Question

I’ve completely stuck with camera in ray tracing. Please, take a look at my calculations and point me out where is the error. I’m using left handed coordinate system.

x,y // range [0..S) x [0..S) //pixels coordinates

Now, let’s transform pixels coordinates to parametric coordinates of camera plane:

xp = x/S * 2 – 1; 
yp = y/S * 2 – 1;

xp, yp // range [-1..1] x [-1..1]

calculation of camera basis:

//eye - camera position
//up - camera up vector
//look_at - camera target point

vec3 w = normalize(look_at-eye);
vec3 u = cross(up,w);
vec3 v = cross(w,u);

so ray direction should have following coordinates:

vec3 dir = look_at – eye + xp*u + yp*v;
ray3 ray = {eye, normalize(dir)};

Answer 1

I think the mistake is here:

vec3 dir = look_at – eye + xp*u + yp*v;

The image plane should have a normal vector w, and either be between the eye and the look at point (the more common way in ray tracers), or be behind the eye (more closely models an actual pinhole camera). So let’s create a scalar zoom_factor. A positive number will put the plane in front of the eye, and a negative one will put it behind the eye (and flip the image).

The center of the image plane is thus:

eye + zoom_factor*w

A point (xp, yp) on the image plane is thus:

eye + zoom_factor*w + xp*u + yp*v

Now you want the direction to be from the eye to this point on this image plane:

vec3 dir = eye + zoom_factor*w + xp*u + yp*v - eye;

The eyes cancel, so it simplifies to:

vec3 dir = zoom_factor*w + xp*u + yp*v

This assumes xp an yp are each in a range like (-0.5, 0.5). Note that (0, 0) is the middle of the image plane with this arrangement.