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 and/or reflection:
“Your Englishman, confronted by something abnormal will always pretend that it isn’t there. If he can’t pretend that, he will look through the object, or round it, or above it or below it, or in any direction except into it. If, however, you force him to look into it, he will at once pretend that he sees the object not for what it is but for something that he would like it to be.”
—James Agate (1877–1947)
“Uncertainty about the outcome is a given in child rearing and not a reflection of a mother’s inadequacy. She should not be misled by her wish to be omnipotent, all-powerful, all-giving, the perfect mother, who will right all the wrongs and make up for all the deprivations of her own childhood. She is simply an imperfect human being with needs of her own.”
—Elaine Heffner (20th century)