat3x2.hpp>             // mat3x2, dmat3x2
#include <glm/mat3x3.hpp>             // mat3, dmat3
#include <glm/mat3x4.hpp>             // mat3x4, dmat2
#include <glm/mat4x2.hpp>             // mat4x2, dmat4x2
#include <glm/mat4x3.hpp>             // mat4x3, dmat4x3
#include <glm/mat4x4.hpp>             // mat4, dmat4
#include <glm/common.hpp>             // all the GLSL common functions: abs, min, mix, isnan, fma, etc.
#include <glm/exponential.hpp>        // all the GLSL exponential functions: pow, log, exp2, sqrt, etc.
#include <glm/geometric.hpp>          // all the GLSL geometry functions: dot, cross, reflect, etc.
#include <glm/integer.hpp>            // all the GLSL integer functions: findMSB, bitfieldExtract, etc.
#include <glm/matrix.hpp>             // all the GLSL matrix functions: transpose, inverse, etc.
#include <glm/packing.hpp>            // all the GLSL packing functions: packUnorm4x8, unpackHalf2x16, etc.
#include <glm/trigonometric.hpp>      // all the GLSL trigonometric functions: radians, cos, asin, etc.
#include <glm/vector_relational.hpp>  // all the GLSL vector relational functions: equal, less, etc.

The following is a code sample using separated core headers and an extension:

// Include GLM core features
#include <glm/vec2.hpp>           // vec2
#include <glm/vec3.hpp>           // vec3
#include <glm/mat4x4.hpp>         // mat4
#include <glm/trigonometric.hpp>  //radians

// Include GLM extension
#include <glm/ext/matrix_transform.hpp>     // translate, rotate
#include <glm/ext/matrix_clip_space.hpp>    // perspective

glm::mat4 transform(glm::vec2 const& Orientation, glm::vec3 const& Translate, glm::vec3 const& Up)
{
    glm::mat4 Proj = glm::perspective(glm::radians(45.f), 1.33f, 0.1f, 10.f);
    glm::mat4 ViewTranslate = glm::translate(glm::mat4(1.f), Translate);
    glm::mat4 ViewRotateX = glm::rotate(ViewTranslate, Orientation.y, Up);
    glm::mat4 View = glm::rotate(ViewRotateX, Orientation.x, Up);
    glm::mat4 Model = glm::mat4(1.0f);
    return Proj * View * Model;
}

1.3. Using extension headers

Using GLM through split headers to minimize the project build time:

// Include GLM vector extensions:
#include <glm/ext/vector_float2.hpp>                // vec2
#include <glm/ext/vector_float3.hpp>                // vec3
#include <glm/ext/vector_trigonometric.hpp>         // radians

// Include GLM matrix extensions:
#include <glm/ext/matrix_float4x4.hpp>              // mat4
#include <glm/ext/matrix_transform.hpp>             // translate, rotate
#include <glm/ext/matrix_clip_space.hpp>            // perspective

glm::mat4 transform(glm::vec2 const& Orientation, glm::vec3 const& Translate, glm::vec3 const& Up)
{
    glm::mat4 Proj = glm::perspective(glm::radians(45.f), 1.33f, 0.1f, 10.f);
    glm::mat4 ViewTranslate = glm::translate(glm::mat4(1.f), Translate);
    glm::mat4 ViewRotateX = glm::rotate(ViewTranslate, Orientation.y, Up);
    glm::mat4 View = glm::rotate(ViewRotateX, Orientation.x, Up);
    glm::mat4 Model = glm::mat4(1.0f);
    return Proj * View * Model;
}

1.4. Dependencies

GLM does not depend on external libraries or headers such as <GL/gl.h>, <GL/glcorearb.h>, <GLES3/gl3.h>, <GL/glu.h>, or <windows.h>.

1.5. Finding GLM with CMake

When installed, GLM provides the CMake package configuration files glmConfig.cmake and glmConfigVersion.cmake.

To use these configurations files, you may need to set the glm_DIR variable to the directory containing the configuration files <installation prefix>/lib/cmake/glm/.

Use the find_package CMake command to load the configurations into your project. Lastly, either link your executable against the glm::glm target or add ${GLM_INCLUDE_DIRS} to your target's include directories:

set(glm_DIR <installation prefix>/lib/cmake/glm) # if necessary
find_package(glm REQUIRED)
target_link_libraries(<your executable> glm::glm)

To use GLM as a submodule in a project instead, use add_subdirectory to expose the same target, or add the directory to your target's

add_subdirectory(glm)
target_link_libraries(<your executable> glm::glm)
# or
target_include_directories(<your executable> glm)

2. Preprocessor configurations

2.1. GLM_FORCE_MESSAGES: Platform auto detection and default configuration

When included, GLM will first automatically detect the compiler used, the C++ standard supported, the compiler arguments used to configure itself matching the build environment.

For example, if the compiler arguments request AVX code generation, GLM will rely on its code path providing AVX optimizations when available.

We can change GLM configuration using specific C++ preprocessor defines that must be declared before including any GLM headers.

Using GLM_FORCE_MESSAGES, GLM will report the configuration as part of the build log.

#define GLM_FORCE_MESSAGES // Or defined when building (e.g. -DGLM_FORCE_SWIZZLE)
#include <glm/glm.hpp>

Example of configuration log generated by GLM_FORCE_MESSAGES:

GLM: version 0.9.9.1
GLM: C++ 17 with extensions
GLM: Clang compiler detected
GLM: x86 64 bits with AVX instruction set build target
GLM: Linux platform detected
GLM: GLM_FORCE_SWIZZLE is undefined. swizzling functions or operators are disabled.
GLM: GLM_FORCE_SIZE_T_LENGTH is undefined. .length() returns a glm::length_t, a typedef of int following GLSL.
GLM: GLM_FORCE_UNRESTRICTED_GENTYPE is undefined. Follows strictly GLSL on valid function genTypes.
GLM: GLM_FORCE_DEPTH_ZERO_TO_ONE is undefined. Using negative one to one depth clip space.
GLM: GLM_FORCE_LEFT_HANDED is undefined. Using right handed coordinate system.

The following subsections describe each configurations and defines.

2.2. GLM_FORCE_PLATFORM_UNKNOWN: Force GLM to no detect the build platform

GLM_FORCE_PLATFORM_UNKNOWN prevents GLM from detecting the build platform.

2.3. GLM_FORCE_COMPILER_UNKNOWN: Force GLM to no detect the C++ compiler

GLM_FORCE_COMPILER_UNKNOWN prevents GLM from detecting the C++ compiler.

2.4. GLM_FORCE_ARCH_UNKNOWN: Force GLM to no detect the build architecture

GLM_FORCE_ARCH_UNKNOWN prevents GLM from detecting the build target architecture.

2.5. GLM_FORCE_CXX_UNKNOWN: Force GLM to no detect the C++ standard

GLM_FORCE_CSS_UNKNOWN prevents GLM from detecting the C++ compiler standard support.

