Alternative Definitions
Since a plane can be defined in several ways (e.g., by vectors or points in them, or by their normal vectors), there are several equivalent definitions of a dihedral angle.
Any plane can be defined by two non-collinear vectors lying in that plane; taking their cross product and normalizing yields the normal unit vector to the plane. Thus, a dihedral angle can be defined by four, pairwise non-collinear vectors.
We may also define the dihedral angle of three non-collinear vectors, and (shown in red, green and blue, respectively, in Figure 1). The vectors and define the first plane, whereas and define the second plane. The dihedral angle corresponds to an exterior spherical angle (Figure 1), which is a well-defined, signed quantity.
where the two-argument atan2 takes care of the sign.
Read more about this topic: Dihedral Angle
Famous quotes containing the words alternative and/or definitions:
“If you have abandoned one faith, do not abandon all faith. There is always an alternative to the faith we lose. Or is it the same faith under another mask?”
—Graham Greene (1904–1991)
“What I do not like about our definitions of genius is that there is in them nothing of the day of judgment, nothing of resounding through eternity and nothing of the footsteps of the Almighty.”
—G.C. (Georg Christoph)