Why Does Using glm::lookAt for the ModelMatrix Produce Incorrect Object Positioning and Rotation in GLM?

Transforming Modeling matrices

Question:
In GLM, despite easily setting ViewMatrix, setting a ModelMatrix using glm::lookAt produces incorrect position and rotation for objects. How can we align object orientation with camera positioning using glm::lookAt or do we need to create custom functions?

Answer:

In computer graphics, transformations are applied to objects in the 3D space to position them accurately. Three primary transformation matrices are involved in this process: ModelMatrix, ViewMatrix, and ProjectionMatrix.

Model coordinates:
Each mesh within a scene has its own local space known as model space. Vertex coordinates are defined within this space, and the ModelMatrix defines the object's position, orientation, and relative size in the world space.

World coordinates:
The world space is the coordinate system of the entire scene where multiple objects are placed.

View space:
The view space is defined relative to the viewing perspective, with the position of the view, line of sight, and upwards direction. The inverse matrix of the view coordinate system is the ViewMatrix, transforming objects from world space into the view (eye) space.

Clip coordinates:
Clip space coordinates are homogenous, enabling clipping of the scene. A point is in clip space if its x, y, and z components are within the range defined by the inverted w component and the w component of the homogenous coordinates.

Projection matrix:
The ProjectionMatrix describes the mapping from 3D points of the scene to 2D points of the viewport, transforming view space to clip space.

Normalized device coordinates:
Perspective divide transforms clip space coordinates into normalized device coordinates within the range (-1, -1, -1) to (1, 1, 1).

Window coordinates:
Normalized device coordinates are linearly mapped to the Window Coordinates (Screen Coordinates) and to the depth for the depth buffer, defining the viewport and depth range.

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