pylab.py

"""The pylab module of ipvyolume."""

from __future__ import absolute_import
from __future__ import division

__all__ = [
    'current',
    'clear',
    'controls_light',
    'figure',
    'gcf',
    'xlim',
    'ylim',
    'zlim',
    'xyzlim',
    'squarelim',
    'plot_trisurf',
    'plot_surface',
    'plot_wireframe',
    'plot_mesh',
    'plot',
    'scatter',
    'quiver',
    'show',
    'animate_glyphs',
    'animation_control',
    'gcc',
    'transfer_function',
    'plot_isosurface',
    'volshow',
    'save',
    'movie',
    'screenshot',
    'savefig',
    'xlabel',
    'ylabel',
    'zlabel',
    'xyzlabel',
    'view',
    'style',
    'plot_plane',
    'selector_default',
]

import os
import time
import warnings
import tempfile
import uuid
import base64

try:
    from io import BytesIO as StringIO
except:
    from cStringIO import StringIO

import six
import numpy as np
import PIL.Image
import matplotlib.style

try:
    import shapely.geometry
except:
    shapely = None
try:
    import skimage.measure
except:
    skimage = None
import ipywidgets
import traitlets
import IPython
from IPython.display import display

import ipyvolume as ipv
import ipyvolume.embed
from ipyvolume import utils


_last_figure = None


def _docsubst(f):
    """Perform docstring substitutions."""
    f.__doc__ = f.__doc__.format(**_doc_snippets)
    return f


_seq_sn = "If an (S, N) array, the first dimension will be used for frames in an animation."
_seq_snm = "If an (S, N, M) array, the first dimension will be used for frames in an animation."

_doc_snippets = {}
_doc_snippets["color"] = (
    "color for each point/vertex/symbol, can be string format, examples for red:'red', '#f00',"
    "'#ff0000' or'rgb(1,0,0), or rgb array of shape (N, 3 or 4) or (S, N, 3 or 4)"
)
_doc_snippets[
    "color2d"
] = "color for each point/vertex string format, examples for red:'red', '#f00', '#ff0000' or 'rgb(1,0,0), or rgb"
" array of shape (2, N, 3 or 4) or (S, 2, N, 3 or 4)"
_doc_snippets[
    "size"
] = "float representing the size of the glyph in percentage of the viewport, where 100 is the full size of the viewport"
_doc_snippets[
    "marker"
] = "name of the marker, options are: 'arrow', 'box', 'diamond', 'sphere', 'point_2d', 'square_2d', 'triangle_2d', "
"'circle_2d'"
_doc_snippets["x"] = "numpy array of shape (N,) or (S, N) with x positions. {}".format(_seq_sn)
_doc_snippets["y"] = "idem for y"
_doc_snippets["z"] = "idem for z"
_doc_snippets["u_dir"] = "numpy array of shape (N,) or (S, N) indicating the x component of a vector. {}".format(
    _seq_sn
)
_doc_snippets["v_dir"] = "idem for y"
_doc_snippets["w_dir"] = "idem for z"
_doc_snippets["u"] = "numpy array of shape (N,) or (S, N) indicating the u (x) coordinate for the texture. {}".format(
    _seq_sn
)
_doc_snippets["v"] = "numpy array of shape (N,) or (S, N) indicating the v (y) coordinate for the texture. {}".format(
    _seq_sn
)
_doc_snippets["x2d"] = "numpy array of shape (N,M) or (S, N, M) with x positions. {}".format(_seq_snm)
_doc_snippets["y2d"] = "idem for y"
_doc_snippets["z2d"] = "idem for z"
_doc_snippets["texture"] = "PIL.Image object or ipywebrtc.MediaStream (can be a seqence)"


class current:
    figure = None
    container = None
    figures = {}
    containers = {}


def clear():
    """Remove current figure (and container)."""
    current.container = None
    current.figure = None


def controls_light(return_widget=False):
    fig = gcf()
    ambient_coefficient = ipywidgets.FloatSlider(
        min=0, max=1, step=0.001, value=fig.ambient_coefficient, description="ambient"
    )
    diffuse_coefficient = ipywidgets.FloatSlider(
        min=0, max=1, step=0.001, value=fig.diffuse_coefficient, description="diffuse"
    )
    specular_coefficient = ipywidgets.FloatSlider(
        min=0, max=1, step=0.001, value=fig.specular_coefficient, description="specular"
    )
    specular_exponent = ipywidgets.FloatSlider(
        min=0, max=10, step=0.001, value=fig.specular_exponent, description="specular exp"
    )
    ipywidgets.jslink((fig, 'ambient_coefficient'), (ambient_coefficient, 'value'))
    ipywidgets.jslink((fig, 'diffuse_coefficient'), (diffuse_coefficient, 'value'))
    ipywidgets.jslink((fig, 'specular_coefficient'), (specular_coefficient, 'value'))
    ipywidgets.jslink((fig, 'specular_exponent'), (specular_exponent, 'value'))
    widgets_bottom = [
        ipywidgets.HBox([ambient_coefficient, diffuse_coefficient]),
        ipywidgets.HBox([specular_coefficient, specular_exponent]),
    ]
    current.container.children += tuple(widgets_bottom)
    if return_widget:
        return widgets_bottom


