GLM

OpenGL Mathematics (GLM) is a header only C++ mathematics library for graphics software based on the OpenGL Shading Language (GLSL) specifications. GLM provides classes and functions designed and implemented with the same naming conventions and functionality than GLSL so that anyone who knows GLSL, can use GLM as well in C++.

Data Types

Vectors

glm::vec3{ }

$\overrightarrow{(0,0,0)}$
glm::vec3{ 1.f }

$\overrightarrow{(1,1,1)}$
glm::vec3{ 1.f, 2.f, 3.f }

$\overrightarrow{(1,2,3)}$
glm::vec4{ glm::vec3{ 1.f, 2.f, 3.f }, 4.f }

$\overrightarrow{(1,2,3,4)}$

Matrices

GLM uses column major ordering by default.

glm::mat3{ 0.f }

$\begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ \end{pmatrix}$
glm::mat3{ 1.f }

$\begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{pmatrix}$

glm::mat3{{1.f, 2.f, 3.f},
          {4.f, 5.f, 6.f},
          {7.f, 8.f, 9.f}}

$\begin{pmatrix} 1 & 4 & 7 \\ 2 & 5 & 8 \\ 3 & 6 & 9 \\ \end{pmatrix}$

glm::mat3{glm::vec3{1.f},
          glm::vec3{2.f},
          {3.f, 3.f, 3.f}}

$\begin{pmatrix} 1 & 2 & 3 \\ 1 & 2 & 3 \\ 1 & 2 & 3 \\ \end{pmatrix}$

glm::mat2x3{{1.f, 2.f, 3.f},
            {4.f, 5.f, 6.f}};

$\begin{pmatrix} 1 & 4 \\ 2 & 5 \\ 3 & 6 \\ \end{pmatrix}$

glm::mat4{ glm::mat3{ 2.f } }

$\begin{pmatrix}2 \cdot I & \begin{matrix} 0\\0\\0 \end{matrix} \\ \begin{matrix} 0 & 0 & 0 \end{matrix} & 1 \end{pmatrix}$

Quaternions

TODO

Calculations

#include <glm/glm.hpp>

glm::vec3 v1{ 1.f, 2.f, 3.f };
glm::vec3 v2{ 4.f, 5.f, 6.f };
glm::mat3 m1{{1.f, 2.f, 3.f},
             {4.f, 5.f, 6.f},
             {7.f, 8.f, 9.f}};
glm::mat3 m2{{1.f, 1.f, 1.f},
             {2.f, 2.f, 2.f},
             {3.f, 3.f, 3.f} };
glm::mat3 m3{{3.f, 3.f, 3.f},
             {2.f, 2.f, 2.f},
             {1.f, 1.f, 1.f}};

2.f * v1

$2 \cdot \overrightarrow{(1,2,3)} = \overrightarrow{(2,4,6)}$
v1 * v2

$\overrightarrow{(1\cdot4,2\cdot5,3\cdot6)} = \overrightarrow{(4,10,18)}$
glm::dot(v1, v2)

$\overrightarrow{(1,2,3)} \cdot \overrightarrow{(4,5,6)} = 32$
glm::cross(v1, v2)

$\overrightarrow{(1,2,3)} \times \overrightarrow{(4,5,6)} = \overrightarrow{(-3,6,-3)}$
` m1 * m2`

$M_1 \times M_2 = \begin{pmatrix} 12 & 24 & 36 \\ 15 & 30 & 45 \\ 18 & 36 & 54 \\ \end{pmatrix}$
v1 * m1

$V_1 \times M_1 = \begin{pmatrix} 14 & 32 & 50 \end{pmatrix}$
m1 * v1

$M_1 \times V_1 = \begin{pmatrix} 30 \\ 36 \\ 42 \end{pmatrix}$
m1 * m2 * m3

$\begin{align*}M_1 \times \left ( M_2 \times M_3 \right ) & = M_1 \times \begin{pmatrix} 18& 12& 6\\ 18& 12& 6\\ 18& 12& 6\end{pmatrix}\\ & = \begin{pmatrix} 216 & 144 & 72 \\ 270 & 180 & 90 \\ 324 & 216 & 108 \end{pmatrix}\end{align*}$

Functions

Basic

glm::radians(x)
glm::degrees(x)
glm::inverse(m)

See GLSL’s functions.

Matrix Transformation

mat4 glm::translate(mat4 m, vec3 pos)
mat4 glm::rotate(mat4 m, vec3 angle, vec3 axis)
mat4 glm::scale(mat4 m, vec3 scale)
mat4 glm::ortho(float left, float right, float bottom, float top, float zNear, float zFar)
mat4 glm::perspective(float fovy, float aspect, float zNear, float zFar)

Type Cast

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

glm::vec3 v1{ 1.f, 2.f, 3.f };
glm::mat3 m1{{1.f, 2.f, 3.f},
             {4.f, 5.f, 6.f},
             {7.f, 8.f, 9.f}};
float* pV1 = glm::value_ptr(v1); // {1, 2, 3}
float* pM1 = glm::value_ptr(m1); // {1, 2, 3, 4, 5, 6, 7, 8, 9}

float pV2[3]{3.f, 2.f, 1.f};
float pM2[9]{ 3.f, 3.f, 3.f, 2.f, 2.f, 2.f, 1.f, 1.f, 1.f };
glm::vec3 v2{glm::make_vec3(pV2)}; // {3, 2, 1}
glm::mat3 m2{glm::make_mat3(pM2)};
//3  3  3
//2  2  2
//1  1  1

tags: Graphics