Why Transform Matrix doesn't work in OpenGL - c++

Question

Say I want to draw a Ball in the scene and here are two different ways to do them.
float SUN_TRANSLATION_MATRIX[] = {
1.0f, 0.0f, 0.0f, 0.0f,
0.0f, 1.0f, 0.0f, 0.0f,
0.0f, 0.0f, 1.0f, -15.0f,
0.0f, 0.0f, 0.0f, 1.0f
};
void displaySolarSystem1(){
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
glTranslatef(0.0f, 0.0f, -15.f);
glColor3f(1.0f, 0.8f, 0.5f);
glutSolidSphere(2.0, 50, 40);
glutSwapBuffers();
}
void displaySolarSystem(){
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
glMultMatrixf(SUN_TRANSLATION_MATRIX);
glColor3f(1.0f, 0.8f, 0.5f);
glutSolidSphere(2.0, 50, 40);
glutSwapBuffers();
}
displaySolarSystem1 applies glTranslatef where displaySolarSystem uses Matrix operation the problem is that displaySolarSystem1 works as expected but the matrix failed.
What went wrong with displaySolarSystem()?

Answer 1

http://www.opengl.org/sdk/docs/man/xhtml/glMultMatrix.xml
Calling glMultMatrix with an argument of m = [...] replaces the current transformation with C × M × v
Which means that transformations are applied by multiplying matrix by vector, not vice versa. So, translation matrix would be something like this
1 0 0 X
0 1 0 Y
0 0 1 Z
0 0 0 1
But this is matrix, that is written in row-major order, and OpenGL takes column-major order matrices, so you need to transpose it.
So, finally, you just need to use glMultTransposeMatrix which, if I remember right, is slightly slower, or transpose your matrix to look like this
float SUN_TRANSLATION_MATRIX[] = {
1.0f, 0.0f, 0.0f, 0.0f,
0.0f, 1.0f, 0.0f, 0.0f,
0.0f, 0.0f, 1.0f, 0.0f,
0.0f, 0.0f, -15.0f, 1.0f
};

Answer 2

Thanks Unwind. The problem was solved by changing glMultMatrixf(SUN_TRANSLATION_MATRIX); to glMultTransposeMatrixf(SUN_TRANSLATION_MATRIX); thanks for your hint of "this is a transposed matrix"