coordinate values after rotation in opengl - c++

Question

Say I have a cube. Say the coordinate values are like this. (1 unit an arm)
GLfloat vertA[3] = { 0.5, 0.5, 0.5};
GLfloat vertB[3] = {-0.5, 0.5, 0.5};
GLfloat vertC[3] = {-0.5,-0.5, 0.5};
GLfloat vertD[3] = { 0.5,-0.5, 0.5};
GLfloat vertE[3] = { 0.5, 0.5,-0.5};
GLfloat vertF[3] = {-0.5, 0.5,-0.5};
GLfloat vertG[3] = {-0.5,-0.5,-0.5};
GLfloat vertH[3] = { 0.5,-0.5,-0.5};
If I translate it like
glTranslatef(1,2,3);
then 1,2 and 3 will be added to x,y and z coordinates respectively. and those are the new coordinate values of the translated cube. But if I rotate it some degree (with or without a translation)
glRotatef(25,0,0,1);
what is the coordinates of the rotated cube now?
I am working new in opengl. I am using c++ on windows.

Answer 1

You should make yourself familiar with linear algebra and transformation matrices.
What glRotate will do is generating a rotation matrix and post-multiplying it to the current matrix. You should be aware of some things here: the glTranslate will not directly add anything to the vertex coordinates, and the glRotate will also not change the coordinates. All what these do is changing a single matrix. This matrix will accumulate the composition of all the transformations, and will be applied once to all the vertices during the draw call.
In your case, a rotation of 25 degrees around the z axis is desired, so the z coordinates will not be changed. The rotation matrix will look like this
| cos(25°) -sin(25°) 0 0 |
| sin(25°) cos(25°) 0 0 |
| 0 0 1 0 |
| 0 0 0 1 |
To apply this matrix to a vector (x,y,z,w)^T, we just multiply the matrix by the vector.
Following the rules of that multiplcation, we get a new vector with
x' = cos(25°)*x -sin(25°)*y
y' = sin(25°)*x +cos(25°)*y
z' = z
w' = w
This is just the rotation alone, not considering the translation. But you can put int the values of zour vertex and will get the transformed result back.

Answer 2

Here you are rotating the current matrix 25 degrees in the z axis. This is the the code for glm::rotate which does the same.
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tmat4x4<T, P> rotate
(
detail::tmat4x4<T, P> const & m,
T const & angle,
detail::tvec3<T, P> const & v
)
{
T c = cos(a);
T s = sin(a);
detail::tvec3<T, P> axis(normalize(v));
detail::tvec3<T, P> temp((T(1) - c) * axis);
detail::tmat4x4<T, P> Rotate(detail::tmat4x4<T, P>::_null);
Rotate[0][0] = c + temp[0] * axis[0];
Rotate[0][1] = 0 + temp[0] * axis[1] + s * axis[2];
Rotate[0][2] = 0 + temp[0] * axis[2] - s * axis[1];
Rotate[1][0] = 0 + temp[1] * axis[0] - s * axis[2];
Rotate[1][1] = c + temp[1] * axis[1];
Rotate[1][2] = 0 + temp[1] * axis[2] + s * axis[0];
Rotate[2][0] = 0 + temp[2] * axis[0] + s * axis[1];
Rotate[2][1] = 0 + temp[2] * axis[1] - s * axis[0];
Rotate[2][2] = c + temp[2] * axis[2];
detail::tmat4x4<T, P> Result(detail::tmat4x4<T, P>::_null);
Result[0] = m[0] * Rotate[0][0] + m[1] * Rotate[0][1] + m[2] * Rotate[0][2];
Result[1] = m[0] * Rotate[1][0] + m[1] * Rotate[1][1] + m[2] * Rotate[1][2];
Result[2] = m[0] * Rotate[2][0] + m[1] * Rotate[2][1] + m[2] * Rotate[2][2];
Result[3] = m[3];
return Result;
}