2.6. GLM_FORCE_CXX**: C++ language detection

GLM will automatically take advantage of compilers’ language extensions when enabled. To increase cross platform compatibility and to avoid compiler extensions, a programmer can define GLM_FORCE_CXX98 before any inclusion of <glm/glm.hpp> to restrict the language feature set C++98:

#define GLM_FORCE_CXX98
#include <glm/glm.hpp>

For C++11, C++14, and C++17 equivalent defines are available:

GLM_FORCE_CXX11
GLM_FORCE_CXX14
GLM_FORCE_CXX17

#define GLM_FORCE_CXX11
#include <glm/glm.hpp>

// If the compiler doesn’t support C++11, compiler errors will happen.

GLM_FORCE_CXX17 overrides GLM_FORCE_CXX14; GLM_FORCE_CXX14 overrides GLM_FORCE_CXX11; and GLM_FORCE_CXX11 overrides GLM_FORCE_CXX98 defines.

2.7. GLM_FORCE_EXPLICIT_CTOR: Requiring explicit conversions

GLSL supports implicit conversions of vector and matrix types. For example, an ivec4 can be implicitly converted into vec4.

Often, this behaviour is not desirable but following the spirit of the library, this is the default behavior in GLM. However, GLM 0.9.6 introduced the define GLM_FORCE_EXPLICIT_CTOR to require explicit conversion for GLM types.

#include <glm/glm.hpp>

void foo()
{
    glm::ivec4 a;
    ...

    glm::vec4 b(a); // Explicit conversion, OK
    glm::vec4 c = a; // Implicit conversion, OK
    ...
}

With GLM_FORCE_EXPLICIT_CTOR define, implicit conversions are not allowed:

#define GLM_FORCE_EXPLICIT_CTOR
#include <glm/glm.hpp>

void foo()
{
    glm::ivec4 a;
    {
        glm::vec4 b(a); // Explicit conversion, OK
        glm::vec4 c = a; // Implicit conversion, ERROR
        ...
}

2.8. GLM_FORCE_INLINE: Force inline

To push further the software performance, a programmer can define GLM_FORCE_INLINE before any inclusion of <glm/glm.hpp> to force the compiler to inline GLM code.

#define GLM_FORCE_INLINE
#include <glm/glm.hpp>

2.9. GLM_FORCE_ALIGNED_GENTYPES: Force GLM to enable aligned types

Every object type has the property called alignment requirement, which is an integer value (of type std::size_t, always a power of 2) representing the number of bytes between successive addresses at which objects of this type can be allocated. The alignment requirement of a type can be queried with alignof or std::alignment_of. The pointer alignment function std::align can be used to obtain a suitably-aligned pointer within some buffer, and std::aligned_storage can be used to obtain suitably-aligned storage.

Each object type imposes its alignment requirement on every object of that type; stricter alignment (with larger alignment requirement) can be requested using C++11 alignas.

In order to satisfy alignment requirements of all non-static members of a class, padding may be inserted after some of its members.

GLM supports both packed and aligned types. Packed types allow filling data structure without inserting extra padding. Aligned GLM types align addresses based on the size of the value type of a GLM type.

#define GLM_FORCE_ALIGNED_GENTYPES
#include <glm/glm.hpp>
#include <glm/gtc/type_aligned.hpp>

typedef glm::aligned_vec4 vec4a;
typedef glm::packed_vec4 vec4p;

2.10. GLM_FORCE_DEFAULT_ALIGNED_GENTYPES: Force GLM to use aligned types by default

GLM allows using aligned types by default for vector types using GLM_FORCE_DEFAULT_ALIGNED_GENTYPES:

#define GLM_FORCE_DEFAULT_ALIGNED_GENTYPES
#include <glm/glm.hpp>

struct MyStruct
{
    glm::vec4 a;
    float b;
    glm::vec3 c;
};

void foo()
{
    printf("MyStruct requires memory padding: %d bytes\n", sizeof(MyStruct));
}

>>> MyStruct requires memory padding: 48 bytes

#include <glm/glm.hpp>

struct MyStruct
{
    glm::vec4 a;
    float b;
    glm::vec3 c;
};

void foo()
{
    printf("MyStruct is tightly packed: %d bytes\n", sizeof(MyStruct));
}

>>> MyStruct is tightly packed: 32 bytes

Note: GLM SIMD optimizations require the use of aligned types

2.11. GLM_FORCE_INTRINSICS: Using SIMD optimizations

GLM provides some SIMD optimizations based on compiler intrinsics. These optimizations will be automatically thanks to compiler arguments when GLM_FORCE_INTRINSICS is defined before including GLM files. For example, if a program is compiled with Visual Studio using /arch:AVX, GLM will detect this argument and generate code using AVX instructions automatically when available.

It’s possible to avoid the instruction set detection by forcing the use of a specific instruction set with one of the fallowing define: GLM_FORCE_SSE2, GLM_FORCE_SSE3, GLM_FORCE_SSSE3, GLM_FORCE_SSE41, GLM_FORCE_SSE42, GLM_FORCE_AVX, GLM_FORCE_AVX2 or GLM_FORCE_AVX512.

The use of intrinsic functions by GLM implementation can be avoided using the define GLM_FORCE_PURE before any inclusion of GLM headers. This can be particularly useful if we want to rely on C++14 constexpr.

#define GLM_FORCE_PURE
#include <glm/glm.hpp>

static_assert(glm::vec4::length() == 4, "Using GLM C++ 14 constexpr support for compile time tests");

// GLM code will be compiled using pure C++ code without any intrinsics

#define GLM_FORCE_SIMD_AVX2
#include <glm/glm.hpp>

// If the compiler doesn’t support AVX2 intrinsics, compiler errors will happen.

Additionally, GLM provides a low level SIMD API in glm/simd directory for users who are really interested in writing fast algorithms.

2.12. GLM_FORCE_PRECISION_**: Default precision

C++ does not provide a way to implement GLSL default precision selection (as defined in GLSL 4.10 specification section 4.5.3) with GLSL-like syntax.

precision mediump int;
precision highp float;

To use the default precision functionality, GLM provides some defines that need to added before any include of glm.hpp:

#define GLM_FORCE_PRECISION_MEDIUMP_INT
#define GLM_FORCE_PRECISION_HIGHP_FLOAT
#include <glm/glm.hpp>

Available defines for floating point types (glm::vec\*, glm::mat\*):

GLM_FORCE_PRECISION_LOWP_FLOAT: Low precision
GLM_FORCE_PRECISION_MEDIUMP_FLOAT: Medium precision
GLM_FORCE_PRECISION_HIGHP_FLOAT: High precision (default)

Available defines for floating point types (glm::dvec\*, glm::dmat\*):

GLM_FORCE_PRECISION_LOWP_DOUBLE: Low precision
GLM_FORCE_PRECISION_MEDIUMP_DOUBLE: Medium precision
GLM_FORCE_PRECISION_HIGHP_DOUBLE: High precision (default)

Available defines for signed integer types (glm::ivec\*):

GLM_FORCE_PRECISION_LOWP_INT: Low precision
GLM_FORCE_PRECISION_MEDIUMP_INT: Medium precision
GLM_FORCE_PRECISION_HIGHP_INT: High precision (default)

Available defines for unsigned integer types (glm::uvec\*):

GLM_FORCE_PRECISION_LOWP_UINT: Low precision
GLM_FORCE_PRECISION_MEDIUMP_UINT: Medium precision
GLM_FORCE_PRECISION_HIGHP_UINT: High precision (default)

2.13. GLM_FORCE_SINGLE_ONLY: Removed explicit 64-bits floating point types

Some platforms (Dreamcast) doesn't support double precision floating point values. To compile on such platforms, GCC has the --m4-single-only build argument. When defining GLM_FORCE_SINGLE_ONLY before including GLM headers, GLM releases the requirement of double precision floating point values support. Effectivement, all the float64 types are no longer defined and double behaves like float.

