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![](media/image1.png){width="3.2006944444444443in" height="1.725in"}
Manual
Version 0.9.8
10 September 2016
Christophe Riccio
<glm@g-truc.net>
![](media/image2.png){width="0.8333333333333334in"
height="0.8333333333333334in"}
The Happy Bunny License (Modified MIT License)
Copyright (c) 2005 - 2016 G-Truc Creation
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.
![](media/image3.jpg){width="7.256956474190726in"
height="4.839622703412074in"}
The MIT License
Copyright (c) 2005 - 2016 G-Truc Creation
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.
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.
![](media/image4.jpeg){width="7.2268416447944in"
height="4.811321084864392in"}
Introduction {#introduction .HeadingA}
============
OpenGL Mathematics (GLM) is a C++ mathematics library for graphics C++
programs based on the [*OpenGL Shading
Language*](http://www.opengl.org/registry/) (GLSL) specifications.
GLM provides classes and functions designed and implemented with the
same naming conventions and functionalities than GLSL so that when a
programmer knows GLSL, he knows GLM as well which makes it really easy
to use.
This project isn't limited to GLSL features. An extension system, based
on the GLSL extension conventions, provides extended capabilities:
matrix transformations, quaternions, data packing, random numbers,
noise, etc...
This library works perfectly with [*OpenGL*](http://www.opengl.org) but
it also ensures interoperability with other third party libraries and
SDK. It is a good candidate for software rendering (raytracing /
rasterisation), image processing, physic simulations and any development
context that requires a simple and convenient mathematics library.
GLM is written in C++98 but can take advantage of C++11 when supported
by the compiler. It is a platform independent library with no dependence
and it officially supports the following compilers:
- [Apple
Clang](https://developer.apple.com/Library/mac/documentation/CompilerTools/Conceptual/LLVMCompilerOverview/index.html)
4.0 and higher\
- [GCC](http://gcc.gnu.org/) 4.2 and higher
- [Intel C++ Composer](https://software.intel.com/en-us/intel-compilers)
XE 2013 and higher\
- [LLVM](http://llvm.org/) 3.0 and higher
- [Visual C++](http://www.visualstudio.com/) 2010 and higher
- [CUDA](https://developer.nvidia.com/about-cuda) 4.0 and higher
(experimental)
- Any conform C++98 or C++11 compiler
The source code and the documentation, including this manual, are
licensed under [the Happy Bunny License (Modified MIT) and the MIT
License](http://glm.g-truc.net/copying.txt).
Thanks for contributing to the project by [submitting
reports](https://github.com/g-truc/glm/issues) for bugs and feature
requests. Any feedback is welcome at
[*glm@g-truc.net*](mailto:glm@g-truc.net).
1. Getting started {#getting-started .HeadingA}
==================
1.1. Setup {#setup .HeadingB}
----------
GLM is a header only library. Hence, there is nothing to build to use
it. To use GLM, a programmer only has to include &lt;glm/glm.hpp&gt; in
his program. This include provides all the GLSL features implemented by
GLM.
Core GLM features can be included using individual headers to allow
faster user program compilations.
&lt;glm/vec2.hpp&gt;: vec2, bvec2, dvec2, ivec2 and uvec2
&lt;glm/vec3.hpp&gt;: vec3, bvec3, dvec3, ivec3 and uvec3
&lt;glm/vec4.hpp&gt;: vec4, bvec4, dvec4, ivec4 and uvec4
&lt;glm/mat2x2.hpp&gt;: mat2, dmat2
&lt;glm/mat2x3.hpp&gt;: mat2x3, dmat2x3
&lt;glm/mat2x4.hpp&gt;: mat2x4, dmat2x4
&lt;glm/mat3x2.hpp&gt;: mat3x2, dmat3x2
&lt;glm/mat3x3.hpp&gt;: mat3, dmat3
&lt;glm/mat3x4.hpp&gt;: mat3x4, dmat2
&lt;glm/mat4x2.hpp&gt;: mat4x2, dmat4x2
&lt;glm/mat4x3.hpp&gt;: mat4x3, dmat4x3
&lt;glm/mat4x4.hpp&gt;: mat4, dmat4
&lt;glm/common.hpp&gt;: all the GLSL common functions
&lt;glm/exponential.hpp&gt;: all the GLSL exponential functions
&lt;glm/geometry.hpp&gt;: all the GLSL geometry functions
&lt;glm/integer.hpp&gt;: all the GLSL integer functions
&lt;glm/matrix.hpp&gt;: all the GLSL matrix functions
&lt;glm/packing.hpp&gt;: all the GLSL packing functions
&lt;glm/trigonometric.hpp&gt;: all the GLSL trigonometric functions
&lt;glm/vector\_relational.hpp&gt;: all the GLSL vector relational
functions
1.2. Faster program compilation {#faster-program-compilation .HeadingB}
-------------------------------
GLM is a header only library that makes a heavy usage of C++ templates.
This design may significantly increase the compile time for files that
use GLM. Hence, it is important to limit GLM inclusion to header and
source files that actually use it. Likewise, GLM extensions should be
included only in program sources using them.
To further help compilation time, GLM 0.9.5 introduced
&lt;glm/fwd.hpp&gt; that provides forward declarations of GLM types.
-------------------------------
// Header file
\#include &lt;glm/fwd.hpp&gt;
// Source file
\#include &lt;glm/glm.hpp&gt;
-------------------------------
-------------------------------
1.3. Use sample of GLM core {#use-sample-of-glm-core .HeadingB}
---------------------------
---------------------------------------------------------------------------
// Include GLM core features
\#include &lt;glm/vec3.hpp&gt;
\#include &lt;glm/vec4.hpp&gt;
\#include &lt;glm/mat4x4.hpp&gt;
\#include &lt;glm/trigonometric.hpp&gt;
// Include GLM extensions
\#include &lt;glm/gtc/matrix\_transform.hpp&gt;
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 {#dependencies .HeadingB}
-----------------
When &lt;glm/glm.hpp&gt; is included, GLM provides all the GLSL features
it implements in C++.
There is no dependence with external libraries or external headers such
as gl.h,
[*glcorearb.h*](http://www.opengl.org/registry/api/GL/glcorearb.h),
gl3.h, glu.h or windows.h. However, if &lt;boost/static\_assert.hpp&gt;
is included, [*Boost static
assert*](http://www.boost.org/doc/libs/1_52_0/doc/html/boost_staticassert.html)
will be used all over GLM code to provide compiled time errors unless
GLM is built with a C++ 11 compiler in which case
[static\_assert](http://en.cppreference.com/w/cpp/language/static_assert).
If neither are detected, GLM will rely on its own implementation of
static assert.
2. Swizzle operators {#swizzle-operators .HeadingA}
====================
A common feature of shader languages like GLSL is the swizzle operators.
Those allow selecting multiple components of a vector and change their
order. For example, “variable.x”, “variable.xzy” and “variable.zxyy”
form respectively a scalar, a three components vector and a four
components vector. With GLSL, swizzle operators can be both R-values and
L-values. Finally, vector components can be accessed using “xyzw”,
“rgba” or “stpq”.
-----------------
vec4 A;
vec2 B;
...
