GLKView GLKMatrix4MakeLookAt description and explanation

Question

For modelviewMatrix I understand how to form translate and scale Matrix. But I am unable to understand how to form viewMatrix using GLKMatrix4MakeLookAt. Can anyone explain how to it works and how to give value to parameters(eye center up X Y Z).

GLK_INLINE GLKMatrix4 GLKMatrix4MakeLookAt(float eyeX, float eyeY, float eyeZ,
                                                  float centerX, float centerY, float centerZ,
                                                  float upX, float upY, float upZ)

Answer 1

GLKMatrix4MakeLookAt creates a viewing matrix (in the same way as gluLookAt does, in case you look at other OpenGL code). As the parameters suggest, it considers the position of the viewer's eye, the point in space they're looking at (e.g., a point on an object), and the up vector, which specifies which direction is "up" (e.g., pointing towards the sky). The viewing matrix generated is the combination of a rotation matrix (composed of a set of orthonormal bases [basis vectors]) and an translation.

Logically, the matrix is basically constructed in a few steps:

1. compute the line-of-sight vector, which is the normalized vector going from the eye's position to the point you're looking at, the center point.
2. compute the cross product of the line-of-sight vector with the up vector, and normalize the resulting vector.
3. compute the cross product of the vector computed in step 2. with the line-of-sight to complete the orthonormal basis.
4. create a 3x3 rotation matrix by setting the first row to the vector created in step 2., the middle row with the vector from step 3., and the bottom row to the negated, normalized line-of-sight vector.

those three steps produce a rotation matrix that will rotate the world coordinate system into eye coordinates (a coordinate system where the eye is located at the origin, and the line-of-sight is down the -z axis. The final viewing matrix is computed by multiplying a translation to the negated eye position, which moves the "world coordinate positioned eye" to the origin for eye coordinates.

Here's a related question showing the code of GLKMatrix4MakeLookAt, and here's a question with more detail about eye coordinates and related coordinate systems: (What exactly are eye space coordinates?) .