Ray tracing, regarding Turner Whitted's original paper

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SUMMARY

Ray tracing, introduced by Turner Whitted in 1979 in his paper "An improved illumination model for shaded display," involves vector calculations critical for understanding light interactions in 3D rendering. The discussion clarifies the concept of vector V', which is defined as the third side of a triangle formed by the normal vector N and the vector (N + V'). V' is scaled by the dot product |V . N|, representing the vertical height adjustment necessary for accurate illumination modeling. This foundational knowledge is essential for anyone studying advanced rendering techniques.

PREREQUISITES
  • Understanding of vector mathematics
  • Familiarity with ray tracing concepts
  • Knowledge of illumination models in computer graphics
  • Basic understanding of dot products and vector scaling
NEXT STEPS
  • Study Turner Whitted's original paper on ray tracing
  • Learn about vector mathematics in computer graphics
  • Explore advanced illumination models beyond Whitted's approach
  • Research practical implementations of ray tracing in modern rendering engines
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Computer graphics students, 3D rendering developers, and anyone interested in the mathematical foundations of ray tracing and illumination models.

alan_k
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As many of you may know, ray tracing was first introduced by Turner Whitted in 1979 in a paper titled "An improved illumination model for shaded display" (can be found on ACM digital library).

On the 2nd page, in part 2 (Improved Model) there are a number of fairly simple vector calculations, unfortunately I can't understand what is vector V' (please refer to the attached screenshot), and why is it scaled by | V . N | ... I would like to ask for your thoughts on this :)

Thanks !

P.S.: unfortunately I can't attach the paper to my post, it is copyrighted by ACM and I think it would be illegal to do so.

EDIT: found a link to the paper from Drexel University here
 

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The diagram shows you the vector (N + V'), as the "horizontal" dotted line ending at the top of the N vector.

So V' is the third side of the triangle with the other two sides N and (N+V'). Ini other words, V' is the V vector scaled to be the same "vertical height" as N.

Earller N was defined as the unit vector (i.e. its length=1) normal to the surface.

So |V.N| is the length of V, times the cosine of the angle between V and N.
 
Hi AlephZero,

Thank you so much for your reply, I appreciate it.