B.yx = A.wy;
B = A.xx;
Vec3 C = A.bgr;
-----------------
-----------------
GLM supports a subset of this functionality as described in the
following sub-sections. Swizzle operators are disabled by default. To
enable them GLM\_SWIZZLE must be defined before any inclusion of
&lt;glm/glm.hpp&gt;. Enabling swizzle operators will massively increase
the size of compiled files and the compilation time.
2.1. Default C++98 implementation {#default-c98-implementation .HeadingB}
---------------------------------
The C++98 implementation exposes the R-value swizzle operators as member
functions of vector types.
----------------------------------------------------
\#define GLM\_SWIZZLE
\#include &lt;glm/glm.hpp&gt;
void foo()
{
> glm::vec4 ColorRGBA(1.0f, 0.5f, 0.0f, 1.0f);
>
> glm::vec3 ColorBGR = ColorRGBA.bgr();
>
> …
>
> glm::vec3 PositionA(1.0f, 0.5f, 0.0f, 1.0f);
>
> glm::vec3 PositionB = PositionXYZ.xyz() \* 2.0f;
>
> …
>
> glm::vec2 TexcoordST(1.0f, 0.5f);
>
> glm::vec4 TexcoordSTPQ = TexcoordST.stst();
>
> …
}
----------------------------------------------------
----------------------------------------------------
Swizzle operators return a copy of the component values hence they can’t
be used as L-values to change the value of the variables.
----------------------------------------------------------------
\#define GLM\_FORCE\_SWIZZLE
\#include &lt;glm/glm.hpp&gt;
void foo()
{
> glm::vec3 A(1.0f, 0.5f, 0.0f);
// /!\\ No compiler error but A is not affected
// This code modify the components of an anonymous copy.
> A.bgr() = glm::vec3(2.0f, 1.5f, 1.0f); // A is not modified!
>
> …
}
----------------------------------------------------------------
----------------------------------------------------------------
2.2. Anonymous union member implementation {#anonymous-union-member-implementation .HeadingB}
-------------------------------------------
Visual C++ supports anonymous structures in union, which is a
non-standard language extension, but it enables a very powerful
implementation of swizzle operators on Windows supporting both L-value
swizzle operators and a syntax that doesn’t require parentheses in some
cases. This implementation is only enabled when the language extension
is enabled and GLM\_SWIZZLE is defined.
------------------------------------------------
\#define GLM\_FORCE\_SWIZZLE
\#include &lt;glm/glm.hpp&gt;
void foo()
{
> glm::vec4 ColorRGBA(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;
>
> …
}
------------------------------------------------
------------------------------------------------
Anonymous union member swizzle operators don’t return vector types
(glm::vec2, glm::vec3 and glm::vec4) but implementation specific objects
that can be automatically interpreted by other swizzle operators and
vector constructors. Unfortunately, those can’t be interpreted by GLM
functions so that the programmer must convert a swizzle operators to a
vector type or call the () operator on a swizzle objects to pass it to
another C++ functions.
---------------------------------------------------------------------------
\#define GLM\_FORCE\_SWIZZLE
\#include &lt;glm/glm.hpp&gt;
void foo()
{
> glm::vec4 Color(1.0f, 0.5f, 0.0f, 1.0f);
>
> …
// Generates compiler errors. Color.rgba is not a vector type.
> glm::vec4 ClampedA = glm::clamp(Color.rgba, 0.f, 1.f); // ERROR
// We need to cast the swizzle operator into glm::vec4
// With by using a constructor
> glm::vec4 ClampedB = glm::clamp(glm::vec4(Color.rgba), 0.f, 1.f); // OK
// Or by using the () operator
> glm::vec4 ClampedC = glm::clamp(Color.rgba(), 0.f, 1.f); // OK
>
> …
}
---------------------------------------------------------------------------
---------------------------------------------------------------------------
3. Preprocessor options {#preprocessor-options .HeadingA}
=======================
3.1. Default precision {#default-precision .HeadingB}
----------------------
In C++, it is not possible to implement GLSL default precision (GLSL
4.10 specification section 4.5.3) using GLSL syntax.
------------------------
precision mediump int;
precision highp float;
------------------------
------------------------
To use the default precision functionality, GLM provides some defines
that need to add before any include of glm.hpp:
----------------------------------------
\#define GLM\_PRECISION\_MEDIUMP\_INT;
\#define GLM\_PRECISION\_HIGHP\_FLOAT;
\#include &lt;glm/glm.hpp&gt;
----------------------------------------
----------------------------------------
Available defines for floating point types (glm::vec\*, glm::mat\*):
GLM\_PRECISION\_LOWP\_FLOAT: Low precision\
GLM\_PRECISION\_MEDIUMP\_FLOAT: Medium precision\
GLM\_PRECISION\_HIGHP\_FLOAT: High precision (default)
Available defines for floating point types (glm::dvec\*, glm::dmat\*):
GLM\_PRECISION\_LOWP\_DOUBLE: Low precision\
GLM\_PRECISION\_MEDIUMP\_DOUBLE: Medium precision\
GLM\_PRECISION\_HIGHP\_DOUBLE: High precision (default)
Available defines for signed integer types (glm::ivec\*):
GLM\_PRECISION\_LOWP\_INT: Low precision
GLM\_PRECISION\_MEDIUMP\_INT: Medium precision
GLM\_PRECISION\_HIGHP\_INT: High precision (default)
Available defines for unsigned integer types (glm::uvec\*):
GLM\_PRECISION\_LOWP\_UINT: Low precision
GLM\_PRECISION\_MEDIUMP\_UINT: Medium precision
GLM\_PRECISION\_HIGHP\_UINT: High precision (default)
3.2. Compile-time message system {#compile-time-message-system .HeadingB}
--------------------------------
GLM includes a notification system which can display some information at
build time:
- Platform: Windows, Linux, Native Client, QNX, etc.
- Compiler: Visual C++, Clang, GCC, ICC, etc.
- Build model: 32bits or 64 bits
- C++ version : C++98, C++11, MS extensions, etc.
- Architecture: x86, SSE, AVX, etc.
- Included extensions
- etc.
This system is disabled by default. To enable this system, define
GLM\_FORCE\_MESSAGES before any inclusion of &lt;glm/glm.hpp&gt;. The
messages are generated only by compiler supporting \#program message and
only once per project build.
-------------------------------
\#define GLM\_FORCE\_MESSAGES
\#include &lt;glm/glm.hpp&gt;
-------------------------------
-------------------------------
3.3. C++ language detection {#c-language-detection .HeadingB}
---------------------------
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 &lt;glm/glm.hpp&gt; to restrict the language feature
set C++98:
-------------------------------
\#define GLM\_FORCE\_CXX98
\#include &lt;glm/glm.hpp&gt;
-------------------------------
-------------------------------
For C++11 and C++14, equivalent defines are available:
GLM\_FORCE\_CXX11, GLM\_FORCE\_CXX14.
-------------------------------
\#define GLM\_FORCE\_CXX11
\#include &lt;glm/glm.hpp&gt;
-------------------------------
-------------------------------
GLM\_FORCE\_CXX14 overrides GLM\_FORCE\_CXX11 and GLM\_FORCE\_CXX11
overrides GLM\_FORCE\_CXX98 defines.
3.4. SIMD support {#simd-support .HeadingB}
-----------------
GLM provides some SIMD optimizations based on [compiler
intrinsics](https://msdn.microsoft.com/en-us/library/26td21ds.aspx).
These optimizations will be automatically thanks to compiler arguments.
