Do not understand captureViews in Diffuse-irradiance tutorial in learnopengl.com - c++

Question

I am learning IBL in https://learnopengl.com/PBR/IBL/Diffuse-irradiance.
The tutorial convert a equirectangular to a cubemap by creating 6 views.
And the views are the following code:
glm::mat4 captureViews[] =
{
glm::lookAt(glm::vec3(0.0f, 0.0f, 0.0f), glm::vec3( 1.0f, 0.0f, 0.0f), glm::vec3(0.0f, -1.0f, 0.0f)),
glm::lookAt(glm::vec3(0.0f, 0.0f, 0.0f), glm::vec3(-1.0f, 0.0f, 0.0f), glm::vec3(0.0f, -1.0f, 0.0f)),
glm::lookAt(glm::vec3(0.0f, 0.0f, 0.0f), glm::vec3( 0.0f, 1.0f, 0.0f), glm::vec3(0.0f, 0.0f, 1.0f)),
glm::lookAt(glm::vec3(0.0f, 0.0f, 0.0f), glm::vec3( 0.0f, -1.0f, 0.0f), glm::vec3(0.0f, 0.0f, -1.0f)),
glm::lookAt(glm::vec3(0.0f, 0.0f, 0.0f), glm::vec3( 0.0f, 0.0f, 1.0f), glm::vec3(0.0f, -1.0f, 0.0f)),
glm::lookAt(glm::vec3(0.0f, 0.0f, 0.0f), glm::vec3( 0.0f, 0.0f, -1.0f), glm::vec3(0.0f, -1.0f, 0.0f))
};
I don't understand the third parameter of glm::lookAt.
glm::lookAt's third parameter is the up vector. I think the captureViews should be:
// zero is [0, 0, 0]
// right is [1, 0, 0]
// left is [-1, 0, 0]
// up is [0, 1, 0]
// down is [0, -1, 0]
// back is [0, 0, 1]
// forward is [0, 0, -1]
glm::mat4 captureViews[] =
{
glm::lookAt(zero, right, up),
glm::lookAt(zero, left, up),
glm::lookAt(zero, up, back),
glm::lookAt(zero, down, forward),
glm::lookAt(zero, back, up),
glm::lookAt(zero, forward, up)
};
But I totally wrong. I don't understand the magic in the tutorial's up vector.
Can anyone explain it for me?

Answer 1

When a cubemap texture is used, then a 3 dimensional direction vector has to be transformed, to 2 dimensional texture coordinate relative to one side of the map.
The relevant part of the specification for this transformtion is OpenGL 4.6 API Core Profile Specification, 8.13 Cube Map Texture Selection, page 253:
When a cube map texture is sampled, the (s t r) texture coordinates are treated
as a direction vector (rx ry rz) emanating from the center of a cube. The q coordinate is ignored. At texture application time, the interpolated per-fragment direction vector selects one of the cube map face’s two-dimensional images based on the largest magnitude coordinate direction (the major axis direction). If two or more coordinates have the identical magnitude, the implementation may define the rule to disambiguate this situation. The rule must be deterministic and depend only on (rx ry rz). The target column in table 8.19 explains how the major axis direction maps to the two-dimensional image of a particular cube map target.
Using the sc, tc, and ma determined by the major axis direction as specified in table 8.19, an updated (s t)
is calculated as follows:
s = 1/2 * (s_c / |m_a| + 1)
t = 1/2 * (t_c / |m_a| + 1)
Major Axis Direction| Target |sc |tc |ma |
--------------------+---------------------------+---+---+---+
+rx |TEXTURE_CUBE_MAP_POSITIVE_X|−rz|−ry| rx|
−rx |TEXTURE_CUBE_MAP_NEGATIVE_X| rz|−ry| rx|
+ry |TEXTURE_CUBE_MAP_POSITIVE_Y| rx| rz| ry|
−ry |TEXTURE_CUBE_MAP_NEGATIVE_Y| rx|−rz| ry|
+rz |TEXTURE_CUBE_MAP_POSITIVE_Z| rx|−ry| rz|
−rz |TEXTURE_CUBE_MAP_NEGATIVE_Z|−rx|−ry| rz|
--------------------+---------------------------+---+---+---+
sc cooresponds the u coordiante and tc to the v cooridnate. So tc has to be in the direction of the view space up vector
Look at the first row of the table:
+rx | TEXTURE_CUBE_MAP_POSITIVE_X | −rz | −ry | rx
This means, for the X+ side (right side) of the cube map, the directions which correspond to the tangent and binormal are
sc = (0, 0, -1)
tc = (0, -1, 0)
This perfectly matches the 1st row of the table glm::mat4 captureViews[]:
glm::lookAt(glm::vec3(0.0f, 0.0f, 0.0f), glm::vec3(1.0f, 0.0f, 0.0f), glm::vec3(0.0f, -1.0f, 0.0f))
because the major direction is given by the line of sight, which is the directon form the eye position to the target (los = target - eye) and so (1, 0, 0).
The up vector (or ts) is (0, -1, 0).
sc is given by the cross product of the line of sight and the up vector (0, 0, -1).