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torus

torus(nR, nr, R=1.0, r=0.5)

Returns a torus mesh.

Parameters:

Name Type Description Default
nR int

number of vertices along the large perimeter of the torus (at least 3)

 required
nr int

number of vertices along the small perimeter of the torus (at least 3)

 required
R float, optional (default 1.)

large radius of torus

 1.0
r float, optional (default 0.5)

small radius of torus

 0.5

Returns:

Name Type Description
V (n,3) numpy array

vertex positions of the torus
F (m,3) numpy array

face positions of the torus

Examples:

>>> import gpytoolbox as gpy
>>> V,F = gpy.torus(4, 3, R=1., r=0.1)
>>> V
array([[ 1.10000000e+00,  0.00000000e+00,  0.00000000e+00],
   [-5.50000000e-01,  9.52627944e-01,  0.00000000e+00],
   [-5.50000000e-01, -9.52627944e-01,  0.00000000e+00],
   [ 1.00000000e+00,  0.00000000e+00,  1.00000000e-01],
   [-5.00000000e-01,  8.66025404e-01,  1.00000000e-01],
   [-5.00000000e-01, -8.66025404e-01,  1.00000000e-01],
   [ 9.00000000e-01,  0.00000000e+00,  1.22464680e-17],
   [-4.50000000e-01,  7.79422863e-01,  1.22464680e-17],
   [-4.50000000e-01, -7.79422863e-01,  1.22464680e-17],
   [ 1.00000000e+00,  0.00000000e+00, -1.00000000e-01],
   [-5.00000000e-01,  8.66025404e-01, -1.00000000e-01],
   [-5.00000000e-01, -8.66025404e-01, -1.00000000e-01]])
>>> F
array([[ 0,  4,  3],
   [ 1,  5,  4],
   [ 2,  3,  5],
   [ 3,  7,  6],
   [ 4,  8,  7],
   [ 5,  6,  8],
   [ 6, 10,  9],
   [ 7, 11, 10],
   [ 8,  9, 11],
   [ 9,  1,  0],
   [10,  2,  1],
   [11,  0,  2],
   [ 0,  1,  4],
   [ 1,  2,  5],
   [ 2,  0,  3],
   [ 3,  4,  7],
   [ 4,  5,  8],
   [ 5,  3,  6],
   [ 6,  7, 10],
   [ 7,  8, 11],
   [ 8,  6,  9],
   [ 9, 10,  1],
   [10, 11,  2],
   [11,  9,  0]])
Source code in src/gpytoolbox/torus.py 
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def torus(nR,
    nr,
    R=1.,
    r=0.5):
    """Returns a torus mesh.

    Parameters
    ----------
    nR : int
        number of vertices along the large perimeter of the torus (at least 3)
    nr : int
        number of vertices along the small perimeter of the torus (at least 3)
    R : float, optional (default 1.)
        large radius of torus
    r : float, optional (default 0.5)
        small radius of torus

    Returns
    -------
    V : (n,3) numpy array
        vertex positions of the torus
    F : (m,3) numpy array
        face positions of the torus

    Examples
    --------
    ```python
    >>> import gpytoolbox as gpy
    >>> V,F = gpy.torus(4, 3, R=1., r=0.1)
    >>> V
    array([[ 1.10000000e+00,  0.00000000e+00,  0.00000000e+00],
       [-5.50000000e-01,  9.52627944e-01,  0.00000000e+00],
       [-5.50000000e-01, -9.52627944e-01,  0.00000000e+00],
       [ 1.00000000e+00,  0.00000000e+00,  1.00000000e-01],
       [-5.00000000e-01,  8.66025404e-01,  1.00000000e-01],
       [-5.00000000e-01, -8.66025404e-01,  1.00000000e-01],
       [ 9.00000000e-01,  0.00000000e+00,  1.22464680e-17],
       [-4.50000000e-01,  7.79422863e-01,  1.22464680e-17],
       [-4.50000000e-01, -7.79422863e-01,  1.22464680e-17],
       [ 1.00000000e+00,  0.00000000e+00, -1.00000000e-01],
       [-5.00000000e-01,  8.66025404e-01, -1.00000000e-01],
       [-5.00000000e-01, -8.66025404e-01, -1.00000000e-01]])
    >>> F
    array([[ 0,  4,  3],
       [ 1,  5,  4],
       [ 2,  3,  5],
       [ 3,  7,  6],
       [ 4,  8,  7],
       [ 5,  6,  8],
       [ 6, 10,  9],
       [ 7, 11, 10],
       [ 8,  9, 11],
       [ 9,  1,  0],
       [10,  2,  1],
       [11,  0,  2],
       [ 0,  1,  4],
       [ 1,  2,  5],
       [ 2,  0,  3],
       [ 3,  4,  7],
       [ 4,  5,  8],
       [ 5,  3,  6],
       [ 6,  7, 10],
       [ 7,  8, 11],
       [ 8,  6,  9],
       [ 9, 10,  1],
       [10, 11,  2],
       [11,  9,  0]])
    ```

    """

    assert nR>=3, "At least 3 vertices along the large perimeter."
    assert nr>=3, "At least 3 vertices along the small perimeter."

    assert R>0.
    assert r>0.

    φ,θ = np.meshgrid(np.linspace(0., 2.*np.pi, nR, endpoint=False),
        np.linspace(0., 2.*np.pi, nr, endpoint=False))
    x = (R + r*np.cos(θ)) * np.cos(φ)
    y = (R + r*np.cos(θ)) * np.sin(φ)
    z = r * np.sin(θ)
    V = np.stack((x.ravel(),y.ravel(),z.ravel()), axis=-1)

    # Indexing algorithm inspired by gptoolbox's create_regular_grid
    # https://github.com/alecjacobson/gptoolbox/blob/master/mesh/create_regular_grid.m
    inds = np.reshape(np.arange(nr*nR), (nr,nR))
    inds = np.concatenate((inds, inds[:,0][:,None]), axis=-1)
    inds = np.concatenate((inds, inds[0,:][None,:]), axis=0)
    i0 = inds[:-1,:-1].ravel()
    i1 = inds[:-1,1:].ravel()
    i2 = inds[1:,:-1].ravel()
    i3 = inds[1:,1:].ravel()
    F = np.stack((np.concatenate((i0,i0)),
        np.concatenate((i3,i1)),
        np.concatenate((i2,i3))),
        axis=-1)

    return V,F