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.
+--------------------------------------------------------------------------+
| \#define GLM\_FORCE\_PURE |
| |
| \#include &lt;glm/glm.hpp&gt;\ |
| \ |
| // GLM code will be compiled using pure C++ code |
+==========================================================================+
+--------------------------------------------------------------------------+
+--------------------------------------------------------------------------+
| \#define GLM\_FORCE\_AVX2 |
| |
| \#include &lt;glm/glm.hpp&gt;\ |
| \ |
| // If the compiler doesn’t support AVX2 instrinsics,\ |
| // 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.
3.5. Force inline {#force-inline .HeadingB}
-----------------
To push further the software performance, a programmer can define
GLM\_FORCE\_INLINE before any inclusion of &lt;glm/glm.hpp&gt; to force
the compiler to inline GLM code.
-------------------------------
\#define GLM\_FORCE\_INLINE
\#include &lt;glm/glm.hpp&gt;
-------------------------------
-------------------------------
3.6. Vector and matrix static size {#vector-and-matrix-static-size .HeadingB}
----------------------------------
GLSL supports the member function .length() for all vector and matrix
types.
-------------------------------
\#include &lt;glm/glm.hpp&gt;
void foo(vec4 const & v)
{
> int Length = v.length();
>
> …
}
-------------------------------
-------------------------------
This function returns a int however this function typically interacts
with STL size\_t based code. GLM provides GLM\_FORCE\_SIZE\_T\_LENGTH
pre-processor option 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 &lt;glm/glm.hpp&gt;
void foo(vec4 const & v)
{
> glm::size\_t Length = v.length();
>
> …
}
--------------------------------------
--------------------------------------
3.7. Disabling default constructor initialization {#disabling-default-constructor-initialization .HeadingB}
-------------------------------------------------
By default and following GLSL specifications, vector and matrix default
constructors initialize the components to zero. This is a reliable
behavior but initialization has a cost and it’s not always necessary.
This behavior can be disable at compilation time by define
GLM\_FORCE\_NO\_CTOR\_INIT before any inclusion of &lt;glm/glm.hpp&gt;
or other GLM include.
GLM default behavior:
-------------------------------------------------
\#include &lt;glm/glm.hpp&gt;
void foo()
{
> glm::vec4 v; // v is (0.0f, 0.0f, 0.0f, 0.0f)
>
> …
}
-------------------------------------------------
-------------------------------------------------
GLM behavior using GLM\_FORCE\_NO\_CTOR\_INIT:
------------------------------------------
\#define GLM\_FORCE\_NO\_CTOR\_INIT
\#include &lt;glm/glm.hpp&gt;
void foo()
{
> glm::vec4 v; // v is fill with garbage
>
> …
}
------------------------------------------
------------------------------------------
Alternatively, GLM allows to explicitly not initialize a variable:
-----------------------------------
\#include &lt;glm/glm.hpp&gt;
void foo()
{
> glm::vec4 v(glm::uninitialize);
>
> …
}
-----------------------------------
-----------------------------------
3.8. Require explicit conversions {#require-explicit-conversions .HeadingB}
---------------------------------
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 behavior is supported in GLM. However, GLM 0.9.6
introduced the define GLM\_FORCE\_EXPLICIT\_CTOR to require explicit
conversion for GLM types.
+--------------------------------------------------------------------------+
| \#include &lt;glm/glm.hpp&gt; |
| |
| 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 &lt;glm/glm.hpp&gt; |
| |
| void foo() |
| |
| { |
| |
| > glm::ivec4 a;\ |
| > … |
| > |
| > glm::vec4 b(a); // Explicit conversion, OK\ |
| > glm::vec4 c = a; // Implicit conversion, ERROR |
| > |
| > … |
| |
| } |
+==========================================================================+
+--------------------------------------------------------------------------+
3.9. Removing genType restriction {#removing-gentype-restriction .HeadingB}
---------------------------------
By default GLM only supports basic types as genType for vector, matrix
and quaternion types:
--------------------------------------------
\#include &lt;glm/glm.hpp&gt;
typedef glm::tvec4&lt;float&gt; my\_fvec4;
--------------------------------------------
--------------------------------------------
GLM 0.9.8 introduced GLM\_FORCE\_UNRESTRICTED\_GENTYPE define to relax
this restriction:
+--------------------------------------------------------------------------+
| \#define GLM\_FORCE\_UNRESTRICTED\_GENTYPE\ |
| \#include &lt;glm/glm.hpp&gt; |
| |
| \#include "half.hpp" // Define “half” class with equivalent behavior |
| than “float” |
| |
| typedef glm::tvec4&lt;half&gt; my\_hvec4; |
+==========================================================================+
+--------------------------------------------------------------------------+
However, defining GLM\_FORCE\_UNRESTRICTED\_GENTYPE is not compatible
with GLM\_FORCE\_SWIZZLE and will generate a compilation error if both
are defined at the same time.
4. Stable extensions {#stable-extensions .HeadingA}
====================
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 &lt;glm/glm.hpp&gt;
\#include &lt;glm/gtc/matrix\_transform.hpp&gt;
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 {#glm_gtc_bitfield .HeadingB}
-----------------------
Fast bitfield operations on scalar and vector variables.
&lt;glm/gtc/bitfield.hpp&gt; need to be included to use these features.
4.2. GLM\_GTC\_color\_space {#glm_gtc_color_space .HeadingB}
---------------------------
Conversion between linear RGB to sRGB and sRGB to linear RGB.
&lt;glm/gtc/color\_space.hpp&gt; need to be included to use these
features.
4.3. GLM\_GTC\_constants {#glm_gtc_constants .HeadingB}
------------------------
Provide a list of built-in constants.
&lt;glm/gtc/constants.hpp&gt; need to be included to use these features.
4.4. GLM\_GTC\_epsilon {#glm_gtc_epsilon .HeadingB}
----------------------
Approximate equal and not equal comparisons with selectable epsilon.
&lt;glm/gtc/epsilon.hpp&gt; need to be included to use these features.
4.5. GLM\_GTC\_functions {#glm_gtc_functions .HeadingB}
------------------------
Useful functions.
&lt;glm/gtc/functions.hpp&gt; need to be included to use these features.
4.6. GLM\_GTC\_integer {#glm_gtc_integer .HeadingB}
----------------------
Provide integer variants of GLM core functions.
&lt;glm/gtc/integer.hpp&gt; need to be included to use these features.
4.7. GLM\_GTC\_matrix\_access {#glm_gtc_matrix_access .HeadingB}
-----------------------------
Define functions to access rows or columns of a matrix easily.
&lt;glm/gtc/matrix\_access.hpp&gt; need to be included to use these
features.
4.8. GLM\_GTC\_matrix\_integer {#glm_gtc_matrix_integer .HeadingB}
------------------------------
Provide integer matrix types. Inverse and determinant functions are not
supported for these types.
&lt;glm/gtc/matrix\_integer.hpp&gt; need to be included to use these
features.
4.9. GLM\_GTC\_matrix\_inverse {#glm_gtc_matrix_inverse .HeadingB}
------------------------------
Define additional matrix inverting functions.
&lt;glm/gtc/matrix\_inverse.hpp&gt; need to be included to use these
features.
4.10. GLM\_GTC\_matrix\_transform {#glm_gtc_matrix_transform .HeadingB}
---------------------------------
Define functions that generate common transformation 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.
