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:
“From the way the grass bends, one can know the direction of the wind.”
—Chinese proverb.
“It is wonderful how well watered this country is.... Generally, you may go any direction in a canoe, by making frequent but not very long portages.”
—Henry David Thoreau (1817–1862)
“The Americans ... have invented so wide a range of pithy and hackneyed phrases that they can carry on an amusing and animated conversation without giving a moment’s reflection to what they are saying and so leave their minds free to consider the more important matters of big business and fornication.”
—W. Somerset Maugham (1874–1965)