OpenGL matrices

For matrix operations to work together nicely, use this convention:

• (x, y, z, 1) is a position in space.
• (x, y, z, 0) is a vector.

Translation matrix
$$\begin{bmatrix}
1 & 0 & 0 & X\
0 & 1 & 0 & Y\
0 & 0 & 1 & Z\
0 & 0 & 0 & 1\
\end{bmatrix}$$

Scaling matrix
$$\begin{bmatrix}
x & 0 & 0 & 0\
0 & y & 0 & 0\
0 & 0 & z & 0\
0 & 0 & 0 & 1\
\end{bmatrix}$$

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TransformedVector = TranslationMatrix * RotationMatrix * ScaleMatrix * OriginalVector;

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// C++ : compute the matrix
glm::mat4 MVPmatrix = projection * view * model; // Remember : inverted !

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// GLSL : apply it
transformed_vertex = MVP * in_vertex;

• Tutorial 3 : Matrices
• OpenGL 101: Matrices - projection, view, model