&lt;glm/gtc/matrix\_transform.hpp&gt; need to be included to use these
features.
4.11. GLM\_GTC\_noise {#glm_gtc_noise .HeadingB}
---------------------
Define 2D, 3D and 4D procedural noise functions.
&lt;glm/gtc/noise.hpp&gt; need to be included to use these features.
![](media/image5.png){width="2.6666666666666665in"
height="2.6666666666666665in"}
Figure 4.11.1: glm::simplex(glm::vec2(x / 16.f, y / 16.f));
![](media/image6.png){width="2.6666666666666665in"
height="2.6666666666666665in"}
Figure 4.11.2: glm::simplex(glm::vec3(x / 16.f, y / 16.f, 0.5f));
![](media/image7.png){width="2.6666666666666665in"
height="2.6666666666666665in"}
Figure 4.11.3: glm::simplex(glm::vec4(x / 16.f, y / 16.f, 0.5f, 0.5f));
![](media/image8.png){width="2.6666666666666665in"
height="2.6666666666666665in"}
Figure 4.11.4: glm::perlin(glm::vec2(x / 16.f, y / 16.f));
![](media/image9.png){width="2.6666666666666665in"
height="2.6666666666666665in"}
Figure 4.11.5: glm::perlin(glm::vec3(x / 16.f, y / 16.f, 0.5f));
![](media/image10.png){width="2.6666666666666665in"
height="2.6666666666666665in"}
Figure 4.11.6: glm::perlin(glm::vec4(x / 16.f, y / 16.f, 0.5f, 0.5f)));
![](media/image11.png){width="2.6666666666666665in"
height="2.6666666666666665in"}
Figure 4.11.7: glm::perlin(glm::vec2(x / 16.f, y / 16.f),
glm::vec2(2.0f));
![](media/image12.png){width="2.6666666666666665in"
height="2.6666666666666665in"}
Figure 4.11.8: glm::perlin(glm::vec3(x / 16.f, y / 16.f, 0.5f),
glm::vec3(2.0f));
![](media/image13.png){width="2.6666666666666665in"
height="2.6666666666666665in"}
Figure 4.11.9: glm::perlin(glm::vec4(x / 16.f, y / 16.f,
glm::vec2(0.5f)), glm::vec4(2.0f));
4.12. GLM\_GTC\_packing {#glm_gtc_packing .HeadingB}
-----------------------
Convert scalar and vector types to packed formats. This extension can
also unpack packed data to the original format. The use of packing
functions will results in precision lost. However, the extension
guarantee that packing a value previously unpacked from the same format
will be perform loselessly.
&lt;glm/gtc/packing.hpp&gt; need to be included to use these features.
4.13. GLM\_GTC\_quaternion {#glm_gtc_quaternion .HeadingB}
--------------------------
Define a quaternion type and several quaternion operations.
&lt;glm/gtc/quaternion.hpp&gt; need to be included to use these
features.
4.14. GLM\_GTC\_random {#glm_gtc_random .HeadingB}
----------------------
Generate random number from various distribution methods.
&lt;glm/gtc/random.hpp&gt; need to be included to use these features.
![](media/image14.png){width="3.5625in" height="2.6666666666666665in"}
Figure 4.14.1: glm::vec4(glm::linearRand(glm::vec2(-1), glm::vec2(1)),
0, 1);
![](media/image15.png){width="3.6041666666666665in"
height="2.6979166666666665in"}
Figure 4.14.2: glm::vec4(glm::circularRand(1.0f), 0, 1);
![](media/image16.png){width="3.625in" height="2.7291666666666665in"}\
Figure 4.14.3: glm::vec4(glm::sphericalRand(1.0f), 1);
![](media/image17.png){width="3.6354166666666665in"
height="2.7395833333333335in"}
Figure 4.14.4: glm::vec4(glm::diskRand(1.0f), 0, 1);
![](media/image18.png){width="3.625in" height="2.71875in"}
Figure 4.14.5: glm::vec4(glm::ballRand(1.0f), 1);
![](media/image19.png){width="3.6458333333333335in"
height="2.7395833333333335in"}
Figure 4.14.6: glm::vec4(glm::gaussRand(glm::vec3(0), glm::vec3(1)), 1);
4.15. GLM\_GTC\_reciprocal {#glm_gtc_reciprocal .HeadingB}
--------------------------
Provide hyperbolic functions: secant, cosecant, cotangent, etc.
&lt;glm/gtc/reciprocal.hpp&gt; need to be included to use these
functionalities.
4.16. GLM\_GTC\_round {#glm_gtc_round .HeadingB}
---------------------
Rounding operation on power of two and multiple values.
&lt;glm/gtc/round.hpp&gt; need to be included to use these
functionalities.
4.17. GLM\_GTC\_type\_aligned {#glm_gtc_type_aligned .HeadingB}
-----------------------------
Aligned vector types.
&lt;glm/gtc/type\_aligned.hpp&gt; need to be included to use these
functionalities.
4.18. GLM\_GTC\_type\_precision {#glm_gtc_type_precision .HeadingB}
-------------------------------
Add vector and matrix types with defined precisions. Eg, i8vec4: vector
of 4 signed integer of 8 bits.
This extension adds defines to set the default precision of each class
of types added:
Available defines for signed 8-bit integer types (glm::i8vec\*):
GLM\_PRECISION\_LOWP\_INT8: Low precision
GLM\_PRECISION\_MEDIUMP\_INT8: Medium precision
GLM\_PRECISION\_HIGHP\_INT8: High precision (default)
Available defines for unsigned 8-bit integer types (glm::u8vec\*):
GLM\_PRECISION\_LOWP\_UINT8: Low precision
GLM\_PRECISION\_MEDIUMP\_UINT8: Medium precision
GLM\_PRECISION\_HIGHP\_UINT8: High precision (default)
Available defines for signed 16-bit integer types (glm::i16vec\*):
GLM\_PRECISION\_LOWP\_INT16: Low precision
GLM\_PRECISION\_MEDIUMP\_INT16: Medium precision
GLM\_PRECISION\_HIGHP\_INT16: High precision (default)
Available defines for unsigned 16-bit integer types (glm::u16vec\*):
GLM\_PRECISION\_LOWP\_UINT16: Low precision
GLM\_PRECISION\_MEDIUMP\_UINT16: Medium precision
GLM\_PRECISION\_HIGHP\_UINT16: High precision (default)
Available defines for signed 32-bit integer types (glm::i32vec\*):
GLM\_PRECISION\_LOWP\_INT32: Low precision
GLM\_PRECISION\_MEDIUMP\_INT32: Medium precision
GLM\_PRECISION\_HIGHP\_INT32: High precision (default)
Available defines for unsigned 32-bit integer types (glm::u32vec\*):
GLM\_PRECISION\_LOWP\_UINT32: Low precision
GLM\_PRECISION\_MEDIUMP\_UINT32: Medium precision
GLM\_PRECISION\_HIGHP\_UINT32: High precision (default)
Available defines for signed 64-bit integer types (glm::i64vec\*):
GLM\_PRECISION\_LOWP\_INT64: Low precision
GLM\_PRECISION\_MEDIUMP\_INT64: Medium precision
GLM\_PRECISION\_HIGHP\_INT64: High precision (default)
Available defines for unsigned 64-bit integer types (glm::u64vec\*):
GLM\_PRECISION\_LOWP\_UINT64: Low precision
GLM\_PRECISION\_MEDIUMP\_UINT64: Medium precision
GLM\_PRECISION\_HIGHP\_UINT64: High precision (default)
Available defines for 32-bit floating-point types (glm::f32vec\*,
glm::f32mat\*, glm::f32quat):
GLM\_PRECISION\_LOWP\_FLOAT32: Low precision
GLM\_PRECISION\_MEDIUMP\_FLOAT32: Medium precision
GLM\_PRECISION\_HIGHP\_FLOAT32: High precision (default)
Available defines for 64-bit floating-point types (glm::f64vec\*,
glm::f64mat\*, glm::f64quat):
GLM\_PRECISION\_LOWP\_FLOAT64: Low precision
GLM\_PRECISION\_MEDIUMP\_FLOAT64: Medium precision
GLM\_PRECISION\_HIGHP\_FLOAT64: High precision (default)
&lt;glm/gtc/type\_precision.hpp&gt; need to be included to use these
functionalities.