2.14. GLM_FORCE_SWIZZLE: Enable swizzle operators

Shader languages like GLSL often feature so-called swizzle expressions, which may be used to freely select and arrange a vector's components. For example, variable.x, variable.xzy and variable.zxyy respectively form a scalar, a 3D vector and a 4D vector. The result of a swizzle expression in GLSL can be either an R-value or an L-value. Swizzle expressions can be written with characters from exactly one of xyzw (usually for positions), rgba (usually for colors), and stpq (usually for texture coordinates).

vec4 A;
vec2 B;

B.yx = A.wy;
B = A.xx;
vec3 C = A.bgr;
vec3 D = B.rsz; // Invalid, won't compile

GLM supports some of this functionality. Swizzling can be enabled by defining GLM_FORCE_SWIZZLE.

Note: Enabling swizzle expressions will massively increase the size of your binaries and the time it takes to compile them!

GLM has two levels of swizzling support described in the following subsections.

2.14.1. Swizzle functions for standard C++ 98

When compiling GLM as C++98, R-value swizzle expressions are simulated through member functions of each vector type.

#define GLM_FORCE_SWIZZLE // Or defined when building (e.g. -DGLM_FORCE_SWIZZLE)
#include <glm/glm.hpp>

void foo()
{
    glm::vec4 const ColorRGBA = glm::vec4(1.0f, 0.5f, 0.0f, 1.0f);
    glm::vec3 const ColorBGR = ColorRGBA.bgr();

    glm::vec3 const PositionA = glm::vec3(1.0f, 0.5f, 0.0f);
    glm::vec3 const PositionB = PositionXYZ.xyz() * 2.0f;

    glm::vec2 const TexcoordST = glm::vec2(1.0f, 0.5f);
    glm::vec4 const TexcoordSTPQ = TexcoordST.stst();
}

Swizzle operators return a copy of the component values, and thus can't be used as L-values to change a vector's values.

#define GLM_FORCE_SWIZZLE
#include <glm/glm.hpp>

void foo()
{
  glm::vec3 const A = glm::vec3(1.0f, 0.5f, 0.0f);

  // No compiler error, but A is not modified.
  // An anonymous copy is being modified (and then discarded).
  A.bgr() = glm::vec3(2.0f, 1.5f, 1.0f); // A is not modified!
}

2.14.2. Swizzle operations for C++ 98 with language extensions

Visual C++, GCC and Clang support, as a non-standard language extension, anonymous structs as union members. This permits a powerful swizzling implementation that both allows L-value swizzle expressions and GLSL-like syntax. To use this feature, the language extension must be enabled by a supporting compiler and GLM_FORCE_SWIZZLE must be #defined.

#define GLM_FORCE_SWIZZLE
#include <glm/glm.hpp>

// Only guaranteed to work with Visual C++!
// Some compilers that support Microsoft extensions may compile this.
void foo()
{
  glm::vec4 ColorRGBA = glm::vec4(1.0f, 0.5f, 0.0f, 1.0f);

  // l-value:
  glm::vec4 ColorBGRA = ColorRGBA.bgra;

  // r-value:
  ColorRGBA.bgra = ColorRGBA;

  // Both l-value and r-value
  ColorRGBA.bgra = ColorRGBA.rgba;
}

This version returns implementation-specific objects that implicitly convert to their respective vector types. As a consequence of this design, these extra types can't be directly used as C++ function arguments; they must be converted through constructors or operator().

#define GLM_FORCE_SWIZZLE
#include <glm/glm.hpp>

using namespace glm;

void foo()
{
  vec4 Color = vec4(1.0f, 0.5f, 0.0f, 1.0f);

  // Generates compiler errors. Color.rgba is not a vector type.
  vec4 ClampedA = clamp(Color.rgba, 0.f, 1.f); // ERROR

  // Explicit conversion through a constructor
  vec4 ClampedB = clamp(vec4(Color.rgba), 0.f, 1.f); // OK

  // Explicit conversion through operator()
  vec4 ClampedC = clamp(Color.rgba(), 0.f, 1.f); // OK
}

Note: The implementation has a caveat: Swizzle operator types must be different on both size of the equal operator or the operation will fail. There is no known fix for this issue to date

2.15. GLM_FORCE_XYZW_ONLY: Only exposes x, y, z and w components

Following GLSL specifications, GLM supports three sets of components to access vector types member: x, y, z, w; r, g, b, a; and s, t, p, q. Also, this is making vector component very expressive in the code, it may make debugging vector types a little cubersom as the debuggers will typically display three time the values for each compoenents due to the existence of the three sets.

To simplify vector types, GLM allows exposing only x, y, z and w components thanks to GLM_FORCE_XYZW_ONLY define.

2.16. GLM_FORCE_LEFT_HANDED: Force left handed coordinate system

By default, OpenGL is using a right handed coordinate system. However, others APIs such as Direct3D have done different choice and relies on the left handed coordinate system.

GLM allows switching the coordinate system to left handed by defining GLM_FORCE_LEFT_HANDED.

2.17. GLM_FORCE_DEPTH_ZERO_TO_ONE: Force the use of a clip space between 0 to 1

By default, OpenGL is using a -1 to 1 clip space in Z-axis. However, others APIs such as Direct3D relies on a clip space between 0 to 1 in Z-axis.

GLM allows switching the clip space in Z-axis to 0 to 1 by defining GLM_FORCE_DEPTH_ZERO_TO_ONE.

2.18. GLM_FORCE_SIZE_T_LENGTH: Vector and matrix static size

GLSL supports the member function .length() for all vector and matrix types.

#include <glm/glm.hpp>

void foo(vec4 const& v)
{
    int Length = v.length();
    ...
}

This function returns an int however this function typically interacts with STL size_t based code. GLM provides GLM_FORCE_SIZE_T_LENGTH pre-processor configuration so that member functions length() return a size_t.

Additionally, GLM defines the type glm::length_t to identify length() returned type, independently from GLM_FORCE_SIZE_T_LENGTH.

#define GLM_FORCE_SIZE_T_LENGTH
#include <glm/glm.hpp>

void foo(vec4 const& v)
{
    glm::length_t Length = v.length();
    ...
}

2.19. GLM_FORCE_UNRESTRICTED_GENTYPE: Removing genType restriction

GLSL has restrictions on types supported by certain functions that may appear excessive. By default, GLM follows the GLSL specification as accurately as possible however it's possible to relax these rules using GLM_FORCE_UNRESTRICTED_GENTYPE define.

