[Hill: 358-366. Foley & van Dam: p. 237-242
(slightly different terminology]
Viewing Transformations
The modelling transformation expresses the
position of objects in the world. We derive the viewing transformation by first
expressing the position of the camera in the world. This transformation is then
inverted to express the position of the world with respect to the camera.
Defining Mcam
A common way of defining the camera position and
orientation is to use:
- an eye point
- a reference point
- an up vector
Building M_cam
The vectors i,j,k can be determined as follows:
These vectors can then be used to form a change-of-basis matrix, which is
composed with a translation to yield the camera-to-world transformation and its
inverse, which is what we really desire.
Positioning the camera in OpenGL
The OpenGL auxilliary library provides
the call gluLookAt() to create the viewing transformation.
gluLookAt(ex,ey,ez,rx,ry,rz,ux,uy,uz>
where (ex,ey,ez) gives the eye point, (rx,ry,rz) gives the
reference or 'lookat' point, and (ux,uy,uz) gives the up
vector.
This function call postmultiplies the current matrix, so the easiest
way to use it is:
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
gluLookAt(ex,ey,ez,rx,ry,rz,ux,uy,uz);
/* setup modelling transformations here */