4.19. GLM\_GTC\_type\_ptr {#glm_gtc_type_ptr .HeadingB}
-------------------------
Handle the interaction between pointers and vector, matrix types.
This extension defines an overloaded function, glm::value\_ptr, which
takes any of the core template types (vec3, mat4, etc.). It returns a
pointer to the memory layout of the object. Matrix types store their
values in column-major order.
This is useful for uploading data to matrices or copying data to buffer
objects.
+--------------------------------------------------------------------------+
| // GLM\_GTC\_type\_ptr extension provides a safe solution:\ |
| \#include &lt;glm/glm.hpp&gt; |
| |
| \#include &lt;glm/gtc/type\_ptr.hpp&gt; |
| |
| void foo() |
| |
| { |
| |
| > glm::vec4 v(0.0f); |
| > |
| > glm::mat4 m(1.0f); |
| > |
| > ... |
| > |
| > glVertex3fv(glm::value\_ptr(v)) |
| > |
| > glLoadMatrixfv(glm::value\_ptr(m)); |
| |
| } |
| |
| // Another solution inspired by STL: |
| |
| \#include &lt;glm/glm.hpp&gt; |
| |
| 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*](http://www.opengl.org/sdk/docs/man2/xhtml/glVertex.xml)(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. *
&lt;glm/gtc/type\_ptr.hpp&gt; need to be included to use these features.
4.20. GLM\_GTC\_ulp {#glm_gtc_ulp .HeadingB}
-------------------
Allow the measurement of the accuracy of a function against a reference
implementation. This extension works on floating-point data and provides
results in
[ULP](http://ljk.imag.fr/membres/Carine.Lucas/TPScilab/JMMuller/ulp-toms.pdf).
&lt;glm/gtc/ulp.hpp&gt; need to be included to use these features.
4.21. GLM\_GTC\_vec1 {#glm_gtc_vec1 .HeadingB}
--------------------
Add \*vec1 types.
&lt;glm/gtc/vec1.hpp&gt; need to be included to use these features.
5. OpenGL interoperability {#opengl-interoperability .HeadingA}
==========================
5.1. GLM replacements for deprecated OpenGL functions {#glm-replacements-for-deprecated-opengl-functions .HeadingB}
------------------------------------------------------
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:
&lt;glm/gtc/matrix\_transform.hpp&gt;
[***glScale{f, d}:
***](http://www.opengl.org/sdk/docs/man2/xhtml/glScale.xml)
--------------------------------
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:
&lt;glm/gtc/matrix\_transform.hpp&gt;
***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:
&lt;glm/gtc/matrix\_transform.hpp&gt;
***glLoadIdentity:***
----------------------------------
glm::mat4(1.0) or glm::mat4();
glm::dmat4(1.0) or glm::dmat4();
----------------------------------
----------------------------------
From GLM core library: &lt;glm/glm.hpp&gt;
***glMultMatrix{f, d}: ***
-------------------------------
glm::mat4() \* glm::mat4();
glm::dmat4() \* glm::dmat4();
-------------------------------
-------------------------------
From GLM core library: &lt;glm/glm.hpp&gt;
***glLoadTransposeMatrix{f, d}: ***
-------------------------------
glm::transpose(glm::mat4());
glm::transpose(glm::dmat4());
-------------------------------
-------------------------------
From GLM core library: &lt;glm/glm.hpp&gt;
***glMultTransposeMatrix{f, d}: ***
-----------------------------------------------
glm::mat4() \* glm::transpose(glm::mat4());
glm::dmat4() \* glm::transpose(glm::dmat4());
-----------------------------------------------
-----------------------------------------------
From GLM core library: &lt;glm/glm.hpp&gt;
[***glFrustum:
***](http://www.opengl.org/sdk/docs/man2/xhtml/glFrustum.xml)
-------------------------------
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);
-------------------------------
-------------------------------
From GLM\_GTC\_matrix\_transform extension:
&lt;glm/gtc/matrix\_transform.hpp&gt;
***glOrtho: ***
-------------------------------
glm::mat4 glm::ortho(
> float left, float right,
>
> float bottom, float top,
>
> float zNear, float zFar);
glm::dmat4 glm::ortho(
> double left, double right,
>
> double bottom, double top,
>
> double zNear, double zFar);
-------------------------------
-------------------------------
From GLM\_GTC\_matrix\_transform extension:
&lt;glm/gtc/matrix\_transform.hpp&gt;
5.2. GLM replacements for GLU functions {#glm-replacements-for-glu-functions .HeadingB}
---------------------------------------
***gluLookAt: ***
------------------------------
glm::mat4 glm::lookAt(
> glm::vec3 const & eye,
>
> glm::vec3 const & center,
>
> glm::vec3 const & up);
glm::dmat4 glm::lookAt(
> glm::dvec3 const & eye,
>
> glm::dvec3 const & center,
>
> glm::dvec3 const & up);
------------------------------
------------------------------
From GLM\_GTC\_matrix\_transform extension:
&lt;glm/gtc/matrix\_transform.hpp&gt;
***gluOrtho2D: ***
--------------------------------------------------------
glm::mat4 glm::ortho(
float left, float right, float bottom, float top);
glm::dmat4 glm::ortho(
double left, double right, double bottom, double top);
--------------------------------------------------------
--------------------------------------------------------
From GLM\_GTC\_matrix\_transform extension:
&lt;glm/gtc/matrix\_transform.hpp&gt;
***gluPerspective: ***
---------------------------------------------------------
glm::mat4 perspective(
float fovy, float aspect, float zNear, float zFar);
glm::dmat4 perspective(
double fovy, double aspect, double zNear, double zFar);
---------------------------------------------------------
---------------------------------------------------------
One difference between GLM and GLU is that fovy is expressed in radians
in GLM instead of degrees.
