RNADiscrepancy.geometry

Module Contents

Functions

cross3_2d	Computes the cross product of 3 points It corresponds to the direction (upward or downward) of the cross product of the two coplanar vectors defined by the two pairs of points (p1, p2), (p1, p3) The sign of the acute angle is the sign of the expression https://en.wikipedia.org/wiki/Cross_product#Computational_geometry
RMSD
angle_rotation	Given a rotation matrix return its angle of rotation uses the fact that trace(rotation_matrix) = 1 + 2cos(theta)
rotation_align_2D_points	Given two points will return the rotation matrix R such that p2 @ R.T is aligned with p1
best_rotation	Given two sets of points and for each an “origin” computes the best rotation to go from set B -> A
best_mean_centered_rotation	Least-squares rigid-body fit transform of two numpy array The center of mass of the nucleotide is at (0, 0, 0) returns rotation : matrix B2A : B moved to over A mean_A, mean_B, sum_square_error, RMSD
best_rotation_translation	Given two sets of points and for each an “origin” computes the best rotation + translation to go from set B -> A A = B @ R.T + t Follows Kabsch algorithm
triangle_xy_sign	Return a direction +-1 of a triangle in the xy plane (ignores 3th dimension) by comparing to p1, p3, p2 it allows to check if two triangles are in the same orientation or not Relies on the computation (p3 - p1) X ( p2 - p1) = sign https://math.stackexchange.com/questions/4560043/orientation-of-a-triangles-vertices-in-3d-space-clockwise-or-counter-clockwise

API

RNADiscrepancy.geometry.cross3_2d(p1: Sequence[float], p2: Sequence[float], p3: Sequence[float]) → float

Computes the cross product of 3 points It corresponds to the direction (upward or downward) of the cross product of the two coplanar vectors defined by the two pairs of points (p1, p2), (p1, p3) The sign of the acute angle is the sign of the expression https://en.wikipedia.org/wiki/Cross_product#Computational_geometry

Args:

p1 (float, flaot) : 2D point p2 (float, flaot) : 2D point p3 (float, flaot) : 2D point

Returns:

signed angle

RNADiscrepancy.geometry.RMSD(A, B) → float

RNADiscrepancy.geometry.angle_rotation(rotation_matrix) → float

Given a rotation matrix return its angle of rotation uses the fact that trace(rotation_matrix) = 1 + 2cos(theta)

Args:

rotation_matrix (matrix n x 3): rotation matrix

Returns:

The angle in radian

RNADiscrepancy.geometry.rotation_align_2D_points(p1: Sequence[float], p2: Sequence[float]) → numpy.typing.NDArray[[float]]

Given two points will return the rotation matrix R such that p2 @ R.T is aligned with p1

RNADiscrepancy.geometry.best_rotation(A: numpy.typing.NDArray[[float]], center_A: numpy.typing.NDArray[float], B: numpy.typing.NDArray[[float]], center_B: numpy.typing.NDArray[float]) → [numpy.typing.NDArray[[float]], numpy.typing.NDArray[float], numpy.typing.NDArray[float], float, float]

Given two sets of points and for each an “origin” computes the best rotation to go from set B -> A

Args:

A (Matrix n X 3) : set of points A center_A (Vector 1 x 3) : center point of A B (Matrix n X 3) : set of points B center_B (Vector 1 x 3) : center point of B

Returns:

Rotation B->A Rotation object B on A center_A center_B sum squared errors RMSD

RNADiscrepancy.geometry.best_mean_centered_rotation(A: numpy.typing.NDArray[[float]], B: numpy.typing.NDArray[[float]]) → numpy.typing.NDArray[[float]]

Least-squares rigid-body fit transform of two numpy array The center of mass of the nucleotide is at (0, 0, 0) returns rotation : matrix B2A : B moved to over A mean_A, mean_B, sum_square_error, RMSD

RNADiscrepancy.geometry.best_rotation_translation(A: numpy.typing.NDArray[[float]], B: numpy.typing.NDArray[[float]]) → [numpy.typing.NDArray[[float]], numpy.typing.NDArray[[float]], float, float, float]

Given two sets of points and for each an “origin” computes the best rotation + translation to go from set B -> A A = B @ R.T + t Follows Kabsch algorithm

Args:

A (Matrix n X 3) : set of points A B (Matrix n X 3) : set of points B

Returns:

Rotation R translation t B2A sum squared errors RMSD

RNADiscrepancy.geometry.triangle_xy_sign(p1: numpy.typing.NDArray[float], p2: numpy.typing.NDArray[float], p3: numpy.typing.NDArray[float]) → int

Return a direction +-1 of a triangle in the xy plane (ignores 3th dimension) by comparing to p1, p3, p2 it allows to check if two triangles are in the same orientation or not Relies on the computation (p3 - p1) X ( p2 - p1) = sign https://math.stackexchange.com/questions/4560043/orientation-of-a-triangles-vertices-in-3d-space-clockwise-or-counter-clockwise

Args:

p1 (npt.NDArray[float]) : position in space of point1 p2 (npt.NDArray[float]) : position in space of point2 p3 (npt.NDArray[float]) : position in space of point3

Return:

A value +-1 of the normal