#include <glm/glm.hpp>

float average(float const A, float const B)
{
    return glm::mix(A, B, 0.5f); // By default glm::mix only supports floating-point types
}

By defining GLM_FORCE_UNRESTRICTED_GENTYPE, we allow using integer types:

#define GLM_FORCE_UNRESTRICTED_GENTYPE
#include <glm/glm.hpp>

int average(int const A, int const B)
{
    return glm::mix(A, B, 0.5f); // integers are ok thanks to GLM_FORCE_UNRESTRICTED_GENTYPE
}

2.20. GLM_FORCE_SILENT_WARNINGS: Silent C++ warnings from language extensions

When using /W4 on Visual C++ or -Wpedantic on GCC, for example, the compilers will generate warnings for using C++ language extensions (/Za with Visual C++) such as anonymous struct. GLM relies on anonymous structs for swizzle operators and aligned vector types. To silent those warnings define GLM_FORCE_SILENT_WARNINGS before including GLM headers.

2.21. GLM_FORCE_QUAT_DATA_XYZW: Force GLM to store quat data as x,y,z,w instead of w,x,y,z

By default GLM stores quaternion components with the w, x, y, z order. GLM_FORCE_QUAT_DATA_XYZW allows switching the quaternion data storage to the x, y, z, w order.

3. Stable extensions

3.1. Scalar types

3.1.1. GLM_EXT_scalar_int_sized

This extension exposes sized and signed integer types.

Include <glm/ext/scalar_int_sized.hpp> to use these features.

3.1.2. GLM_EXT_scalar_uint_sized

This extension exposes sized and unsigned integer types.

#include <glm/ext/scalar_common.hpp>

glm::uint64 pack(glm::uint32 A, glm::uint16 B, glm::uint8 C, glm::uint8 D)
{
	glm::uint64 ShiftA = 0;
	glm::uint64 ShiftB = sizeof(glm::uint32) * 8;
	glm::uint64 ShiftC = (sizeof(glm::uint32) + sizeof(glm::uint16)) * 8;
	glm::uint64 ShiftD = (sizeof(glm::uint32) + sizeof(glm::uint16) + sizeof(glm::uint8)) * 8;
	return (glm::uint64(A) << ShiftA) | (glm::uint64(B) << ShiftB) | (glm::uint64(C) << ShiftC) | (glm::uint64(D) << ShiftD);
}

Include <glm/ext/scalar_uint_sized.hpp> to use these features.

3.2. Scalar functions

3.2.1. GLM_EXT_scalar_common

This extension exposes support for min and max functions taking more than two scalar arguments. Also, it adds fmin and fmax variants which prevents NaN propagation.

#include <glm/ext/scalar_common.hpp>

float positiveMax(float const a, float const b)
{
    return glm::fmax(a, b, 0.0f);
}

Include <glm/ext/scalar_common.hpp> to use these features.

3.2.2. GLM_EXT_scalar_relational

This extension exposes equal and notEqual scalar variants which takes an epsilon argument.

#include <glm/ext/scalar_relational.hpp>

bool epsilonEqual(float const a, float const b)
{
    float const CustomEpsilon = 0.0001f;
    return glm::equal(a, b, CustomEpsilon);
}

Include <glm/ext/scalar_relational.hpp> to use these features.

3.2.3. GLM_EXT_scalar_constants

This extension exposes useful constants such as epsilon and pi.

#include <glm/ext/scalar_constants.hpp>

float circumference(float const Diameter)
{
    return glm::pi<float>() * Diameter;
}

#include <glm/common.hpp> // abs
#include <glm/ext/scalar_constants.hpp> // epsilon

bool equalULP1(float const a, float const b)
{
    return glm::abs(a - b) <= glm::epsilon<float>();
}

Include <glm/ext/scalar_constants.hpp> to use these features.

3.2.4. GLM_EXT_scalar_ulp

This extension exposes function that measure of accuracy in numeric calculations.

#include <glm/ext/scalar_ulp.hpp>

bool test_ulp(float x)
{
    float const a = glm::next_float(x); // return a float a ULP away from the float argument.
    return float_distance(a, x) == 1; // check both float are a single ULP away.
}

Include <glm/ext/scalar_ulp.hpp> to use these features.

3.3. Vector types

3.3.1. GLM_EXT_vector_float1

This extension exposes single-precision floating point vector with 1 component: vec1.

Include <glm/ext/vector_float1.hpp> to use these features.

3.3.2. GLM_EXT_vector_float2

This extension exposes single-precision floating point vector with 2 components: vec2.

Include <glm/ext/vector_float2.hpp> to use these features.

3.3.3. GLM_EXT_vector_float3

This extension exposes single-precision floating point vector with 3 components: vec3.

Include <glm/ext/vector_float3.hpp> to use these features.

3.3.4. GLM_EXT_vector_float4

This extension exposes single-precision floating point vector with 4 components: vec4.

Include <glm/ext/vector_float4.hpp> to use these features.

3.3.5. GLM_EXT_vector_double1

This extension exposes double-precision floating point vector with 1 component: dvec1.

Include <glm/ext/vector_double1.hpp> to use these features.

3.3.6. GLM_EXT_vector_double2

This extension exposes double-precision floating point vector with 2 components: dvec2.

Include <glm/ext/vector_double2.hpp> to use these features.

3.3.7. GLM_EXT_vector_double3

This extension exposes double-precision floating point vector with 3 components: dvec3.

Include <glm/ext/vector_double3.hpp> to use these features.

3.3.8. GLM_EXT_vector_double4

This extension exposes double-precision floating point vector with 4 components: dvec4.

Include <glm/ext/vector_double4.hpp> to use these features.

3.3.9. GLM_EXT_vector_int1

This extension exposes signed integer vector with 1 component: ivec1.

Include <glm/ext/vector_int1.hpp> to use these features.

3.3.10. GLM_EXT_vector_int2

This extension exposes signed integer vector with 2 components: ivec2.

Include <glm/ext/vector_int2.hpp> to use these features.

3.3.11. GLM_EXT_vector_int3

This extension exposes signed integer vector with 3 components: ivec3.

Include <glm/ext/vector_int3.hpp> to use these features.

3.3.12. GLM_EXT_vector_int4

This extension exposes signed integer vector with 4 components: ivec4.

Include <glm/ext/vector_int4.hpp> to use these features.

3.3.13. GLM_EXT_vector_int1

This extension exposes unsigned integer vector with 1 component: uvec1.

Include <glm/ext/vector_uint1.hpp> to use these features.

3.3.14. GLM_EXT_vector_uint2

This extension exposes unsigned integer vector with 2 components: uvec2.

Include <glm/ext/vector_uint2.hpp> to use these features.

3.3.15. GLM_EXT_vector_uint3

This extension exposes unsigned integer vector with 3 components: uvec3.

Include <glm/ext/vector_uint3.hpp> to use these features.

3.3.16. GLM_EXT_vector_uint4

This extension exposes unsigned integer vector with 4 components: uvec4.

Include <glm/ext/vector_uint4.hpp> to use these features.

