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copyleft.swept_volume

swept_volume(V, F, transformations=None, rotations=None, translations=None, align_rotations_with_velocity=False, eps=0.05, num_seeds=100, num_faces=None, verbose=False)

Find region covered by object a long a trajectory

Computes the swept volume of a triangle mesh along a trajectory, given as translations keyframes which are interpolated as a Catmull-Rom spline, and rotations which are interpolated using quaternion spherical linear interpolation.

Parameters:

Name Type Description Default
V numpy double array

Matrix of mesh vertex coordinates

 required
F numpy int array

Matrix of mesh triangle indices into V

 required
transformations list of numpy double array, optional (default None)

List of transformation matrices in homogeneous coordinates (if not None, superseeds all other trajectory inputs)

 None
rotations list of numpy double array, optional (default None)

List of rotation matrices

 None
translations list of numpy double array, optional (default None)

List of translation vectors (must be set if transformations is None)

 None
align_rotations_with_velocity bool, optional (default False)

If rotations is None and this option is True, rotations are chosen roughyl such that the shape aligns with the velocity vector

 False
eps double, optional (default 0.05)

Voxel edge-length (finer will be slower but provide a finer output)

 0.05
num_seeds int, optional (default 100)

Number of seeds to initialize swept volume fronts (see "Swept Volumes via Spacetime Numerical Continuation" for more information). Should be set higher only for extremely complicated self-intersecting paths.

 100
num_faces int, optional (default None)

If not None, will decimate output to have this desired number of faces.

 None
verbose bool, optional (default False)

Whether to print runtime and other performance information.

 False

Returns:

Name Type Description
U numpy double array

Matrix of swept volume mesh vertex coordinates
G numpy int array

Matrix of swept volume mesh triangle indices into U

See Also

decimate.

Notes

This follows the implementation described in "Swept Volumes via Spacetime Numerical Continuation" by Silvia Sellán, Noam Aigerman and Alec Jacobson.

Examples:

from gpytoolbox import read_mesh  
from gpytoolbox.copyleft import swept_volume
# Read sample mesh
v, f = gpytoolbox.read_mesh("test/unit_tests_data/bunny_oded.obj")
# Translation vectors to make Catmull-Rom spline
translation_0 = np.array([0,0,0])
translation_1 = np.array([1,0,-1])
translation_2 = np.array([2,0,1])
translation_3 = np.array([3,0,0])
translations = [translation_0,translation_1,translation_2,translation_3]
# Call swept volume function
u,g = swept_volume(v,f,translations=translations,eps=0.05,
verbose=False,align_rotations_with_velocity=False)
Source code in src/gpytoolbox/copyleft/swept_volume.py 
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def swept_volume(V,F,transformations=None,rotations=None,translations=None,align_rotations_with_velocity=False,eps=0.05,num_seeds=100,num_faces=None,verbose=False):
    """Find region covered by object a long a trajectory

    Computes the swept volume of a triangle mesh along a trajectory, given as translations keyframes which are interpolated as a Catmull-Rom spline, and rotations which are interpolated using quaternion spherical linear interpolation.

    Parameters
    ----------
    V : numpy double array
        Matrix of mesh vertex coordinates
    F : numpy int array
        Matrix of mesh triangle indices into V
    transformations : list of numpy double array, optional (default None)
        List of transformation matrices in homogeneous coordinates (if not None, superseeds all other trajectory inputs)
    rotations : list of numpy double array, optional (default None)
        List of rotation matrices
    translations : list of numpy double array, optional (default None)
        List of translation vectors (must be set if transformations is None)
    align_rotations_with_velocity : bool, optional (default False)
        If rotations is None and this option is True, rotations are chosen *roughyl* such that the shape aligns with the velocity vector
    eps : double, optional (default 0.05)
        Voxel edge-length (finer will be slower but provide a finer output)
    num_seeds : int, optional (default 100)
        Number of seeds to initialize swept volume fronts (see "Swept Volumes via Spacetime Numerical Continuation" for more information). Should be set higher only for extremely complicated self-intersecting paths.
    num_faces : int, optional (default None)
        If not None, will decimate output to have this desired number of faces.
    verbose : bool, optional (default False)
        Whether to print runtime and other performance information.


    Returns
    -------
    U : numpy double array
        Matrix of swept volume mesh vertex coordinates
    G : numpy int array
        Matrix of swept volume mesh triangle indices into U

    See Also
    --------
    decimate.

    Notes
    -----
    This follows the implementation described in "Swept Volumes via Spacetime Numerical Continuation" by Silvia Sellán, Noam Aigerman and Alec Jacobson.

    Examples
    --------
    ```python
    from gpytoolbox import read_mesh  
    from gpytoolbox.copyleft import swept_volume
    # Read sample mesh
    v, f = gpytoolbox.read_mesh("test/unit_tests_data/bunny_oded.obj")
    # Translation vectors to make Catmull-Rom spline
    translation_0 = np.array([0,0,0])
    translation_1 = np.array([1,0,-1])
    translation_2 = np.array([2,0,1])
    translation_3 = np.array([3,0,0])
    translations = [translation_0,translation_1,translation_2,translation_3]
    # Call swept volume function
    u,g = swept_volume(v,f,translations=translations,eps=0.05,
    verbose=False,align_rotations_with_velocity=False)
    ```
    """

    try:
        from gpytoolbox_bindings_copyleft import _swept_volume_impl
    except:
        raise ImportError("Gpytoolbox cannot import its C++ binding.")



    if(translations is not None):
        transformations = []
        num_transformations = len(translations)
        for i in range(num_transformations):
            this_transformation = np.eye(4)
            this_transformation[0:3,3] = translations[i]
            if (rotations is not None):
                this_transformation[0:3,0:3] = rotations[i]
            elif (align_rotations_with_velocity):
                vel_0 = np.array([1,0,0])
                # Three cases
                if i==0: # We are at the first point
                    vel_1 = translations[1] - translations[0]
                elif i==(num_transformations-1):
                    vel_1 = translations[num_transformations-1] - translations[num_transformations-2]
                else:
                    vel_1 = translations[i+1] - translations[i-1]
                vel_1 = vel_1/np.linalg.norm(vel_1)
                rotation = rotation_matrix_from_vectors(vel_0, vel_1)
                this_transformation[0:3,0:3] = rotation
            transformations.append(this_transformation)

    transformations_big_mat = np.vstack(transformations)
    v,f = _swept_volume_impl(V,F.astype(np.int32),transformations_big_mat,eps,num_seeds,verbose)

    if(num_faces is not None):
        v,f,_,_ = decimate(v,f,num_faces=num_faces)


    return v,f