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
Famous quotes containing the words direction of, direction and/or reflection:
“Dressed to die, the sensual strut begun,
With my red veins full of money,
In the final direction of the elementary town
I advance for as long as forever is.”
—Dylan Thomas (1914–1953)
“She saw she had fallen into the hands of one of those doctors who have strayed too far from aperients in the direction of the soul.”
—Rebecca West (1892–1983)
“There are three principal means of acquiring knowledge available to us: observation of nature, reflection, and experimentation. Observation collects facts; reflection combines them; experimentation verifies the result of that combination. Our observation of nature must be diligent, our reflection profound, and our experiments exact. We rarely see these three means combined; and for this reason, creative geniuses are not common.”
—Denis Diderot (1713–1784)