Formula derivation and understanding.

[Jiahao-Ma]

Hi Jinhui,

Thanks for sharing such great work! When reading your paper, there are two points confusing me.

For the first one, if we get the surface normal, the ray of incidence, how can we compute the refracted ray based on Snell's law? In the paper you only give the results and omit the intermediate process, can you please provide more information about the derivation process? Or relevant information would be fine.

What's more, for the distance loss, why do we need to multiply refracted light twice? Is the refracted ray at this point a unit vector?

Your answers are very important to me and I look forward to hearing from you!

Cheers,
Jiahao

[jhxiong]

Thanks for your interests in this work.

• The derivation of the Snell's law is quite common so I skipped the derivation process. I just find a link for this derivation: https://physics.stackexchange.com/questions/435512/snells-law-in-vector-form (the highest scored answer). Slight difference in the notation, but the formation is almost the same.
• The first dot product is to compute the length of the projection (return a scalar value), and the second multiply is to compute the projected vector (return a vector). Refracted ray r is a unit vector. This link (https://en.wikipedia.org/wiki/Vector_projection) explains vector projection.