def figure(
    key=None,
    width=400,
    height=500,
    lighting=True,
    controls=True,
    controls_vr=False,
    controls_light=False,
    debug=False,
    **kwargs
):
    """Create a new figure if no key is given, or return the figure associated with key.

    :param key: Python object that identifies this figure
    :param int width: pixel width of WebGL canvas
    :param int height:  .. height ..
    :param bool lighting: use lighting or not
    :param bool controls: show controls or not
    :param bool controls_vr: show controls for VR or not
    :param bool debug: show debug buttons or not
    :return: :any:`Figure`
    """
    if key is not None and key in current.figures:
        current.figure = current.figures[key]
        current.container = current.containers[key]
    elif isinstance(key, ipv.Figure) and key in current.figures.values():
        key_index = list(current.figures.values()).index(key)
        key = list(current.figures.keys())[key_index]
        current.figure = current.figures[key]
        current.container = current.containers[key]
    else:
        current.figure = ipv.Figure(width=width, height=height, **kwargs)
        current.container = ipywidgets.VBox()
        current.container.children = [current.figure]
        if key is None:
            key = uuid.uuid4().hex
        current.figures[key] = current.figure
        current.containers[key] = current.container
        if controls:
            # stereo = ipywidgets.ToggleButton(value=current.figure.stereo, description='stereo', icon='eye')
            # l1 = ipywidgets.jslink((current.figure, 'stereo'), (stereo, 'value'))
            # current.container.children += (ipywidgets.HBox([stereo, ]),)
            pass  # stereo and fullscreen are now include in the js code (per view)
        if controls_vr:
            eye_separation = ipywidgets.FloatSlider(value=current.figure.eye_separation, min=-10, max=10, icon='eye')
            ipywidgets.jslink((eye_separation, 'value'), (current.figure, 'eye_separation'))
            current.container.children += (eye_separation,)
        if controls_light:
            globals()['controls_light']()
        if debug:
            show = ipywidgets.ToggleButtons(options=["Volume", "Back", "Front", "Coordinate"])
            current.container.children += (show,)
            # ipywidgets.jslink((current.figure, 'show'), (show, 'value'))
            traitlets.link((current.figure, 'show'), (show, 'value'))
    return current.figure


def gcf():
    """Get current figure, or create a new one.

    :return: :any:`Figure`
    """
    if current.figure is None:
        return figure()
    else:
        return current.figure


def _grow_limit(limits, values):
    if isinstance(values, (tuple, list)) and len(values) == 2:
        newvmin, newvmax = values
    else:
        try:
            values[0]  # test if scalar
        except TypeError:
            newvmin = values
            newvmax = values
        else:
            finites = np.isfinite(values)
            newvmin = np.min(values[finites])
            newvmax = np.max(values[finites])
    if limits is None:
        return newvmin, newvmax
    else:
        vmin, vmax = limits
        return min(newvmin, vmin), max(newvmax, vmax)


def _grow_limits(x, y, z):
    fig = gcf()
    xlim(*_grow_limit(fig.xlim, x))
    ylim(*_grow_limit(fig.ylim, y))
    zlim(*_grow_limit(fig.zlim, z))


def xlim(xmin, xmax):
    """Set limits of x axis."""
    fig = gcf()
    fig.xlim = [xmin, xmax]


def ylim(ymin, ymax):
    """Set limits of y axis."""
    fig = gcf()
    fig.ylim = [ymin, ymax]


def zlim(zmin, zmax):
    """Set limits of zaxis."""
    fig = gcf()
    fig.zlim = [zmin, zmax]


def xyzlim(vmin, vmax=None):
    """Set limits or all axis the same, if vmax not given, use [-vmin, vmin]."""
    if vmax is None:
        vmin, vmax = -vmin, vmin
    xlim(vmin, vmax)
    ylim(vmin, vmax)
    zlim(vmin, vmax)


def squarelim():
    """Set all axes with equal aspect ratio, such that the space is 'square'."""
    fig = gcf()
    xmin, xmax = fig.xlim
    ymin, ymax = fig.ylim
    zmin, zmax = fig.zlim
    width = max([abs(xmax - xmin), abs(ymax - ymin), abs(zmax - zmin)])
    xc = (xmin + xmax) / 2
    yc = (ymin + ymax) / 2
    zc = (zmin + zmax) / 2
    xlim(xc - width / 2, xc + width / 2)
    ylim(yc - width / 2, yc + width / 2)
    zlim(zc - width / 2, zc + width / 2)


default_color = "red"
default_color_selected = "white"
default_size = 2
default_size_selected = default_size * 1.3


@_docsubst
def plot_trisurf(x, y, z, triangles=None, lines=None, color=default_color, u=None, v=None, texture=None):
    """Draw a polygon/triangle mesh defined by a coordinate and triangle indices.

