# How to compute the matrix used by gluLookAt

Hi,

I try to compute the matrix generated by gluLookAt to use it to render my scene.

I have good results with gluLookAt, but not using the matrix i compute.

To compute the matrix i use this code:

``````GLGXMATRIX* GLGXMatrixLookAt( GLGXMATRIX* pResult,GLGXVECTOR3 *pPosition,GLGXVECTOR3 *pTarget,GLGXVECTOR3 *pUp)
{
GLGXVECTOR3 forward = *pTarget - *pPosition;
GLGXVec3Normalize(&forward,&forward);

GLGXVECTOR3  up;
GLGXVec3Normalize(&up,pUp);

GLGXVECTOR3 side;
GLGXVec3Cross(&side, &up, &forward);

pResult->_11 = side.x;
pResult->_12 = side.y;
pResult->_13 = side.z;
pResult->_14 = 0.0f;

pResult->_21 = up.x;
pResult->_22 = up.y;
pResult->_23 = up.z;
pResult->_24 = 0.0f;

pResult->_31 = forward.x;
pResult->_32 = forward.y;
pResult->_33 = forward.z;
pResult->_34 = 0.0f;

pResult->_41 = -pPosition->x;
pResult->_42 = -pPosition->y;
pResult->_43 = -pPosition->z;
pResult->_44 = 1.0f;

// where matrix._11,..._12,..._13,..._14,..._21... equal matrix[0],...[1],...[2],...[3],...[4],...

return pResult;
}
``````

To render my scene i use:

``````glMatrixMode( GL_MODELVIEW );

/*
gluLookAt(this->Scene->Cameras[0].Loc.x,this->Scene->Cameras[0].Loc.y,this->Scene->Cameras[0].Loc.z,
this->Scene->Cameras[0].Eye.x,this->Scene->Cameras[0].Eye.y,this->Scene->Cameras[0].Eye.z,
this->Scene->Cameras[0].Up.x, this->Scene->Cameras[0].Up.y, this->Scene->Cameras[0].Up.z);
*/

GLGXMATRIX matrix; // Is Identity
GLGXMatrixLookAt(&matrix,&this->Scene->Cameras[0].Loc,&this->Scene->Cameras[0].Eye,&this->Scene->Cameras[0].Up);

glPushMatrix(); // Not used with gluLookAt

glMultMatrixf(matrix);  // Not used with gluLookAt

this->Scene->Lights[0].Set();

glColor3ub(255,0,255);
this->Scene->Render();

glPopMatrix(); // Not used with gluLookAt
``````

The camera seems to be upside down. I can’t find what is wrong. I have tried to reverse the vectors, the cross products, …
Is it in rendering ?

The man page for gluLookAt tell exactly how the matrix is computed, why don’t you just compare with that?

I don’t know where to find this man page. Is it under Linux ? Is it in a web page ?

http://publib.boulder.ibm.com/infocenter…f/gluLookAt.htm

They compute again the Up vector. I don’t know why, but i have tried to do what they write. And i have the same result.

The up vector is recomputed to guarantee an ortho-normal coordinate system. The up vector provided to gluLookAt isn’t necessarily orthogonal to the view vector, but the one used to build the lookat-matrix has to be. Recomputing the up vector is mandatory.

Here’s the code (LsgMatrix_setLookAt) i use to compute a lookat matrix:

``````e: eye position
c: lookat center
u: up vector

Z = normalize(e - c)
X = normalize(up x Z)
Y = Z x X

M1 is a matrix whose columns are (X, 0), (Y, 0), (Z, 0) (0,0,0,1)
M2 is a matrix whose columns are (1,0,0,0), (0,1,0,0), (0,0,1,0), (-e.x, -e.y, -e.z, 1)

The lookat matrix is the product of M1 and M2

L = M1 * M2
``````

Thanks.