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)
“When you know what men are capable of you marvel neither at their sublimity nor their baseness. There are no limits in either direction apparently.”
—Henry Miller (1891–1980)
“Fanny was not there! How she would have enjoyed the scene.... I could not but think of her, and in spite of my efforts to prevent, the unbidden tear would flow. Alas! I cannot feel the satisfaction some appear to do in the reflection that her eyes beheld the scene from the other world.”
—Rutherford Birchard Hayes (1822–1893)