From 25f56aa07d101ba24255aabbd60a0ffdd5640507 Mon Sep 17 00:00:00 2001 From: Matt Wala Date: Wed, 4 Dec 2019 22:54:00 -0600 Subject: [PATCH] Fix names of generate_torus() parameters (closes #12) Also, improve the documentation of generate_torus(). --- doc/images/torus.png | Bin 0 -> 82548 bytes meshmode/mesh/generation.py | 58 ++++++++++++++++++++++++++++-------- 2 files changed, 45 insertions(+), 13 deletions(-) create mode 100644 doc/images/torus.png diff --git a/doc/images/torus.png b/doc/images/torus.png new file mode 100644 index 0000000000000000000000000000000000000000..e2e2e297104bd4bae89d31e93c9a2163dc45a62d GIT binary patch literal 82548 zcmeAS@N?(olHy`uVBq!ia0y~yU^HZ4U^v0S#=yYP(0`4Wfq{XsILO_JVcj{ImkbPy zk(nV8B@w}FfdWk9dNvV1jxdjX$U{hgLkz0_PT9T+xk(-lOY*k^a1Xf{{S8N3m z)>l#hD=EpgRf_NpP;kyKN>wn`Gto0pvg1-vP_QXVNwW%aaf50vN=dU-$|xx*u+rBr zFE7_CH`dE9O4m2Ew6xSWFw!?N(k)6!(=D#dD@m--%_~-h7y>iLCAB!YD6^m>Ge1uO zWNu8_uq!JoCm-NuHhggL(Xl6@r%s&c=u{IBSCZAu z?>PQP#^R+$<)MZ-8WsJDdz&j*H^^CbUI=ICPEJmqZk~Iq#QrD9fqgfaSiRnKoc;X# z5FwjvxL$*xiu3 z#QflHv3pmSOrIF%vS(Z9>M*;-3V-;wIW!9Wo?P(*-{0Mhwzjq1D?0g)g<83- zTDi^oa6t{`IEyc7_}U) zH)%7kRe2dv@Os&TkPmy0SWnz7dZ*k+HD9twZB5M1qM+~Z?uPDQedvFM>0rVy;l1bQ ze+vx>+Fkb6YOd$ap6NL}D`u=RbljTYW$1bL+DgYeO}Xq$t`7IaUhKZ}&9R$(y=x4w z2LJlW@!6+rbl1*xu*|scpxttYt({L+YK>B39mfSNq414M6pecKG(TXpZCU=YhuO7D z#Bzq4!h45>POW@mdNDs7yu7@mrX^Svym)Z1S^ndkI-BMEA9;^(I{2OnbFWKHncBW? 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r_outer - b = r_inner - u, v = np.mgrid[0:2*np.pi:2*np.pi/n_outer, 0:2*np.pi:2*np.pi/n_inner] +def generate_torus_and_cycle_vertices(r_major, r_minor, + n_major=20, n_minor=10, order=1): + a = r_major + b = r_minor + u, v = np.mgrid[0:2*np.pi:2*np.pi/n_major, 0:2*np.pi:2*np.pi/n_minor] - # http://www.math.hmc.edu/~gu/curves_and_surfaces/surfaces/torus.html + # https://web.archive.org/web/20160410151837/https://www.math.hmc.edu/~gu/curves_and_surfaces/surfaces/torus.html # noqa x = np.cos(u)*(a+b*np.cos(v)) y = np.sin(u)*(a+b*np.cos(v)) z = b*np.sin(v) @@ -468,11 +468,11 @@ def generate_torus_and_cycle_vertices(r_outer, r_inner, .transpose(0, 2, 1).copy().reshape(3, -1)) def idx(i, j): - return (i % n_outer) + (j % n_inner) * n_outer + return (i % n_major) + (j % n_minor) * n_major vertex_indices = ([(idx(i, j), idx(i+1, j), idx(i, j+1)) - for i in range(n_outer) for j in range(n_inner)] + for i in range(n_major) for j in range(n_minor)] + [(idx(i+1, j), idx(i+1, j+1), idx(i, j+1)) - for i in range(n_outer) for j in range(n_inner)]) + for i in range(n_major) for j in range(n_minor)]) vertex_indices = np.array(vertex_indices, dtype=np.int32) grp = make_group_from_vertices(vertices, vertex_indices, order) @@ -513,15 +513,47 @@ def generate_torus_and_cycle_vertices(r_outer, r_inner, Mesh( vertices, [grp.copy(nodes=nodes)], is_conforming=True), - [idx(i, 0) for i in range(n_outer)], - [idx(0, j) for j in range(n_inner)]) + [idx(i, 0) for i in range(n_major)], + [idx(0, j) for j in range(n_minor)]) # }}} -def generate_torus(r_outer, r_inner, n_outer=20, n_inner=10, order=1): +def generate_torus(r_major, r_minor, n_major=20, n_minor=10, order=1): + r"""Generate a torus. + + .. figure:: images/torus.png + :align: center + + Shown: A torus with major circle (magenta) and minor circle (red). + Source: https://commons.wikimedia.org/wiki/File:Torus_cycles.svg + (public domain image by Krishnavedala). + + The torus is obtained as the image of the parameter domain + :math:`(u, v) \in [0, 2\pi) \times [0, 2 \pi)` under the map + + .. math:: + \begin{align} + x &= \cos(u) (r_\text{major} + r_\text{minor} \cos(v)) \\ + y &= \sin(u) (r_\text{major} + r_\text{minor} \sin(v)) \\ + z &= r_\text{minor} \sin(v) + \end{align} + + where :math:`r_\text{major}` and :math:`r_\text{minor}` are the radii of the + major and minor circles, respectively. The parameter domain is tiled with + :math:`n_\text{major} \times n_\text{minor}` contiguous rectangles, and then + each rectangle is subdivided into two triangles. + + :arg r_major: radius of the major circle + :arg r_minor: radius of the minor circle + :arg n_major: number of elements along major circle + :arg n_minor: number of elements along minor circle + :arg order: element order + :returns: a :class:`meshmode.mesh.Mesh` of a torus + + """ mesh, a_cycle, b_cycle = generate_torus_and_cycle_vertices( - r_outer, r_inner, n_outer, n_inner, order) + r_major, r_minor, n_major, n_minor, order) return mesh -- GitLab