GLM rotation matrix differs from expected result - opengl

Question

I am trying to create a rotation matrix around the X-axis using glm::gtc::matrix_transform::rotate:
glm::rotate(glm::mat4f(1.0f), glm::radians(90.f), glm::vec3f(1.f, 0.f, 0.f));
I expected the resulting matrix to be (translational offsets removed):
1, 0, 0
0, cos(90), -sin(90)
0, sin(90), cos(90)
0, 0, 0
(See e.g. https://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations)
However, the result is slightly off, i.e.:
1, 0, 0
0, 0.9996240, -0.0274121
0, 0.0274121, 0.9996240
0, 0, 0
I looked at https://github.com/g-truc/glm/blob/master/glm/gtc/matrix_transform.inl and surely enough, the implementation uses a weird factor c + (1 - c) that would explain the results.
My question is now, why? Why is the definition of glm's rotation matrix different? What is the theory behind it?

Answer 1

glm implementation uses this formula from Wikipedia.
The following lines of code are identical to the formula:
Result[0][0] = c + (1 - c) * axis.x * axis.x;
Result[0][1] = (1 - c) * axis.x * axis.y + s * axis.z;
Result[0][2] = (1 - c) * axis.x * axis.z - s * axis.y;
Result[0][3] = 0;
Result[1][0] = (1 - c) * axis.y * axis.x - s * axis.z;
Result[1][1] = c + (1 - c) * axis.y * axis.y;
Result[1][2] = (1 - c) * axis.y * axis.z + s * axis.x;
Result[1][3] = 0;
Result[2][0] = (1 - c) * axis.z * axis.x + s * axis.y;
Result[2][1] = (1 - c) * axis.z * axis.y - s * axis.x;
Result[2][2] = c + (1 - c) * axis.z * axis.z;
Result[2][3] = 0;
There is nothing weird in c + (1 - c) because c + (1 - c) * axis.x * axis.x is the same as c + ((1 - c) * axis.x * axis.x). Do not forget about operator precedence.
Most likely you are having issues with floating-point precision loss.