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Curvature Modules

Calculate various curvature metrics for traces.

angle_diff_signed(v1: npt.NDArray[np.float64], v2: npt.NDArray[np.float64])

Calculate the signed angle difference between two point vecrtors in 2D space.

Positive angles are clockwise, negative angles are counterclockwise.

Parameters:

Name Type Description Default
v1 NDArray[float64]

First vector.

 required
v2 NDArray[float64]

Second vector.

 required

Returns:

Type Description
float

The signed angle difference in radians.
Source code in topostats\measure\curvature.py 
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def angle_diff_signed(v1: npt.NDArray[np.float64], v2: npt.NDArray[np.float64]):
    """
    Calculate the signed angle difference between two point vecrtors in 2D space.

    Positive angles are clockwise, negative angles are counterclockwise.

    Parameters
    ----------
    v1 : npt.NDArray[np.float64]
        First vector.
    v2 : npt.NDArray[np.float64]
        Second vector.

    Returns
    -------
    float
        The signed angle difference in radians.
    """
    if v1.shape != (2,) or v2.shape != (2,):
        raise ValueError("Vectors must be of shape (2,)")

    angle = np.arctan2(v2[1], v2[0]) - np.arctan2(v1[1], v1[0])
    if angle > np.pi:
        angle -= 2 * np.pi
    elif angle < -np.pi:
        angle += 2 * np.pi

    return angle

calculate_curvature_stats_image(topostats_object: TopoStats) -> None

Perform curvature analysis for a whole image of grains.

Curvature statistics are added to the Molecule.curvature_stats attribute of the traces that are being processed.

Parameters:

Name Type Description Default
topostats_object TopoStats

TopoStats object with attribute grain_crop. Should be post-splining.

 required
Source code in topostats\measure\curvature.py 
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def calculate_curvature_stats_image(
    topostats_object: TopoStats,
) -> None:
    """
    Perform curvature analysis for a whole image of grains.

    Curvature statistics are added to the ``Molecule.curvature_stats`` attribute of the traces that are being processed.

    Parameters
    ----------
    topostats_object : TopoStats
        ``TopoStats`` object with attribute ``grain_crop``. Should be post-splining.
    """
    # Iterate over grains
    for _, grain_crop in topostats_object.grain_crops.items():
        # Iterate over molecules
        if grain_crop.ordered_trace is not None and grain_crop.ordered_trace.molecule_data is not None:
            for _, molecule_data in grain_crop.ordered_trace.molecule_data.items():
                trace_nm = molecule_data.splined_coords * topostats_object.pixel_to_nm_scaling
                # Check if the molecule is circular or linear
                if molecule_data.end_to_end_distance == 0.0:
                    # Molecule is circular
                    molecule_data.curvature_stats = np.abs(discrete_angle_difference_per_nm_circular(trace_nm))
                else:
                    # Molecule is linear
                    molecule_data.curvature_stats = np.abs(discrete_angle_difference_per_nm_linear(trace_nm))

discrete_angle_difference_per_nm_circular(trace_nm: npt.NDArray[np.float64]) -> npt.NDArray[np.float64]

Calculate the discrete angle difference per nm along a trace.

Parameters:

Name Type Description Default
trace_nm NDArray[float64]

The coordinate trace, in nanometre units.

 required

Returns:

Type Description
NDArray[float64]

The discrete angle difference per nm.
Source code in topostats\measure\curvature.py 
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def discrete_angle_difference_per_nm_circular(
    trace_nm: npt.NDArray[np.float64],
) -> npt.NDArray[np.float64]:
    """
    Calculate the discrete angle difference per nm along a trace.

    Parameters
    ----------
    trace_nm : npt.NDArray[np.float64]
        The coordinate trace, in nanometre units.

    Returns
    -------
    npt.NDArray[np.float64]
        The discrete angle difference per nm.
    """
    angles_per_nm = np.zeros(trace_nm.shape[0])
    for index, point in enumerate(trace_nm):
        if index == 0:
            v1 = point - trace_nm[-1]
            v2 = trace_nm[index + 1] - point
        elif index == trace_nm.shape[0] - 1:
            v1 = point - trace_nm[index - 1]
            v2 = trace_nm[0] - point
        else:
            v1 = point - trace_nm[index - 1]
            v2 = trace_nm[index + 1] - point

        # Normalise vectors to unit length
        norm_v1 = v1 / np.linalg.norm(v1)
        norm_v2 = v2 / np.linalg.norm(v2)

        # Calculate the signed angle difference between the previous direction and the current direction
        angle = angle_diff_signed(norm_v1, norm_v2)

        # Calculate distance travelled between previous point and the current point
        distance = np.linalg.norm(v1)

        # Calculate the angle difference per nm
        angles_per_nm[index] = angle / distance

    return angles_per_nm

discrete_angle_difference_per_nm_linear(trace_nm: npt.NDArray[np.float64]) -> npt.NDArray[np.float64]

Calculate the discrete angle difference per nm along a trace.

Parameters:

Name Type Description Default
trace_nm NDArray[float64]

The coordinate trace, in nanometre units.

 required

Returns:

Type Description
NDArray[float64]

The discrete angle difference per nm.
Source code in topostats\measure\curvature.py 
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def discrete_angle_difference_per_nm_linear(
    trace_nm: npt.NDArray[np.float64],
) -> npt.NDArray[np.float64]:
    """
    Calculate the discrete angle difference per nm along a trace.

    Parameters
    ----------
    trace_nm : npt.NDArray[np.float64]
        The coordinate trace, in nanometre units.

    Returns
    -------
    npt.NDArray[np.float64]
        The discrete angle difference per nm.
    """
    angles_per_nm = np.zeros(trace_nm.shape[0])
    for index, point in enumerate(trace_nm):
        if index == 0:
            # No previous point so cannot calculate angle
            v2 = trace_nm[index + 1] - point
            angle = 0.0
            distance = np.linalg.norm(v2)
        elif index == trace_nm.shape[0] - 1:
            # No next point so cannot calculate angle
            v1 = point - trace_nm[index - 1]
            angle = 0.0
            distance = np.linalg.norm(v1)
        else:
            v1 = point - trace_nm[index - 1]
            v2 = trace_nm[index + 1] - point

            # Normalise vectors to unit length
            norm_v1 = v1 / np.linalg.norm(v1)
            norm_v2 = v2 / np.linalg.norm(v2)

            # Calculate the signed angle difference between the previous direction and the current direction
            angle = angle_diff_signed(norm_v1, norm_v2)

            # Calculate distance travelled between previous point and the current point
            distance = np.linalg.norm(v1)

        angles_per_nm[index] = angle / distance

    return angles_per_nm