3.3.17. GLM_EXT_vector_bool1

This extension exposes boolean vector with 1 component: bvec1.

Include <glm/ext/vector_bool1.hpp> to use these features.

3.3.18. GLM_EXT_vector_bool2

This extension exposes boolean vector with 2 components: bvec2.

Include <glm/ext/vector_bool2.hpp> to use these features.

3.3.19. GLM_EXT_vector_bool3

This extension exposes boolean vector with 3 components: bvec3.

Include <glm/ext/vector_bool3.hpp> to use these features.

3.3.20. GLM_EXT_vector_bool4

This extension exposes boolean vector with 4 components: bvec4.

Include <glm/ext/vector_bool4.hpp> to use these features.

3.4. Vector types with precision qualifiers

3.4.1. GLM_EXT_vector_float1_precision

This extension exposes single-precision floating point vector with 1 component using various precision in term of ULPs: lowp_vec1, mediump_vec1 and highp_vec1.

Include <glm/ext/vector_float1_precision.hpp> to use these features.

3.4.2. GLM_EXT_vector_float2_precision

This extension exposes single-precision floating point vector with 2 components using various precision in term of ULPs: lowp_vec2, mediump_vec2 and highp_vec2.

Include <glm/ext/vector_float2_precision.hpp> to use these features.

3.4.3. GLM_EXT_vector_float3_precision

This extension exposes single-precision floating point vector with 3 components using various precision in term of ULPs: lowp_vec3, mediump_vec3 and highp_vec3.

Include <glm/ext/vector_float3_precision.hpp> to use these features.

3.4.4. GLM_EXT_vector_float4_precision

This extension exposes single-precision floating point vector with 4 components using various precision in term of ULPs: lowp_vec4, mediump_vec4 and highp_vec4.

Include <glm/ext/vector_float4_precision.hpp> to use these features.

3.4.5. GLM_EXT_vector_double1_precision

This extension exposes double-precision floating point vector with 1 component using various precision in term of ULPs: lowp_dvec1, mediump_dvec1 and highp_dvec1.

Include <glm/ext/vector_double1_precision.hpp> to use these features.

3.4.6. GLM_EXT_vector_double2_precision

This extension exposes double-precision floating point vector with 2 components using various precision in term of ULPs: lowp_dvec2, mediump_dvec2 and highp_dvec2.

Include <glm/ext/vector_double2_precision.hpp> to use these features.

3.4.7. GLM_EXT_vector_double3_precision

This extension exposes double-precision floating point vector with 3 components using various precision in term of ULPs: lowp_dvec3, mediump_dvec3 and highp_dvec3.

Include <glm/ext/vector_double3_precision.hpp> to use these features.

3.4.8. GLM_EXT_vector_double4_precision

This extension exposes double-precision floating point vector with 4 components using various precision in term of ULPs: lowp_dvec4, mediump_dvec4 and highp_dvec4.

Include <glm/ext/vector_double4_precision.hpp> to use these features.

3.5. Vector functions

3.5.1. GLM_EXT_vector_common

This extension exposes support for min and max functions taking more than two vector arguments. Also, it adds fmin and fmax variants which prevents NaN propagation.

#include <glm/ext/vector_float2.hpp> // vec2
#include <glm/ext/vector_common.hpp> // fmax

float positiveMax(float const a, float const b)
{
    return glm::fmax(a, b, 0.0f);
}

Include <glm/ext/vector_common.hpp> to use these features.

3.5.2. GLM_EXT_vector_relational

This extension exposes equal and notEqual vector variants which takes an epsilon argument.

#include <glm/ext/vector_float2.hpp> // vec2
#include <glm/ext/vector_relational.hpp> // equal, all

bool epsilonEqual(glm::vec2 const& A, glm::vec2 const& B)
{
    float const CustomEpsilon = 0.0001f;
    return glm::all(glm::equal(A, B, CustomEpsilon));
}

Include <glm/ext/vector_relational.hpp> to use these features.

3.5.3. GLM_EXT_vector_ulp

This extension exposes function that measure of accuracy in numeric calculations.

#include <glm/ext/vector_ulp.hpp>
#include <glm/ext/vector_float4.hpp>
#include <glm/ext/vector_int4.hpp>

bool test_ulp(glm::vec4 const& x)
{
    glm::vec4 const a = glm::next_float(x); // return a float a ULP away from the float argument.
    return glm::all(float_distance(a, x) == glm::ivec4(1)); // check both float are a single ULP away.
}

Include <glm/ext/vector_ulp.hpp> to use these features.

3.6. Matrix types

3.6.1. GLM_EXT_matrix_float2x2

This extension exposes single-precision floating point vector with 2 columns by 2 rows: mat2x2.

Include <glm/ext/matrix_float2x2.hpp> to use these features.

3.6.2. GLM_EXT_matrix_float2x3

This extension exposes single-precision floating point vector with 2 columns by 3 rows: mat2x3.

Include <glm/ext/matrix_float2x3.hpp> to use these features.

3.6.3. GLM_EXT_matrix_float2x4

This extension exposes single-precision floating point vector with 2 columns by 4 rows: mat2x4.

Include <glm/ext/matrix_float2x4.hpp> to use these features.

3.6.4. GLM_EXT_matrix_float3x2

This extension exposes single-precision floating point vector with 3 columns by 2 rows: mat3x2.

Include <glm/ext/matrix_float3x2.hpp> to use these features.

3.6.5. GLM_EXT_matrix_float3x3

This extension exposes single-precision floating point vector with 3 columns by 3 rows: mat3x3.

Include <glm/ext/matrix_float3x3.hpp> to use these features.

3.6.6. GLM_EXT_matrix_float3x4

This extension exposes single-precision floating point vector with 3 columns by 4 rows: mat3x4.

Include <glm/ext/matrix_float3x4.hpp> to use these features.

3.6.7. GLM_EXT_matrix_float4x2

This extension exposes single-precision floating point vector with 4 columns by 2 rows: mat4x2.

Include <glm/ext/matrix_float4x2.hpp> to use these features.

3.6.8. GLM_EXT_matrix_float4x3

This extension exposes single-precision floating point vector with 4 columns by 3 rows: mat4x3.

Include <glm/ext/matrix_float4x3.hpp> to use these features.

3.6.9. GLM_EXT_matrix_float4x4

This extension exposes single-precision floating point vector with 4 columns by 4 rows: mat4x4.

Include <glm/ext/matrix_float4x4.hpp> to use these features.

3.6.10. GLM_EXT_matrix_double2x2

This extension exposes double-precision floating point vector with 2 columns by 2 rows: dmat2x2.

Include <glm/ext/matrix_double2x2.hpp> to use these features.

3.6.11. GLM_EXT_matrix_double2x3

This extension exposes double-precision floating point vector with 2 columns by 3 rows: dmat2x3.

Include <glm/ext/matrix_double2x3.hpp> to use these features.

3.6.12. GLM_EXT_matrix_double2x4

This extension exposes double-precision floating point vector with 2 columns by 4 rows: dmat2x4.

Include <glm/ext/matrix_double2x4.hpp> to use these features.