    The following example plots a rectangle in the z==2 plane, consisting of 2 triangles:

    >>> plot_trisurf([0, 0, 3., 3.], [0, 4., 0, 4.], 2,
           triangles=[[0, 2, 3], [0, 3, 1]])

    Note that the z value is constant, and thus not a list/array. For guidance, the triangles
    refer to the vertices in this manner::

        ^ ydir
        |
        2 3
        0 1  ---> x dir

    Note that if you want per face/triangle colors, you need to duplicate each vertex.


    :param x: {x}
    :param y: {y}
    :param z: {z}
    :param triangles: numpy array with indices referring to the vertices, defining the triangles, with shape (M, 3)
    :param lines: numpy array with indices referring to the vertices, defining the lines, with shape (K, 2)
    :param color: {color}
    :param u: {u}
    :param v: {v}
    :param texture: {texture}
    :return: :any:`Mesh`
    """
    fig = gcf()
    if triangles is not None:
        triangles = np.array(triangles).astype(dtype=np.uint32)
    if lines is not None:
        lines = np.array(lines).astype(dtype=np.uint32)
    mesh = ipv.Mesh(x=x, y=y, z=z, triangles=triangles, lines=lines, color=color, u=u, v=v, texture=texture)
    _grow_limits(np.array(x).reshape(-1), np.array(y).reshape(-1), np.array(z).reshape(-1))
    fig.meshes = fig.meshes + [mesh]
    return mesh


@_docsubst
def plot_surface(x, y, z, color=default_color, wrapx=False, wrapy=False):
    """Draws a 2d surface in 3d, defined by the 2d ordered arrays x,y,z.

    :param x: {x2d}
    :param y: {y2d}
    :param z: {z2d}
    :param color: {color2d}
    :param bool wrapx: when True, the x direction is assumed to wrap, and polygons are drawn between the end end begin points
    :param bool wrapy: simular for the y coordinate
    :return: :any:`Mesh`
    """
    return plot_mesh(x, y, z, color=color, wrapx=wrapx, wrapy=wrapy, wireframe=False)


@_docsubst
def plot_wireframe(x, y, z, color=default_color, wrapx=False, wrapy=False):
    """Draws a 2d wireframe in 3d, defines by the 2d ordered arrays x,y,z.

    See also :any:`ipyvolume.pylab.plot_mesh`

    :param x: {x2d}
    :param y: {y2d}
    :param z: {z2d}
    :param color: {color2d}
    :param bool wrapx: when True, the x direction is assumed to wrap, and polygons are drawn between the begin and end points
    :param bool wrapy: idem for y
    :return: :any:`Mesh`
    """
    return plot_mesh(x, y, z, color=color, wrapx=wrapx, wrapy=wrapy, wireframe=True, surface=False)


def plot_mesh(
    x, y, z, color=default_color, wireframe=True, surface=True, wrapx=False, wrapy=False, u=None, v=None, texture=None
):
    """Draws a 2d wireframe+surface in 3d: generalization of :any:`plot_wireframe` and :any:`plot_surface`.

    :param x: {x2d}
    :param y: {y2d}
    :param z: {z2d}
    :param color: {color2d}
    :param bool wireframe: draw lines between the vertices
    :param bool surface: draw faces/triangles between the vertices
    :param bool wrapx: when True, the x direction is assumed to wrap, and polygons are drawn between the begin and end points
    :param boool wrapy: idem for y
    :param u: {u}
    :param v: {v}
    :param texture: {texture}
    :return: :any:`Mesh`
    """
    fig = gcf()

