Changing the projection reference point in Open GL

Question

By default, the eye an the projection reference point PRP are in (0,0,0). I can change the eye position with gluLookAt(), but how can I change the PRP (i.e., the convergence position for a set of parallel lines) for a perspective projection in OpenGL?

Answer 1

Eye position, projection reference point PRP, camera center, or projection center are all just different words for the same thing.

gluLookAt() applied to the GL_MODELVIEW matrix works for both, parallel and perspective projection.

You can choose between parallel and perspective projection by setting up the GL_PROJECTION matrix. For perspective projection this can be done using the gluPerspective() function.

Creating a perspective projection matrix in OpenGL

Edit: (after revised question)

If the PRP is not at the eye position, you can not use gluPerspective(). Instead you have to create your own GL_PROJECTION matrix. Following the formula that you have now provided, this results in the 4 x 4 matrix:

$$\mathtt{A} =\begin{bmatrix} z_c-z_{pp} & 0 & -x_c & x_c \cdot z_{pp}\\ 0 & z_c-z_{pp} & -y_c & y_c \cdot z_{pp} \\ 0 & 0 & \frac{\mathrm{far}+\mathrm{near}}{\mathrm{near}-\mathrm{far}} & \frac{2 \cdot \mathrm{far} \cdot \mathrm{near}}{\mathrm{near}-\mathrm{far}} \\ 0 & 0 & -1 & z_c \end{bmatrix} $$

I have done a quick OpenGL/WebGL rendering test with the GSN Composer. Follow the link and move the mouse over the render output to change $x_c$ and $y_c$ of the projection reference point $(x_c, y_c, z_c)$:

Example: ProjectionReferencePoint | GSN Composer

Answer 2

If you are talking about an oblique perspective projection in which the line joining the eye and center of the projection plane is not perpendicular to the plane like here (upper left),

This can be generated by the glFrustum() call. Normally when you describe perspective projection they set

left = -right

bottom = -top

so that these are centered around the Z-axis. In order to generate an oblique projection you can use the above mentioned method which takes input the coordinates for left, right, top, bottom, near and far planes.

The other way around is to build your own custom projection matrix, and load it directly. The matrix should be stored as an array

GLfloat mat[16] = {...} GlLoadMatrix(mat)