3.6.13. GLM_EXT_matrix_double3x2

This extension exposes double-precision floating point vector with 3 columns by 2 rows: dmat3x2.

Include <glm/ext/matrix_double3x2.hpp> to use these features.

3.6.14. GLM_EXT_matrix_double3x3

This extension exposes double-precision floating point vector with 3 columns by 3 rows: dmat3x3.

Include <glm/ext/matrix_double3x3.hpp> to use these features.

3.6.15. GLM_EXT_matrix_double3x4

This extension exposes double-precision floating point vector with 3 columns by 4 rows: dmat3x4.

Include <glm/ext/matrix_double3x4.hpp> to use these features.

3.6.16. GLM_EXT_matrix_double4x2

This extension exposes double-precision floating point vector with 4 columns by 2 rows: dmat4x2.

Include <glm/ext/matrix_double4x2.hpp> to use these features.

3.6.17. GLM_EXT_matrix_double4x3

This extension exposes double-precision floating point vector with 4 columns by 3 rows: dmat4x3.

Include <glm/ext/matrix_double4x3.hpp> to use these features.

3.6.18. GLM_EXT_matrix_double4x4

This extension exposes double-precision floating point vector with 4 columns by 4 rows: dmat4x4.

Include <glm/ext/matrix_double4x4.hpp> to use these features.

3.7. Matrix types with precision qualifiers

3.7.1. GLM_EXT_matrix_float2x2_precision

This extension exposes single-precision floating point vector with 2 columns by 2 rows using various precision in term of ULPs: lowp_mat2x2, mediump_mat2x2 and highp_mat2x2.

Include <glm/ext/matrix_float2x2_precision.hpp> to use these features.

3.7.2. GLM_EXT_matrix_float2x3_precision

This extension exposes single-precision floating point vector with 2 columns by 3 rows using various precision in term of ULPs: lowp_mat2x3, mediump_mat2x3 and highp_mat2x3.

Include <glm/ext/matrix_float2x3_precision.hpp> to use these features.

3.7.3. GLM_EXT_matrix_float2x4_precision

This extension exposes single-precision floating point vector with 2 columns by 4 rows using various precision in term of ULPs: lowp_mat2x4, mediump_mat2x4 and highp_mat2x4.

Include <glm/ext/matrix_float2x4_precision.hpp> to use these features.

3.7.4. GLM_EXT_matrix_float3x2_precision

This extension exposes single-precision floating point vector with 3 columns by 2 rows using various precision in term of ULPs: lowp_mat3x2, mediump_mat3x2 and highp_mat3x2.

Include <glm/ext/matrix_float3x2_precision.hpp> to use these features.

3.7.5. GLM_EXT_matrix_float3x3_precision

This extension exposes single-precision floating point vector with 3 columns by 3 rows using various precision in term of ULPs: lowp_mat3x3, mediump_mat3x3 and highp_mat3x3.

Include <glm/ext/matrix_float3x3_precision.hpp> to use these features.

3.7.6. GLM_EXT_matrix_float3x4_precision

This extension exposes single-precision floating point vector with 3 columns by 4 rows using various precision in term of ULPs: lowp_mat3x4, mediump_mat3x4 and highp_mat3x4.

Include <glm/ext/matrix_float3x4_precision.hpp> to use these features.

3.7.7. GLM_EXT_matrix_float4x2_precision

This extension exposes single-precision floating point vector with 4 columns by 2 rows using various precision in term of ULPs: lowp_mat4x2, mediump_mat4x2 and highp_mat4x2.

Include <glm/ext/matrix_float4x2_precision.hpp> to use these features.

3.7.8. GLM_EXT_matrix_float4x3_precision

This extension exposes single-precision floating point vector with 4 columns by 3 rows using various precision in term of ULPs: lowp_mat4x3, mediump_mat4x3 and highp_mat4x3.

Include <glm/ext/matrix_float4x3_precision.hpp> to use these features.

3.7.9. GLM_EXT_matrix_float4x4_precision

This extension exposes single-precision floating point vector with 4 columns by 4 rows using various precision in term of ULPs: lowp_mat4x4, mediump_mat4x4 and highp_mat4x4.

Include <glm/ext/matrix_float4x4_precision.hpp> to use these features.

3.7.10. GLM_EXT_matrix_double2x2_precision

This extension exposes double-precision floating point vector with 2 columns by 2 rows using various precision in term of ULPs: lowp_dmat2x2, mediump_dmat2x2 and highp_dmat2x2.

Include <glm/ext/matrix_double2x2_precision.hpp> to use these features.

3.7.11. GLM_EXT_matrix_double2x3_precision

This extension exposes double-precision floating point vector with 2 columns by 3 rows using various precision in term of ULPs: lowp_dmat2x3, mediump_dmat2x3 and highp_dmat2x3.

Include <glm/ext/matrix_double2x3_precision.hpp> to use these features.

3.7.12. GLM_EXT_matrix_double2x4_precision

This extension exposes double-precision floating point vector with 2 columns by 4 rows using various precision in term of ULPs: lowp_dmat2x4, mediump_dmat2x4 and highp_dmat2x4.

Include <glm/ext/matrix_double2x4_precision.hpp> to use these features.

3.7.13. GLM_EXT_matrix_double3x2_precision

This extension exposes double-precision floating point vector with 3 columns by 2 rows using various precision in term of ULPs: lowp_dmat3x2, mediump_dmat3x2 and highp_dmat3x2.

Include <glm/ext/matrix_double3x2_precision.hpp> to use these features.

3.7.14. GLM_EXT_matrix_double3x3_precision

This extension exposes double-precision floating point vector with 3 columns by 3 rows using various precision in term of ULPs: lowp_dmat3x3, mediump_dmat3x3 and highp_dmat3x3.

Include <glm/ext/matrix_double3x3_precision.hpp> to use these features.

3.7.15. GLM_EXT_matrix_double3x4_precision

This extension exposes double-precision floating point vector with 3 columns by 4 rows using various precision in term of ULPs: lowp_dmat3x4, mediump_dmat3x4 and highp_dmat3x4.

Include <glm/ext/matrix_double3x4_precision.hpp> to use these features.

3.7.16. GLM_EXT_matrix_double4x2_precision

This extension exposes double-precision floating point vector with 4 columns by 2 rows using various precision in term of ULPs: lowp_dmat4x2, mediump_dmat4x2 and highp_dmat4x2.

Include <glm/ext/matrix_double4x2_precision.hpp> to use these features.

3.7.17. GLM_EXT_matrix_double4x3_precision

This extension exposes double-precision floating point vector with 4 columns by 3 rows using various precision in term of ULPs: lowp_dmat4x3, mediump_dmat4x3 and highp_dmat4x3.

Include <glm/ext/matrix_double4x3_precision.hpp> to use these features.

3.7.18. GLM_EXT_matrix_double4x4_precision

This extension exposes double-precision floating point vector with 4 columns by 4 rows using various precision in term of ULPs: lowp_dmat4x4, mediump_dmat4x4 and highp_dmat4x4.