    # assert len(x.shape) == 2
    # assert len(y.shape) == 2
    # assert len(z.shape) == 2
    # if isinstance(color, np.ndarray):
    # 	assert len(color.shape) == 3
    # 	assert color.shape[:2] == x.shape
    # 	color = color.reshape(-1)

    def dim(x):
        d = 0
        el = x
        while True:
            try:
                el = el[0]
                d += 1
            except:
                break
        return d

    if dim(x) == 2:
        nx, ny = x.shape
    else:
        nx, ny = x[0].shape

    # assert len(x.shape) == 2, "Array x must be 2 dimensional."
    # assert len(y.shape) == 2, "Array y must be 2 dimensional."
    # assert len(z.shape) == 2, "Array z must be 2 dimensional."
    # assert x.shape == y.shape, "Arrays x and y must have same shape."
    # assert y.shape == z.shape, "Arrays y and z must have same shape."
    # convert x, y, z from shape (nx, ny) to (nx * ny) or
    # (frame, nx, ny) to (frame, nx*ny)
    def reshape(ar):
        if dim(ar) == 3:
            return [k.reshape(-1) for k in ar]
        else:
            return ar.reshape(-1)

    x = reshape(x)
    y = reshape(y)
    z = reshape(z)
    # similar for texture coordinates
    if u is not None:
        u = reshape(u)
    if v is not None:
        v = reshape(v)

    # convert color from shape (nx, ny, {3,4}) to (nx * ny, {3, 4}) or
    # (frame, nx, ny, {3,4}) to (frame, nx*ny, {3,4})
    def reshape_color(ar):
        if dim(ar) == 4:
            return [k.reshape(-1, k.shape[-1]) for k in ar]
        else:
            return ar.reshape(-1, ar.shape[-1])

    if isinstance(color, np.ndarray):
        color = reshape_color(color)

    _grow_limits(np.array(x).reshape(-1), np.array(y).reshape(-1), np.array(z).reshape(-1))
    triangles, lines = _make_triangles_lines((nx, ny), wrapx, wrapy)
    mesh = ipv.Mesh(
        x=x,
        y=y,
        z=z,
        triangles=triangles if surface else None,
        color=color,
        lines=lines if wireframe else None,
        u=u,
        v=v,
        texture=texture,
    )
    fig.meshes = fig.meshes + [mesh]
    return mesh


@_docsubst
def plot(x, y, z, color=default_color, **kwargs):
    """Plot a line in 3d.

    :param x: {x}
    :param y: {y}
    :param z: {z}
    :param color: {color}
    :param kwargs: extra arguments passed to the Scatter constructor
    :return: :any:`Scatter`
    """
    fig = gcf()
    _grow_limits(x, y, z)
    defaults = dict(
        visible_lines=True, color_selected=None, size_selected=1, size=1, connected=True, visible_markers=False
    )
    kwargs = dict(defaults, **kwargs)
    s = ipv.Scatter(x=x, y=y, z=z, color=color, **kwargs)
    s.material.visible = False
    fig.scatters = fig.scatters + [s]
    return s


@_docsubst
def scatter(
    x,
    y,
    z,
    color=default_color,
    size=default_size,
    size_selected=default_size_selected,
    color_selected=default_color_selected,
    marker="diamond",
    selection=None,
    grow_limits=True,
    **kwargs
):
    """Plot many markers/symbols in 3d.

    :param x: {x}
    :param y: {y}
    :param z: {z}
    :param color: {color}
    :param size: {size}
    :param size_selected: like size, but for selected glyphs
    :param color_selected:  like color, but for selected glyphs
    :param marker: {marker}
    :param selection: numpy array of shape (N,) or (S, N) with indices of x,y,z arrays of the selected markers, which
                      can have a different size and color
    :param kwargs:
    :return: :any:`Scatter`
    """
    fig = gcf()
    if grow_limits:
        _grow_limits(x, y, z)
    s = ipv.Scatter(
        x=x,
        y=y,
        z=z,
        color=color,
        size=size,
        color_selected=color_selected,
        size_selected=size_selected,
        geo=marker,
        selection=selection,
        **kwargs
    )
    fig.scatters = fig.scatters + [s]
    return s


@_docsubst
def quiver(
    x,
    y,
    z,
    u,
    v,
    w,
    size=default_size * 10,
    size_selected=default_size_selected * 10,
    color=default_color,
    color_selected=default_color_selected,
    marker="arrow",
    **kwargs
):
    """Create a quiver plot, which is like a scatter plot but with arrows pointing in the direction given by u, v and w.

    :param x: {x}
    :param y: {y}
    :param z: {z}
    :param u: {u_dir}
    :param v: {v_dir}
    :param w: {w_dir}
    :param size: {size}
    :param size_selected: like size, but for selected glyphs
    :param color: {color}
    :param color_selected: like color, but for selected glyphs
    :param marker: (currently only 'arrow' would make sense)
    :param kwargs: extra arguments passed on to the Scatter constructor
    :return: :any:`Scatter`
    """
    fig = gcf()
    _grow_limits(x, y, z)
    if 'vx' in kwargs or 'vy' in kwargs or 'vz' in kwargs:
        raise KeyError('Please use u, v, w instead of vx, vy, vz')
    s = ipv.Scatter(
        x=x,
        y=y,
        z=z,
        vx=u,
        vy=v,
        vz=w,
        color=color,
        size=size,
        color_selected=color_selected,
        size_selected=size_selected,
        geo=marker,
        **kwargs
    )
    fig.scatters = fig.scatters + [s]
    return s