From GLM\_GTC\_matrix\_transform extension:
&lt;glm/gtc/matrix\_transform.hpp&gt;
***gluPickMatrix:***
---------------------------------
glm::mat4 pickMatrix(
> glm::vec2 const & center,
>
> glm::vec2 const & delta,
>
> glm::ivec4 const & viewport);
glm::dmat4 pickMatrix(
> glm::dvec2 const & center,
>
> glm::dvec2 const & delta,
>
> glm::ivec4 const & viewport);
---------------------------------
---------------------------------
From GLM\_GTC\_matrix\_transform extension:
&lt;glm/gtc/matrix\_transform.hpp&gt;
[**gluProject:**](http://www.opengl.org/sdk/docs/man2/xhtml/gluProject.xml)
-------------------------------------------
glm::vec3 project(
> glm::vec3 const & obj,
>
> glm::mat4 const & model,
>
> glm::mat4 const & proj,
>
> glm::{i, ' '}vec4 const & viewport);
glm::dvec3 project(
> glm::dvec3 const & obj,
>
> glm::dmat4 const & model,
>
> glm::dmat4 const & proj,
>
> glm::{i, ' ', d}vec4 const & viewport);
-------------------------------------------
-------------------------------------------
From GLM\_GTC\_matrix\_transform extension:
&lt;glm/gtc/matrix\_transform.hpp&gt;
***gluUnProject: ***
-------------------------------------------
glm::vec3 unProject(
> glm::vec3 const & win,
>
> glm::mat4 const & model,
>
> glm::mat4 const & proj,
>
> glm::{i, ' '}vec4 const & viewport);
glm::dvec3 unProject(
> glm::dvec3 const & win,
>
> glm::dmat4 const & model,
>
> glm::dmat4 const & proj,
>
> glm::{i, ' ', d}vec4 const & viewport);
-------------------------------------------
-------------------------------------------
From GLM\_GTC\_matrix\_transform extension:
&lt;glm/gtc/matrix\_transform.hpp&gt;
6. Known issues {#known-issues .HeadingA}
===============
This section reports the divergences of GLM with GLSL.
6.1. not function {#not-function .HeadingB}
-----------------
The GLSL keyword not is also a keyword in C++. To prevent name
collisions, ensure cross compiler support and a high API consistency,
the GLSL not function has been implemented with the name not\_.
6.2. Precision qualifiers support {#precision-qualifiers-support .HeadingB}
---------------------------------
GLM supports GLSL precision qualifiers through prefixes instead of
qualifiers. For example, additionally to vec4, GLM exposes lowp\_vec4,
mediump\_vec4 and highp\_vec4 types.
Similarly to GLSL, GLM precision qualifiers are used to handle trade-off
between performances and precisions of operations in term of
[ULPs](http://en.wikipedia.org/wiki/Unit_in_the_last_place).
By default, all the types use high precision.
---------------------------------------
// Using precision qualifier in GLSL:
ivec3 foo(in vec4 v)
{
> highp vec4 a = v;
>
> mediump vec4 b = a;
>
> lowp ivec3 c = ivec3(b);
>
> return c;
}
// Using precision qualifier in GLM:
\#include &lt;glm/glm.hpp&gt;
ivec3 foo(const vec4 & v)
{
> highp\_vec4 a = v;
>
> medium\_vec4 b = a;
>
> lowp\_ivec3 c = glm::ivec3(b);
>
> return c;
}
---------------------------------------
---------------------------------------
7. FAQ {#faq .HeadingA}
======
7.1 Why GLM follows GLSL specification and conventions? {#why-glm-follows-glsl-specification-and-conventions .HeadingB}
-------------------------------------------------------
Following GLSL conventions is a really strict policy of GLM. It has been
designed following the idea that everyone does its own math library with
his own conventions. The idea is that brilliant developers (the OpenGL
ARB) worked together and agreed to make GLSL. Following GLSL conventions
is a way to find consensus. Moreover, basically when a developer knows
GLSL, he knows GLM.
7.2. Does GLM run GLSL program? {#does-glm-run-glsl-program .HeadingB}
-------------------------------
No, GLM is a C++ implementation of a subset of GLSL.
7.3. Does a GLSL compiler build GLM codes? {#does-a-glsl-compiler-build-glm-codes .HeadingB}
------------------------------------------
No, this is not what GLM attends to do.
7.4. Should I use ‘GTX’ extensions? {#should-i-use-gtx-extensions .HeadingB}
-----------------------------------
GTX extensions are qualified to be experimental extensions. In GLM this
means that these extensions might change from version to version without
any restriction. In practice, it doesn’t really change except time to
time. GTC extensions are stabled, tested and perfectly reliable in time.
Many GTX extensions extend GTC extensions and provide a way to explore
features and implementations and APIs and then are promoted to GTC
extensions. This is fairly the way OpenGL features are developed;
through extensions.
7.5. Where can I ask my questions? {#where-can-i-ask-my-questions .HeadingB}
----------------------------------
A good place is the *[OpenGL
Toolkits](http://www.opengl.org/discussion_boards/ubbthreads.php?ubb=postlist&Board=10&page=1)
forum* on [OpenGL.org](http://www.opengl.org/).
7.6. Where can I find the documentation of extensions? {#where-can-i-find-the-documentation-of-extensions .HeadingB}
------------------------------------------------------
The Doxygen generated documentation includes a complete list of all
extensions available. Explore this [*API
documentation*](http://glm.g-truc.net/html/index.html) to get a complete
view of all GLM capabilities!
7.7. Should I use ‘using namespace glm;’? {#should-i-use-using-namespace-glm .HeadingB}
-----------------------------------------
NO! Chances are that if using namespace glm; is called, especially in a
header file, name collisions will happen as GLM is based on GLSL which
uses common tokens for types and functions. Avoiding using namespace
glm; will a higher compatibility with third party library and SDKs.
7.8. Is GLM fast? {#is-glm-fast .HeadingB}
-----------------
GLM is mainly designed to be convenient and that's why it is written
against the GLSL specification.
Following the Pareto principle where 20% of the code consumes 80% of the
execution time, GLM operates perfectly on the 80% of the code that
consumes 20% of the performances. Furthermore, thanks to the lowp,
mediump and highp qualifiers, GLM provides approximations which trade
precision for performance. Finally, GLM can automatically produce SIMD
optimized code for functions of its implementation.
However, on performance critical code paths, we should expect that
dedicated algorithms should be written to reach peak performance.
7.9. When I build with Visual C++ with /W4 warning level, I have warnings... {#when-i-build-with-visual-c-with-w4-warning-level-i-have-warnings... .HeadingB}
----------------------------------------------------------------------------
You should not have any warnings even in /W4 mode. However, if you
expect such level for your code, then you should ask for the same level
to the compiler by at least disabling the Visual C++ language extensions
(/Za) which generates warnings when used. If these extensions are
enabled, then GLM will take advantage of them and the compiler will
generate warnings.
7.10. Why some GLM functions can crash because of division by zero? {#why-some-glm-functions-can-crash-because-of-division-by-zero .HeadingB}
-------------------------------------------------------------------
GLM functions crashing is the result of a domain error that follows the
precedent given by C and C++ libraries. For example, it’s a domain error
to pass a null vector to glm::normalize function.
7.11. What unit for angles is used in GLM? {#what-unit-for-angles-is-used-in-glm .HeadingB}
------------------------------------------
GLSL is using radians but GLU is using degrees to express angles. This
has caused GLM to use inconsistent units for angles. Starting with GLM
0.9.6, all GLM functions are using radians. For more information, follow
the [link](http://www.g-truc.net/post-0693.html#menu).
8. Code samples {#code-samples .HeadingA}
===============
This series of samples only shows various GLM features without
consideration of any sort.
