Direction of Reflection
The direction of a reflected ray is determined by the vector of incidence and the surface normal vector. Given an incident direction from the surface to the light source and the surface normal direction the specularly reflected direction (all unit vectors) is:
where is a scalar obtained with the dot product. Different authors may define the incident and reflection directions with different signs. Assuming these Euclidean vectors are represented in column form, the equation can be equivalently expressed as a matrix-vector multiplication:
where is the so-called Householder transformation matrix, defined as:
denotes transposition and is the identity matrix.
Read more about this topic: Specular Reflection
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—Denis Diderot (1713–1784)