def show(extra_widgets=[]):
    """Display (like in IPython.display.dispay(...)) the current figure."""
    gcf()  # make sure we have something..
    display(gcc())
    for widget in extra_widgets:
        display(widget)


def animate_glyphs(*args, **kwargs):
    """Deprecated: please use animation_control."""
    warnings.warn("Please use animation_control(...)", DeprecationWarning, stacklevel=2)
    animation_control(*args, **kwargs)


def animation_control(object, sequence_length=None, add=True, interval=200):
    """Animate scatter, quiver or mesh by adding a slider and play button.

    :param object: :any:`Scatter` or :any:`Mesh` object (having an sequence_index property), or a list of these to
                   control multiple.
    :param sequence_length: If sequence_length is None we try try our best to figure out, in case we do it badly,
            you can tell us what it should be. Should be equal to the S in the shape of the numpy arrays as for instance
            documented in :any:`scatter` or :any:`plot_mesh`.
    :param add: if True, add the widgets to the container, else return a HBox with the slider and play button. Useful when you
            want to customise the layout of the widgets yourself.
    :param interval: interval in msec between each frame
    :return: If add is False, if returns the ipywidgets.HBox object containing the controls
    """
    if isinstance(object, (list, tuple)):
        objects = object
    else:
        objects = [object]
    del object
    if sequence_length is None:
        # get all non-None arrays
        sequence_lengths = []
        for object in objects:
            sequence_lengths_previous = list(sequence_lengths)
            values = [getattr(object, name) for name in "x y z vx vy vz".split() if hasattr(object, name)]
            values = [k for k in values if k is not None]
            # sort them such that the higest dim is first
            values.sort(key=lambda key: -len(key.shape))
            try:
                sequence_length = values[0].shape[0]  # assume this defines the sequence length
                if isinstance(object, ipv.Mesh):  # for a mesh, it does not make sense to have less than 1 dimension
                    if len(values[0].shape) >= 2:  # if just 1d, it is most likely not an animation
                        sequence_lengths.append(sequence_length)
                else:
                    sequence_lengths.append(sequence_length)
            except IndexError:  # scalars get ignored
                pass
            if hasattr(object, 'color'):
                color = object.color
                if color is not None:
                    shape = color.shape
                    if len(shape) == 3:  # would be the case for for (frame, point_index, color_index)
                        sequence_lengths.append(shape[0])
                    # TODO: maybe support arrays of string type of form (frame, point_index)
            if len(sequence_lengths) == len(sequence_lengths_previous):
                raise ValueError('no frame dimension found for object: {}'.format(object))
        sequence_length = max(sequence_lengths)
    fig = gcf()
    fig.animation = interval
    fig.animation_exponent = 1.0
    play = ipywidgets.Play(min=0, max=sequence_length - 1, interval=interval, value=0, step=1)
    slider = ipywidgets.FloatSlider(min=0, max=play.max, step=1)
    ipywidgets.jslink((play, 'value'), (slider, 'value'))
    for object in objects:
        ipywidgets.jslink((slider, 'value'), (object, 'sequence_index'))
    control = ipywidgets.HBox([play, slider])
    if add:
        current.container.children += (control,)
    else:
        return control


def gcc():
    """Return the current container, that is the widget holding the figure and all the control widgets, buttons etc."""
    gcf()  # make sure we have something..
    return current.container


def transfer_function(
    level=[0.1, 0.5, 0.9], opacity=[0.01, 0.05, 0.1], level_width=0.1, controls=True, max_opacity=0.2
):
    """Create a transfer function, see volshow."""
    tf_kwargs = {}
    # level, opacity and widths can be scalars
    try:
        level[0]
    except:
        level = [level]
    try:
        opacity[0]
    except:
        opacity = [opacity] * 3
    try:
        level_width[0]
    except:
        level_width = [level_width] * 3
        # clip off lists
    min_length = min(len(level), len(level_width), len(opacity))
    level = list(level[:min_length])
    opacity = list(opacity[:min_length])
    level_width = list(level_width[:min_length])
    # append with zeros
    while len(level) < 3:
        level.append(0)
    while len(opacity) < 3:
        opacity.append(0)
    while len(level_width) < 3:
        level_width.append(0)
    for i in range(1, 4):
        tf_kwargs["level" + str(i)] = level[i - 1]
        tf_kwargs["opacity" + str(i)] = opacity[i - 1]
        tf_kwargs["width" + str(i)] = level_width[i - 1]
    tf = ipv.TransferFunctionWidgetJs3(**tf_kwargs)
    gcf()  # make sure a current container/figure exists
    if controls:
        current.container.children = (tf.control(max_opacity=max_opacity),) + current.container.children
    return tf


def plot_isosurface(data, level=None, color=default_color, wireframe=True, surface=True, controls=True, extent=None):
    """Plot a surface at constant value (like a 2d contour).

