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)
“It is not easy to construct by mere scientific synthesis a foolproof system which will lead our children in a desired direction and avoid an undesirable one. Obviously, good can come only from a continuing interplay between that which we, as students, are gradually learning and that which we believe in, as people.”
—Erik H. Erikson (20th century)
“With some people solitariness is an escape not from others but from themselves. For they see in the eyes of others only a reflection of themselves.”
—Eric Hoffer (1902–1983)