Module qsym2::auxiliary::geometry

Geometrical objects and manipulations.

Structs

• CartesianConditions
  Structure to handle inequality conditions written in terms of Cartesian coordinates.
• SphericalConditions
  Structure to handle inequality conditions written in terms of spherical angular coordinates.
• SphericalConditionsBuilder
  Builder for SphericalConditions.

Enums

• ImproperRotationKind
  Enumerated type to classify the type of improper rotation given an angle and axis.
• PositiveHemisphere
  Enumerated type to handle positive hemispheres in Cartesian or spherical conditions.
• SphericalConditionsBuilderError
  Error type for SphericalConditionsBuilder
• SphericalCoordinate
  Enumerated type to handle spherical angular coordinates.

Constants

• IMINV
  Inversion-centre improper rotation kind.
• IMSIG
  Mirror-plane improper rotation kind.

Traits

• Transform
  Geometrical transformability in three dimensions.

Functions

• check_regular_polygon
  Checks if a sequence of atoms are vertices of a regular polygon.
• check_standard_positive_pole
  Check if a rotation axis is in the standard positive hemisphere.
• get_proper_fraction
  Determines the reduced fraction $k/n$ where $k$ and $n$ are both integers representing a proper rotation $C_n^k$ corresponding to a specified rotation angle.
• get_standard_positive_pole
  Returns the standard positive pole of a rotation axis.
• improper_rotation_matrix
  Returns a $3 \times 3$ transformation matrix in $\mathbb{R}^3$ corresponding to an improper rotation through angle about axis raised to the power power.
• normalise_rotation_angle
  Returns the rotation angle adjusted to be in the interval $(-\pi, +\pi]$ and the number of $2\pi$-folds required to bring the original angle to that interval.
• normalise_rotation_fraction
  Returns the rotation fraction adjusted to be in the interval $(-1/2, +1/2]$ and the number of $1$-folds required to bring the original fraction to that interval.
• proper_rotation_matrix
  Returns a $3 \times 3$ rotation matrix in $\mathbb{R}^3$ corresponding to a rotation through angle about axis raised to the power power.