    :param data: 3d numpy array
    :param float level: value where the surface should lie
    :param color: color of the surface, although it can be an array, the length is difficult to predict beforehand,
                  if per vertex color are needed, it is better to set them on the returned mesh afterwards.
    :param bool wireframe: draw lines between the vertices
    :param bool surface: draw faces/triangles between the vertices
    :param bool controls: add controls to change the isosurface
    :param extent: list of [[xmin, xmax], [ymin, ymax], [zmin, zmax]] values that define the bounding box of the mesh,
                   otherwise the viewport is used
    :return: :any:`Mesh`
    """
    if level is None:
        level = np.median(data)
    if hasattr(skimage.measure, 'marching_cubes_lewiner'):
        values = skimage.measure.marching_cubes_lewiner(data, level)
    else:
        values = skimage.measure.marching_cubes(data, level)  # pylint: disable=no-member
    verts, triangles = values[:2]  # version 0.13 returns 4 values, normals, values
    # in the future we may want to support normals and the values (with colormap)
    # and require skimage >= 0.13
    x, y, z = verts.T

    # Rescale coordinates to given limits
    if extent:
        xlim, ylim, zlim = extent
        x = x * np.diff(xlim) / (data.shape[0] - 1) + xlim[0]
        y = y * np.diff(ylim) / (data.shape[1] - 1) + ylim[0]
        z = z * np.diff(zlim) / (data.shape[2] - 1) + zlim[0]
        _grow_limits(*extent)

    mesh = plot_trisurf(x, y, z, triangles=triangles, color=color)
    if controls:
        vmin, vmax = np.percentile(data, 1), np.percentile(data, 99)
        step = (vmax - vmin) / 250
        level_slider = ipywidgets.FloatSlider(value=level, min=vmin, max=vmax, step=step, icon='eye')
        recompute_button = ipywidgets.Button(description='update')
        controls = ipywidgets.HBox(children=[level_slider, recompute_button])
        current.container.children += (controls,)

        def recompute(*_ignore):
            level = level_slider.value
            recompute_button.description = "updating..."
            if hasattr(skimage.measure, 'marching_cubes_lewiner'):
                values = skimage.measure.marching_cubes_lewiner(data, level)
            else:
                values = skimage.measure.marching_cubes(data, level)  # pylint: disable=no-member
            verts, triangles = values[:2]  # version 0.13 returns 4 values, normals, values
            # in the future we may want to support normals and the values (with colormap)
            # and require skimage >= 0.13
            x, y, z = verts.T
            with mesh.hold_sync():
                mesh.x = x
                mesh.y = y
                mesh.z = z
                mesh.triangles = triangles.astype(dtype=np.uint32)
                recompute_button.description = "update"

        recompute_button.on_click(recompute)
    return mesh


def volshow(
    data,
    lighting=False,
    data_min=None,
    data_max=None,
    max_shape=256,
    tf=None,
    stereo=False,
    ambient_coefficient=0.5,
    diffuse_coefficient=0.8,
    specular_coefficient=0.5,
    specular_exponent=5,
    downscale=1,
    level=[0.1, 0.5, 0.9],
    opacity=[0.01, 0.05, 0.1],
    level_width=0.1,
    controls=True,
    max_opacity=0.2,
    memorder='C',
    extent=None,
):
    """Visualize a 3d array using volume rendering.

    Currently only 1 volume can be rendered.


    :param data: 3d numpy array
    :param origin: origin of the volume data, this is to match meshes which have a different origin
    :param domain_size: domain size is the size of the volume
    :param bool lighting: use lighting or not, if set to false, lighting parameters will be overriden
    :param float data_min: minimum value to consider for data, if None, computed using np.nanmin
    :param float data_max: maximum value to consider for data, if None, computed using np.nanmax
    :parap int max_shape: maximum shape for the 3d cube, if larger, the data is reduced by skipping/slicing (data[::N]),
                          set to None to disable.
    :param tf: transfer function (or a default one)
    :param bool stereo: stereo view for virtual reality (cardboard and similar VR head mount)
    :param ambient_coefficient: lighting parameter
    :param diffuse_coefficient: lighting parameter
    :param specular_coefficient: lighting parameter
    :param specular_exponent: lighting parameter
    :param float downscale: downscale the rendering for better performance, for instance when set to 2, a 512x512
                            canvas will show a 256x256 rendering upscaled, but it will render twice as fast.
    :param level: level(s) for the where the opacity in the volume peaks, maximum sequence of length 3
    :param opacity: opacity(ies) for each level, scalar or sequence of max length 3
    :param level_width: width of the (gaussian) bumps where the opacity peaks, scalar or sequence of max length 3
    :param bool controls: add controls for lighting and transfer function or not
    :param float max_opacity: maximum opacity for transfer function controls
    :param extent: list of [[xmin, xmax], [ymin, ymax], [zmin, zmax]] values that define the bounds of the volume,
                   otherwise the viewport is used
    :return:
    """
    fig = gcf()

