How to Define a Model Matrix Without Using glm::lookAt()?

Transforming the Model Matrix

To define the position and orientation of an object in a 3D scene, one typically uses the model matrix. While glm::lookAt() is a convenient function for setting up a view matrix, it may not be directly applicable to the model matrix.

Model Transformation

The model matrix transforms vertex positions from the model space (the local coordinate system of the object) to the world space (the coordinate system of the entire scene). It comprises three main elements:

• Position: Translates the object along the x, y, and z axes.
• Rotation: Rotates the object around the x, y, and z axes.
• Scale: Adjusts the size of the object.

Creating a Model Matrix

Instead of using glm::lookAt(), you can define a model matrix manually using the following structure:

[ X-axis.x, X-axis.y, X-axis.z, 0 ]
[ Y-axis.x, Y-axis.y, Y-axis.z, 0 ]
[ Z-axis.x, Z-axis.y, Z-axis.z, 0 ]
[ trans.x,  trans.y,  trans.z,  1 ]

For example, if you want to position an object at (0.4, 0.0, 0.0) and rotate it by 45 degrees around the x-axis, you would define the model matrix as:

[ 1.0,  0.0,  0.0,  0.0 ]
[ 0.0,  0.707, 0.707, 0.0 ]
[ 0.0, -0.707, 0.707, 0.0 ]
[ 0.4,  0.0,  0.0,  1.0 ]

Shader Implementation

In your vertex shader, you can then transform the vertex position using the model matrix as follows:

gl_Position = CameraMatrix * ModelMatrix * Pos;

Where:

• CameraMatrix is the view-projection matrix.
• ModelMatrix is the model matrix defined above.
• Pos is the vertex position in model space.

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