Prove Redbook's error with a local method

According to Redbook's explanation, in automatic texture coordinate generation, the gl_object_linear mode does not need to use the model view matrix. The gl_eye_linear mode uses the Model View matrix. Then we can make a series of tests to verify the above conclusions:

1. Use gl_eye_linear mode to generate texture coordinates. Set the Model View matrix and projection matrix to enable OGL to perform coordinate transformation with a fixed rendering pipeline.

Test results: The program results are normal. The texture coordinates are related to the eye coordinates and change with the eye coordinates.

2. Use gl_eye_linear mode to generate texture coordinates. Set the Model View matrix to a matrix of units, and perform Model View transformation by yourself. Only the OGL can perform projection transformation in a fixed pipeline.

Test results: The program results are normal.

3. Use gl_object_linear mode to generate texture coordinates. Set the Model View matrix and projection matrix to enable OGL to perform coordinate transformation with a fixed rendering pipeline.

Test results: The program results are normal, and the texture coordinates are related to the object coordinate, which does not change with the eye coordinate.

4. Use gl_object_linear mode to generate texture coordinates. Set the Model View matrix to a matrix of units, and perform Model View transformation by yourself. Only the OGL can perform projection transformation in a fixed pipeline.

Test result: the program result is abnormal and the effect is the same as that in gl_eye_linear mode.

Conclusion: The model view matrix is not required for the gl_eye_linear mode, and the model view matrix is required for the gl_object_linear mode.

In addition, if we assume that Redbook is indeed reversed, the formula for generating automatic texture coordinates in gl_object_linear mode is:

T = (p * M-1) * Vt;

In experiment 4, we set the Model View matrix as the unit matrix, and there are:

T = (p * M-1) * Vt = p * Vt;

The result is in the same gl_eye_linear mode. This is the same as what we have observed.

Maybe Redbook is really wrong.