    if tf is None:
        tf = transfer_function(level, opacity, level_width, controls=controls, max_opacity=max_opacity)
    if data_min is None:
        data_min = np.nanmin(data)
    if data_max is None:
        data_max = np.nanmax(data)
    if memorder == 'F':
        data = data.T

    if extent is None:
        extent = [(0, k) for k in data.shape[::-1]]

    if extent:
        _grow_limits(*extent)

    vol = ipv.Volume(
        data_original=data,
        tf=tf,
        data_min=data_min,
        data_max=data_max,
        show_min=data_min,
        show_max=data_max,
        extent_original=extent,
        data_max_shape=max_shape,
        ambient_coefficient=ambient_coefficient,
        diffuse_coefficient=diffuse_coefficient,
        specular_coefficient=specular_coefficient,
        specular_exponent=specular_exponent,
        rendering_lighting=lighting,
    )

    vol._listen_to(fig)

    if controls:
        widget_opacity_scale = ipywidgets.FloatLogSlider(base=10, min=-2, max=2, description="opacity")
        widget_brightness = ipywidgets.FloatLogSlider(base=10, min=-1, max=1, description="brightness")
        ipywidgets.jslink((vol, 'opacity_scale'), (widget_opacity_scale, 'value'))
        ipywidgets.jslink((vol, 'brightness'), (widget_brightness, 'value'))
        widgets_bottom = [ipywidgets.HBox([widget_opacity_scale, widget_brightness])]
        current.container.children += tuple(widgets_bottom)

    fig.volumes = fig.volumes + [vol]

    return vol


def save(
    filepath,
    makedirs=True,
    title=u'IPyVolume Widget',
    all_states=False,
    offline=False,
    scripts_path='js',
    drop_defaults=False,
    template_options=(("extra_script_head", ""), ("body_pre", ""), ("body_post", "")),
    devmode=False,
    offline_cors=False,
):
    """Save the current container to a HTML file.

    By default the HTML file is not standalone and requires an internet connection to fetch a few javascript
    libraries. Use offline=True to download these and make the HTML file work without an internet connection.

    :param str filepath: The file to write the HTML output to.
    :param bool makedirs: whether to make directories in the filename path, if they do not already exist
    :param str title: title for the html page
    :param bool all_states: if True, the state of all widgets know to the widget manager is included, else only those in widgets
    :param bool offline: if True, use local urls for required js/css packages and download all js/css required packages
            (if not already available), such that the html can be viewed with no internet connection
    :param str scripts_path: the folder to save required js/css packages to (relative to the filepath)
    :param bool drop_defaults: Whether to drop default values from the widget states
    :param template_options: list or dict of additional template options
    :param bool devmode: if True, attempt to get index.js from local js/dist folder
    :param bool offline_cors: if True, sets crossorigin attribute of script tags to anonymous

    """
    ipyvolume.embed.embed_html(
        filepath,
        current.container,
        makedirs=makedirs,
        title=title,
        all_states=all_states,
        offline=offline,
        scripts_path=scripts_path,
        drop_defaults=drop_defaults,
        template_options=template_options,
        devmode=devmode,
        offline_cors=offline_cors,
    )


def _change_azimuth_angle(fig, frame, fraction):
    with fig:
        view(azimuth=fraction * 360)


def movie(
    f="movie.mp4",
    function=_change_azimuth_angle,
    fps=30,
    frames=30,
    endpoint=False,
    cmd_template_ffmpeg="ffmpeg -y -r {fps} -i {tempdir}/frame-%5d.png -vcodec h264 -pix_fmt yuv420p {filename}",
    cmd_template_gif="convert -delay {delay} {loop} {tempdir}/frame-*.png {filename}",
    gif_loop=0,
):
    """Create a movie out of many frames in e.g. mp4 or gif format.

    If the filename ends in `.gif`, `convert` is used to convert all frames to an animated gif using the `cmd_template_gif`
    template. Otherwise `ffmpeg is assumed to know the file format`.

