# Formula for rays in ray tracing

Each time the camera generates a ray, the first task of the renderer is to determine which object, if any, that ray intersects first and where the intersection occurs. This intersection point is the visible point along the ray, and we will want to simulate the interaction of light with the object at this point. To find the intersection, we must test the ray for intersection against all objects in the scene and select the one that the ray intersects first. Given a ray $r$, we first start by writing it in parametric form: $$r(t)=o+td\,,$$ where $o$ is the ray's origin, $d$ is its direction vector, and $t$ is a parameter whose legal range is $[0, ∞)$.

My Question is - How is the equation $r(t)=o+td$ formed from theory? For example, why is there $+$ instead of $-$ or $*$ or $/$, etc?

• Have you tried plotting your other proposed formulas? – Louis Mar 5 '15 at 11:08
• was looking for a different article but this should do - realtimecollisiondetection.net/blog/?p=13 calculating the scalar triple product between the ray and the triangle(or any planar shape) is probably the most universal way to do it(no precomputation required, gives you UVT values). Not fast enough for realtime brute force raytracing though, even if it is the fastest method with that kind of flexibility and accuracy that i know of. You might get close with really clever scene sorting though. – user29075 Mar 5 '15 at 12:12