Dihedral angle

A dihedral angle is the angle between two planes that meet along a line. It measures the planes’ relative orientation around their shared intersection.

Plane: A flat surface extending infinitely in two dimensions, often specified by a point and a normal vector. Each side of a dihedral angle is a plane.
Angle between two planes: The smaller angle between two planes, calculated from their normal vectors. This convention gives the acute or right angle associated with a pair of planes.
Torsion angle: The signed angle between two planes defined by four ordered points, commonly describing rotation around a bond. Molecular torsion is a direct application of dihedral-angle measurement.
Line angle: The angle between two lines, usually measured in a plane or from their direction vectors. A dihedral compares planes, whereas a line angle compares directions.
Line: A straight, one-dimensional geometric object extending indefinitely in both directions. The two planes meet along this shared line.
Signed dihedral angle: A dihedral angle whose sign records the direction of rotation from one plane to another. Its sign distinguishes orientations that an unsigned angle treats alike.
Ramachandran plot: A plot of protein backbone torsion angles phi and psi, used to assess allowed conformations. It maps two successive backbone dihedral angles to protein structure.
Solid angle: A three-dimensional measure of the extent of a region as seen from a point, measured in steradians. A solid angle spans directions in space rather than measuring the orientation of two planes.
Normal vector: A vector perpendicular to a surface or plane. The angle between plane normals helps determine the angle between the planes.
Four-point dihedral angle: A signed angle defined by four points, using the planes formed by the first three and last three points. This coordinate construction is widely used to compute torsions.

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