Look at geometry of reflection

Note that for our rays: **R**in
= -**R**d

The projection of **R**in onto
**N** is **N** cos (q) so

**R**out = **N**
cos(q) + **S**

**R**in + **S** =
**N **cos(q)

**S** = **N**
cos(q) - **R**in

**R**out = 2**N**cos(q) - **R**in
= 2**N**(**N · R**in) - **R**in

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