Include <glm/ext/matrix_double4x4_precision.hpp> to use these features.

3.8. Matrix functions

3.8.1. GLM_EXT_matrix_relational

This extension exposes equal and notEqual matrix variants which takes an optional epsilon argument.

#include <glm/ext/vector_bool4.hpp> // bvec4
#include <glm/ext/matrix_float4x4.hpp> // mat4
#include <glm/ext/matrix_relational.hpp> // equal, all

bool epsilonEqual(glm::mat4 const& A, glm::mat4 const& B)
{
    float const CustomEpsilon = 0.0001f;
    glm::bvec4 const ColumnEqual = glm::equal(A, B, CustomEpsilon); // Evaluation per column
    return glm::all(ColumnEqual);
}

Include <glm/ext/matrix_relational.hpp> to use these features.

3.8.2. GLM_EXT_matrix_transform

This extension exposes matrix transformation functions: translate, rotate and scale.

#include <glm/ext/vector_float2.hpp> // vec2
#include <glm/ext/vector_float3.hpp> // vec3
#include <glm/ext/matrix_float4x4.hpp> // mat4x4
#include <glm/ext/matrix_transform.hpp> // translate, rotate, scale, identity

glm::mat4 computeModelViewMatrix(float Translate, glm::vec2 const & Rotate)
{
	glm::mat4 View = glm::translate(glm::identity(), glm::vec3(0.0f, 0.0f, -Translate));
	View = glm::rotate(View, Rotate.y, glm::vec3(-1.0f, 0.0f, 0.0f));
	View = glm::rotate(View, Rotate.x, glm::vec3(0.0f, 1.0f, 0.0f));
	glm::mat4 Model = glm::scale(glm::identity(), glm::vec3(0.5f));
	return View * Model;
}

Include <glm/ext/matrix_transform.hpp> to use these features.

3.8.3. GLM_EXT_matrix_clip_space

This extension exposes functions to transform scenes into the clip space.

#include <glm/ext/matrix_float4x4.hpp> // mat4x4
#include <glm/ext/matrix_clip_space.hpp> // perspective
#include <glm/trigonometric.hpp> // radians

glm::mat4 computeProjection(float Width, float Height)
{
	return glm::perspective(glm::radians(45.0f), Width / Height, 0.1f, 100.f);
}

Include <glm/ext/matrix_clip_space.hpp> to use these features.

3.8.4. GLM_EXT_matrix_projection

This extension exposes functions to map object coordinates into window coordinates and reverse

Include <glm/ext/matrix_projection.hpp> to use these features.

3.9. Quaternion types

3.9.1. GLM_EXT_quaternion_float

This extension exposes single-precision floating point quaternion: quat.

Include <glm/ext/quaternion_float.hpp> to use these features.

3.9.2. GLM_EXT_quaternion_double

This extension exposes double-precision floating point quaternion: dquat.

Include <glm/ext/quaternion_double.hpp> to use these features.

3.10. Quaternion types with precision qualifiers

3.10.1. GLM_EXT_quaternion_float_precision

This extension exposes single-precision floating point quaternion using various precision in term of ULPs: lowp_quat, mediump_quat and highp_quat.

Include <glm/ext/quaternion_float_precision.hpp> to use these features.

3.10.2. GLM_EXT_quaternion_double_precision

This extension exposes double-precision floating point quaternion using various precision in term of ULPs: lowp_dquat, mediump_dquat and highp_dquat.

Include <glm/ext/quaternion_double_precision.hpp> to use these features.

3.11. Quaternion functions

3.11.1. GLM_EXT_quaternion_common

This extension exposes common quaternion functions such as slerp, conjugate and inverse.

Include <glm/ext/quaternion_common.hpp> to use these features.

3.11.2. GLM_EXT_quaternion_geometric

This extension exposes geometric quaternion functions such as length, normalize, dot and cross.

Include <glm/ext/quaternion_geometric.hpp> to use these features.

3.11.3. GLM_EXT_quaternion_trigonometric

This extension exposes trigonometric quaternion functions such as angle and axis.

Include <glm/ext/quaternion_trigonometric.hpp> to use these features.

3.11.4. GLM_EXT_quaternion_exponential

This extensions expose exponential functions for quaternions such as exp, log, pow and sqrt.

Include <glm/ext/quaternion_exponential.hpp> to use these features.

3.11.5. GLM_EXT_quaternion_relational

This extension exposes relational functions to compare quaternions.

Include <glm/ext/quaternion_relational.hpp> to use these features.

3.11.6. GLM_EXT_quaternion_transform

This extension exposes functions to transform objects.

Include <glm/ext/quaternion_transform.hpp> to use these features.

4. Recommended extensions

GLM extends the core GLSL feature set with extensions. These extensions include: quaternion, transformation, spline, matrix inverse, color spaces, etc.

To include an extension, we only need to include the dedicated header file. Once included, the features are added to the GLM namespace.

#include <glm/glm.hpp>
#include <glm/gtc/matrix_transform.hpp>

int foo()
{
    glm::vec4 Position = glm::vec4(glm:: vec3(0.0f), 1.0f);
    glm::mat4 Model = glm::translate(glm::mat4(1.0f), glm::vec3(1.0f));

    glm::vec4 Transformed = Model * Position;
    ...

    return 0;
}

When an extension is included, all the dependent core functionalities and extensions will be included as well.

4.1. GLM_GTC_bitfield

Fast bitfield operations on scalar and vector variables.

<glm/gtc/bitfield.hpp> need to be included to use these features.

4.2. GLM_GTC_color_space

Conversion between linear RGB and sRGB color spaces.

<glm/gtc/color_space.hpp> need to be included to use these features.

4.3. GLM_GTC_constants

Provide a list of built-in constants.

<glm/gtc/constants.hpp> need to be included to use these features.

4.4. GLM_GTC_epsilon

Approximate equality comparisons for floating-point numbers, possibly with a user-defined epsilon.

<glm/gtc/epsilon.hpp> need to be included to use these features.

4.5. GLM_GTC_integer

Integer variants of core GLM functions.

<glm/gtc/integer.hpp> need to be included to use these features.

4.6. GLM_GTC_matrix_access

Functions to conveniently access the individual rows or columns of a matrix.

<glm/gtc/matrix_access.hpp> need to be included to use these features.

4.7. GLM_GTC_matrix_integer

Integer matrix types similar to the core floating-point matrices. Some operations (such as inverse and determinant) are not supported.

<glm/gtc/matrix_integer.hpp> need to be included to use these features.

4.8. GLM_GTC_matrix_inverse

Additional matrix inverse functions.

<glm/gtc/matrix_inverse.hpp> need to be included to use these features.

4.9. GLM_GTC_matrix_transform

Matrix transformation functions that follow the OpenGL fixed-function conventions.

For example, the lookAt function generates a transformation matrix that projects world coordinates into eye coordinates suitable for projection matrices (e.g. perspective, ortho). See the OpenGL compatibility specifications for more information about the layout of these generated matrices.

The matrices generated by this extension use standard OpenGL fixed-function conventions. For example, the lookAt function generates a transform from world space into the specific eye space that the projective matrix functions (perspective, ortho, etc) are designed to expect. The OpenGL compatibility specifications define the particular layout of this eye space.