8.1. Compute a triangle normal {#compute-a-triangle-normal .HeadingB}
------------------------------
-------------------------------------------------------------------
\#include &lt;glm/glm.hpp&gt; // vec3 normalize cross
glm::vec3 computeNormal
(
> glm::vec3 const & a,
>
> glm::vec3 const & b,
>
> glm::vec3 const & c
)
{
return glm::normalize(glm::cross(c - a, b - a));
}
// A much faster but less accurate alternative:
\#include &lt;glm/glm.hpp&gt; // vec3 cross
\#include &lt;glm/gtx/fast\_square\_root.hpp&gt; // fastNormalize
glm::vec3 computeNormal
(
> glm::vec3 const & a,
>
> glm::vec3 const & b,
>
> glm::vec3 const & c
)
{
return glm::fastNormalize(glm::cross(c - a, b - a));
}
-------------------------------------------------------------------
-------------------------------------------------------------------
8.2. Matrix transform {#matrix-transform .HeadingB}
---------------------
---------------------------------------------------------------------
// vec3, vec4, ivec4, mat4
\#include &lt;glm/glm.hpp&gt;
// translate, rotate, scale, perspective
\#include &lt;glm/gtc/matrix\_transform.hpp&gt;
// value\_ptr
\#include &lt;glm/gtc/type\_ptr.hpp&gt;
void setUniformMVP
(
> GLuint Location,
>
> glm::vec3 const & Translate,
>
> glm::vec3 const & Rotate
)
{
> glm::mat4 Projection =
>
> glm::perspective(45.0f, 4.0f / 3.0f, 0.1f, 100.f);
>
> glm::mat4 ViewTranslate = glm::translate(
>
> glm::mat4(1.0f),
>
> Translate);
>
> glm::mat4 ViewRotateX = glm::rotate(
>
> ViewTranslate,
>
> Rotate.y, glm::vec3(-1.0f, 0.0f, 0.0f));
>
> glm::mat4 View = glm::rotate(
>
> ViewRotateX,
>
> Rotate.x, glm::vec3(0.0f, 1.0f, 0.0f));
>
> glm::mat4 Model = glm::scale(
>
> glm::mat4(1.0f),
>
> glm::vec3(0.5f));
>
> glm::mat4 MVP = Projection \* View \* Model;
>
> glUniformMatrix4fv(Location, 1, GL\_FALSE, glm::value\_ptr(MVP));
}
---------------------------------------------------------------------
---------------------------------------------------------------------
8.3. Vector types {#vector-types .HeadingB}
-----------------
---------------------------------------------------------------------------
\#include &lt;glm/glm.hpp&gt; //vec2
\#include &lt;glm/gtc/type\_precision.hpp&gt; //hvec2, i8vec2, i32vec2
std::size\_t const VertexCount = 4;
// Float quad geometry
std::size\_t const PositionSizeF32 = VertexCount \* sizeof(glm::vec2);
glm::vec2 const PositionDataF32\[VertexCount\] =
{
glm::vec2(-1.0f,-1.0f),
glm::vec2( 1.0f,-1.0f),
glm::vec2( 1.0f, 1.0f),
glm::vec2(-1.0f, 1.0f)
};
// Half-float quad geometry
std::size\_t const PositionSizeF16 = VertexCount \* sizeof(glm::hvec2);
glm::hvec2 const PositionDataF16\[VertexCount\] =
{
glm::hvec2(-1.0f, -1.0f),
glm::hvec2( 1.0f, -1.0f),
glm::hvec2( 1.0f, 1.0f),
glm::hvec2(-1.0f, 1.0f)
};
// 8 bits signed integer quad geometry
std::size\_t const PositionSizeI8 = VertexCount \* sizeof(glm::i8vec2);
glm::i8vec2 const PositionDataI8\[VertexCount\] =
{
glm::i8vec2(-1,-1),
glm::i8vec2( 1,-1),
glm::i8vec2( 1, 1),
glm::i8vec2(-1, 1)
};
// 32 bits signed integer quad geometry
std::size\_t const PositionSizeI32 = VertexCount \* sizeof(glm::i32vec2);
glm::i32vec2 const PositionDataI32\[VertexCount\] =
{
> glm::i32vec2(-1,-1),
>
> glm::i32vec2( 1,-1),
>
> glm::i32vec2( 1, 1),
>
> glm::i32vec2(-1, 1)
};
---------------------------------------------------------------------------
---------------------------------------------------------------------------
8.4. Lighting {#lighting .HeadingB}
-------------
-----------------------------------------------------------------
\#include &lt;glm/glm.hpp&gt; // vec3 normalize reflect dot pow
\#include &lt;glm/gtx/random.hpp&gt; // vecRand3
// vecRand3, generate a random and equiprobable normalized vec3
glm::vec3 lighting
(
> intersection const & Intersection,
>
> material const & Material,
>
> light const & Light,
>
> glm::vec3 const & View
)
{
> glm::vec3 Color = glm::vec3(0.0f);
>
> glm::vec3 LightVertor = glm::normalize(
>
> Light.position() - Intersection.globalPosition() +
>
> glm::vecRand3(0.0f, Light.inaccuracy());
>
> if(!shadow(
>
> Intersection.globalPosition(),
>
> Light.position(),
>
> LightVertor))
>
> {
>
> float Diffuse = glm::dot(Intersection.normal(), LightVector);
>
> if(Diffuse &lt;= 0.0f)
>
> return Color;
>
> if(Material.isDiffuse())
>
> Color += Light.color() \* Material.diffuse() \* Diffuse;
>
> if(Material.isSpecular())
>
> {
>
> glm::vec3 Reflect = glm::reflect(
>
> -LightVector,
>
> Intersection.normal());
>
> float Dot = glm::dot(Reflect, View);
>
> float Base = Dot &gt; 0.0f ? Dot : 0.0f;
>
> float Specular = glm::pow(Base, Material.exponent());
>
> Color += Material.specular() \* Specular;
>
> }
}
return Color;
}
-----------------------------------------------------------------
-----------------------------------------------------------------
9. References {#references .HeadingA}
=============
9.1. GLM development {#glm-development .HeadingB}
--------------------
- [GLM website](http://glm.g-truc.net)
![](media/image20.png){width="2.870138888888889in"
height="1.6145833333333333in"}- [GLM HEAD
snapshot](https://github.com/g-truc/glm/archive/master.zip)
- GLM bug report and feature request
- [G-Truc Creation’s page](http://www.g-truc.net/project-0016.html)
9.2. OpenGL specifications {#opengl-specifications .HeadingB}
--------------------------
- OpenGL 4.3 core specification
- [GLSL 4.30
specification](http://www.opengl.org/registry/doc/GLSLangSpec.4.30.7.diff.pdf)
![](media/image21.png){width="2.859722222222222in"
height="1.6083333333333334in"}- [*GLU 1.3
specification*](http://www.opengl.org/documentation/specs/glu/glu1_3.pdf)
9.3. External links {#external-links .HeadingB}
-------------------
- [*The OpenGL Toolkits forum to ask questions about
GLM*](http://www.opengl.org/discussion_boards/ubbthreads.php?ubb=postlist&Board=10&page=1)
- [GLM on stackoverflow](http://stackoverflow.com/search?q=GLM)
![](media/image22.png){width="2.870138888888889in" height="1.6145833333333333in"}9.4. Projects using GLM {#projects-using-glm .HeadingB}
---------------------------------------------------------------------------------------------------------
***[Leo’s Forture](http://www.leosfortune.com/) ***
Leo’s Fortune is a platform adventure game where you hunt down the
cunning and mysterious thief that stole your gold. Available on PS4,
Xbox One, PC, Mac, iOS and Android.
Beautifully hand-crafted levels bring the story of Leo to life in this
epic adventure.
“I just returned home to find all my gold has been stolen! For some
devious purpose, the thief has dropped pieces of my gold like
breadcrumbs through the woods.”
“Despite this pickle of a trap, I am left with no choice but to follow
the trail.”
“Whatever lies ahead, I must recover my fortune.” -Leopold
![](media/image23.jpg){width="1.9270833333333333in"
height="2.375in"}[***OpenGL 4.0 Shading Language
Cookbook***](http://www.packtpub.com/opengl-4-0-shading-language-cookbook/book?tag=rk/opengl4-abr1/0811)
A full set of recipes demonstrating simple and advanced techniques for
producing high-quality, real-time 3D graphics using GLSL 4.0.
How to use the OpenGL Shading Language to implement lighting and shading
techniques.
Use the new features of GLSL 4.0 including tessellation and geometry
shaders.
How to use textures in GLSL as part of a wide variety of techniques from
basic texture mapping to deferred shading.
![](media/image24.jpg){width="2.5in"
height="1.40625in"}![](media/image25.jpg){width="2.5in"
height="1.40625in"}[***Outerra***](http://outerra.com/)
![](media/image26.jpg){width="2.5in"
height="1.40625in"}![](media/image27.jpg){width="2.5in"
height="1.40625in"}3D planetary engine for seamless planet rendering
from space down to the surface. Can use arbitrary resolution of
elevation data, refining it to centimetre resolution using fractal
algorithms.
***Falcor***
Real-time rendering research framework by NVIDIA.
![](media/image28.png){width="4.0005588363954505in"
height="1.9273523622047244in"}***Cinder***
Cinder is a free and open source library for professional-quality
creative coding in C++.
Cinder is a C++ library for programming with aesthetic intent - the sort
of development often called creative coding. This includes domains like
graphics, audio, video, and computational geometry. Cinder is
cross-platform, with official support for OS X, Windows, iOS, and WinRT.
![](media/image29.png){width="2.5in" height="1.875in"}Cinder is
production-proven, powerful enough to be the primary tool for
professionals, but still suitable for learning and experimentation.
Cinder is released under the [2-Clause BSD
License](http://opensource.org/licenses/BSD-2-Clause).
[***opencloth***](http://code.google.com/p/opencloth/)
A collection of source codes implementing cloth simulation algorithms in
OpenGL.
![](media/image30.png){width="2.5in"
height="3.2291666666666665in"}Simple, easy-to-follow examples with GLSL
source code, as well as a basic description of the theory behind each
technique.
[***Are you using GLM in a project?***](mailto:glm@g-truc.net)
9.5. OpenGL tutorials using GLM {#opengl-tutorials-using-glm .HeadingB}
--------------------------------
- [*The OpenGL Samples
Pack*](http://www.g-truc.net/project-0026.html#menu), samples that show
how to set up all the different new features
- [*Learning Modern 3D Graphics
rogramming*](http://www.arcsynthesis.org/gltut/), a great OpenGL
tutorial using GLM by Jason L. McKesson
- [*Morten
Nobel-Jørgensen’s*](http://blog.nobel-joergensen.com/2011/04/02/glm-brilliant-math-library-for-opengl/)
review and use an [*OpenGL
renderer*](https://github.com/mortennobel/RenderE)
- [*Swiftless’ OpenGL
tutorial*](http://www.swiftless.com/opengltuts.html) using GLM by Donald
Urquhart
- [*Rastergrid*](http://rastergrid.com/blog/), many technical articles
with companion programs using GLM by Daniel Rákos\
- [*OpenGL Tutorial*](http://www.opengl-tutorial.org), tutorials for
OpenGL 3.1 and later
- [*OpenGL Programming on
Wikibooks*](http://en.wikibooks.org/wiki/OpenGL_Programming): For
beginners who are discovering OpenGL.
- [*3D Game Engine Programming*](http://3dgep.com/): Learning the latest
3D Game Engine Programming techniques.
- [Game
Tutorials](mailto:http://www.gametutorials.com/opengl-4-matrices-and-glm/),
graphics and game programming.
- [open.gl](mailto:https://open.gl/), OpenGL tutorial
-
[c-jump](mailto:http://www.c-jump.com/bcc/common/Talk3/Math/GLM/GLM.html),
GLM tutorial
- [Learn OpenGL](mailto:http://learnopengl.com/), OpenGL tutorial
*- [Are you using GLM in a tutorial?](mailto:glm@g-truc.net)*
9.6. Equivalent for other languages {#equivalent-for-other-languages .HeadingB}
-----------------------------------
- [*GlmSharp*](https://github.com/Philip-Trettner/GlmSharp): Open-source
semi-generated GLM-flavored math library for .NET/C\#.
- [glm-js](https://github.com/humbletim/glm-js): JavaScript adaptation
of the OpenGL Mathematics (GLM) C++ library interfaces
- [Java OpenGL Mathematics (GLM)](https://github.com/java-graphics/glm)
- [JGLM](https://github.com/jroyalty/jglm) - Java OpenGL Mathematics
Library
- [SwiftGL Math
Library](https://github.com/SwiftGL/Math/blob/master/Sources/glm.swift)
- [glm-go](https://github.com/jbowtie/glm-go): Simple linear algebra
library similar in spirit to GLM
- [openll](https://github.com/Polkm/openll): Lua bindings for OpenGL,
GLM, GLFW, OpenAL, SOIL and PhysicsFS
- [glm-rs](https://github.com/dche/glm-rs): GLSL mathematics for Rust
programming language
9.7. Alternatives to GLM {#alternatives-to-glm .HeadingB}
------------------------
- [*CML*](http://cmldev.net/): The CML (Configurable Math Library) is a
free C++ math library for games and graphics.
- [*Eigen*](http://eigen.tuxfamily.org/): A more heavy weight math
library for general linear algebra in C++.
- [*glhlib*](http://glhlib.sourceforge.net/): A much more than glu C
library.
- Are you using or working on an alternative library to GLM?
9.8. Acknowledgements {#acknowledgements .HeadingB}
---------------------
GLM is developed and maintained by [*Christophe
Riccio*](http://www.g-truc.net) but many contributors have made this
project what it is.
Special thanks to:
- Ashima Arts and Stefan Gustavson for their work on
[*webgl-noise*](https://github.com/ashima/webgl-noise) which has been
used for GLM noises implementation.
- [*Arthur
Winters*](http://athile.net/library/wiki/index.php?title=Athile_Technologies)
for the C++11 and Visual C++ swizzle operators implementation and tests.
- Joshua Smith and Christoph Schied for the discussions and the
experiments around the swizzle operator implementation issues.
- Guillaume Chevallereau for providing and maintaining the [*nightlight
build system*](http://my.cdash.org/index.php?project=GLM).
- Ghenadii Ursachi for GLM\_GTX\_matrix\_interpolation implementation.
- Mathieu Roumillac for providing some implementation ideas.
- [*Grant James*](http://www.zeuscmd.com/) for the implementation of all
combination of none-squared matrix products.
- All the GLM users that have report bugs and hence help GLM to become a
great library!