<glm/gtc/matrix_transform.hpp> need to be included to use these features.

4.10. GLM_GTC_noise

Define 2D, 3D and 4D procedural noise functions.

<glm/gtc/noise.hpp> need to be included to use these features.

Figure 4.10.1: glm::simplex(glm::vec2(x / 16.f, y / 16.f));

Figure 4.10.2: glm::simplex(glm::vec3(x / 16.f, y / 16.f, 0.5f));

Figure 4.10.3: glm::simplex(glm::vec4(x / 16.f, y / 16.f, 0.5f, 0.5f));

Figure 4.10.4: glm::perlin(glm::vec2(x / 16.f, y / 16.f));

Figure 4.10.5: glm::perlin(glm::vec3(x / 16.f, y / 16.f, 0.5f));

Figure 4.10.6: glm::perlin(glm::vec4(x / 16.f, y / 16.f, 0.5f, 0.5f)));

Figure 4.10.7: glm::perlin(glm::vec2(x / 16.f, y / 16.f), glm::vec2(2.0f));

Figure 4.10.8: glm::perlin(glm::vec3(x / 16.f, y / 16.f, 0.5f), glm::vec3(2.0f));

Figure 4.10.9: glm::perlin(glm::vec4(x / 16.f, y / 16.f, glm::vec2(0.5f)), glm::vec4(2.0f));

4.11. GLM_GTC_packing

Convert scalar and vector types to and from packed formats, saving space at the cost of precision. However, packing a value into a format that it was previously unpacked from is guaranteed to be lossless.

<glm/gtc/packing.hpp> need to be included to use these features.

4.12. GLM_GTC_quaternion

Quaternions and operations upon thereof.

<glm/gtc/quaternion.hpp> need to be included to use these features.

4.13. GLM_GTC_random

Probability distributions in up to four dimensions.

<glm/gtc/random.hpp> need to be included to use these features.

Figure 4.13.1: glm::vec4(glm::linearRand(glm::vec2(-1), glm::vec2(1)), 0, 1);

Figure 4.13.2: glm::vec4(glm::circularRand(1.0f), 0, 1);

Figure 4.13.3: glm::vec4(glm::sphericalRand(1.0f), 1);

Figure 4.13.4: glm::vec4(glm::diskRand(1.0f), 0, 1);

Figure 4.13.5: glm::vec4(glm::ballRand(1.0f), 1);

Figure 4.13.6: glm::vec4(glm::gaussRand(glm::vec3(0), glm::vec3(1)), 1);

4.14. GLM_GTC_reciprocal

Reciprocal trigonometric functions (e.g. secant, cosecant, tangent).

<glm/gtc/reciprocal.hpp> need to be included to use the features of this extension.

4.15. GLM_GTC_round

Various rounding operations and common special cases thereof.

<glm/gtc/round.hpp> need to be included to use the features of this extension.

4.16. GLM_GTC_type_aligned

Aligned vector types.

<glm/gtc/type_aligned.hpp> need to be included to use the features of this extension.

4.17. GLM_GTC_type_precision

Vector and matrix types with defined precisions, e.g. i8vec4, which is a 4D vector of signed 8-bit integers.

<glm/gtc/type\_precision.hpp> need to be included to use the features of this extension.

4.18. GLM_GTC_type_ptr

Facilitate interactions between pointers to basic types (e.g. float*) and GLM types (e.g. mat4).

This extension defines an overloaded function, glm::value_ptr, which returns a pointer to the memory layout of any GLM vector or matrix (vec3, mat4, etc.). Matrix types store their values in column-major order. This is useful for uploading data to matrices or for copying data to buffer objects.

// GLM_GTC_type_ptr provides a safe solution:
#include <glm/glm.hpp>
#include <glm/gtc/type_ptr.hpp>

void foo()
{
    glm::vec4 v(0.0f);
    glm::mat4 m(1.0f);
    ...
    glVertex3fv(glm::value_ptr(v))
    glLoadMatrixfv(glm::value_ptr(m));
}

// Another solution, this one inspired by the STL:
#include <glm/glm.hpp>

void foo()
{
    glm::vec4 v(0.0f);
    glm::mat4 m(1.0f);
    ...
    glVertex3fv(&v[0]);
    glLoadMatrixfv(&m[0][0]);
}

Note: It would be possible to implement glVertex3fv(glm::vec3(0)) in C++ with the appropriate cast operator that would result as an implicit cast in this example. However cast operators may produce programs running with unexpected behaviours without build error or any form of notification.

<glm/gtc/type_ptr.hpp> need to be included to use these features.

4.19. GLM_GTC_ulp

Measure a function's accuracy given a reference implementation of it. This extension works on floating-point data and provides results in ULP.

<glm/gtc/ulp.hpp> need to be included to use these features.

4.20. GLM_GTC_vec1

Add *vec1 types.

<glm/gtc/vec1.hpp> need to be included to use these features.

5. OpenGL interoperability

5.1. GLM replacements for deprecated OpenGL functions

OpenGL 3.1 specification has deprecated some features that have been removed from OpenGL 3.2 core profile specification. GLM provides some replacement functions.

glRotate{f, d}:

glm::mat4 glm::rotate(glm::mat4 const& m, float angle, glm::vec3 const& axis);
glm::dmat4 glm::rotate(glm::dmat4 const& m, double angle, glm::dvec3 const& axis);

From GLM_GTC_matrix_transform extension: <glm/gtc/matrix_transform.hpp>

glScale{f, d}:

glm::mat4 glm::scale(glm::mat4 const& m, glm::vec3 const& factors);
glm::dmat4 glm::scale(glm::dmat4 const& m, glm::dvec3 const& factors);

From GLM_GTC_matrix_transform extension: <glm/gtc/matrix_transform.hpp>

glTranslate{f, d}:

glm::mat4 glm::translate(glm::mat4 const& m, glm::vec3 const& translation);
glm::dmat4 glm::translate(glm::dmat4 const& m, glm::dvec3 const& translation);

From GLM_GTC_matrix_transform extension: <glm/gtc/matrix_transform.hpp>

glLoadIdentity:

glm::mat4(1.0) or glm::mat4();
glm::dmat4(1.0) or glm::dmat4();

From GLM core library: <glm/glm.hpp>

glMultMatrix{f, d}:

glm::mat4() * glm::mat4();
glm::dmat4() * glm::dmat4();

From GLM core library: <glm/glm.hpp>

glLoadTransposeMatrix{f, d}:

glm::transpose(glm::mat4());
glm::transpose(glm::dmat4());

From GLM core library: <glm/glm.hpp>

glMultTransposeMatrix{f, d}:

glm::mat4() * glm::transpose(glm::mat4());
glm::dmat4() * glm::transpose(glm::dmat4());

From GLM core library: <glm/glm.hpp>

glFrustum:

glm::mat4 glm::frustum(float left, float right, float bottom, float top, float zNear, float zFar);
glm::dmat4 glm::frustum(double left, double right, double bottom, double top, double zNear, double zFar);