    Example:

    >>> def set_angles(fig, i, fraction):
    >>>     fig.angley = fraction*np.pi*2
    >>> # 4 second movie, that rotates around the y axis
    >>> p3.movie('test2.gif', set_angles, fps=20, frames=20*4,
            endpoint=False)

    Note that in the example above we use `endpoint=False` to avoid to first and last frame to be the same

    :param str f: filename out output movie (e.g. 'movie.mp4' or 'movie.gif')
    :param function: function called before each frame with arguments (figure, framenr, fraction)
    :param fps: frames per seconds
    :param int frames: total number of frames
    :param bool endpoint: if fraction goes from [0, 1] (inclusive) or [0, 1) (endpoint=False is useful for loops/rotatations)
    :param str cmd_template_ffmpeg: template command when running ffmpeg (non-gif ending filenames)
    :param str cmd_template_gif: template command when running imagemagick's convert (if filename ends in .gif)
    :param gif_loop: None for no loop, otherwise the framenumber to go to after the last frame
    :return: the temp dir where the frames are stored
    """
    movie_filename = f
    tempdir = tempfile.mkdtemp()
    output = ipywidgets.Output()
    display(output)
    fig = gcf()
    for i in range(frames):
        with output:
            fraction = i / (frames - 1.0 if endpoint else frames)
            function(fig, i, fraction)
            frame_filename = os.path.join(tempdir, "frame-%05d.png" % i)
            savefig(frame_filename, output_widget=output)
    with output:
        if movie_filename.endswith(".gif"):
            if gif_loop is None:
                loop = ""
            else:
                loop = "-loop %d" % gif_loop
            delay = 100 / fps
            cmd = cmd_template_gif.format(delay=delay, loop=loop, tempdir=tempdir, filename=movie_filename)
        else:
            cmd = cmd_template_ffmpeg.format(fps=fps, tempdir=tempdir, filename=movie_filename)
        print(cmd)
        os.system(cmd)
    return tempdir


def _screenshot_data(
    timeout_seconds=10,
    output_widget=None,
    format="png",
    width=None,
    height=None,
    fig=None,
    headless=False,
    devmode=False,
):
    if fig is None:
        fig = gcf()
    else:
        assert isinstance(fig, ipv.Figure)
    if headless:
        tempdir = tempfile.mkdtemp()
        tempfile_ = os.path.join(tempdir, 'headless.html')
        save(tempfile_, offline=True, scripts_path=tempdir, devmode=devmode)
        import ipyvolume.headless

        data = ipyvolume.headless._screenshot_data("file://" + tempfile_)
        if data is None:
            raise ValueError('Error capturing data from headless browser')
    else:
        if output_widget is None:
            output_widget = ipywidgets.Output()
            display(output_widget)
        # use lists to avoid globals
        done = [False]
        data = [None]

        def screenshot_handler(image_data):
            with output_widget:
                # print("data")
                # print(data)
                done[0] = True
                data[0] = image_data

        fig.on_screenshot(screenshot_handler)
        try:
            fig.screenshot(width=width, height=height, mime_type="image/" + format)
            t0 = time.time()
            timeout = False
            ipython = IPython.get_ipython()
            while (not done[0]) and not timeout:
                ipython.kernel.do_one_iteration()
                with output_widget:
                    time.sleep(0.05)
                    timeout = (time.time() - t0) > timeout_seconds
            with output_widget:
                if timeout and not done[0]:
                    raise ValueError("timed out, no image data returned")
        finally:
            with output_widget:
                fig.on_screenshot(screenshot_handler, remove=True)
        data = data[0]
    data = data[data.find(",") + 1 :]
    return base64.b64decode(data)


def screenshot(
    width=None,
    height=None,
    format="png",
    fig=None,
    timeout_seconds=10,
    output_widget=None,
    headless=False,
    devmode=False,
):
    """Save the figure to a PIL.Image object.

    :param int width: the width of the image in pixels
    :param int height: the height of the image in pixels
    :param format: format of output data (png, jpeg or svg)
    :type fig: ipyvolume.widgets.Figure or None
    :param fig: if None use the current figure
    :type timeout_seconds: int
    :param timeout_seconds: maximum time to wait for image data to return
    :type output_widget: ipywidgets.Output
    :param output_widget: a widget to use as a context manager for capturing the data
    :param bool headless: if True, use headless chrome to take screenshot
    :param bool devmode: if True, attempt to get index.js from local js/dist folder
    :return: PIL.Image

    """
    assert format in ['png', 'jpeg', 'svg'], "image format must be png, jpeg or svg"
    data = _screenshot_data(
        timeout_seconds=timeout_seconds,
        output_widget=output_widget,
        format=format,
        width=width,
        height=height,
        fig=fig,
        headless=headless,
        devmode=devmode,
    )
    f = StringIO(data)
    return PIL.Image.open(f)


def savefig(
    filename, width=None, height=None, fig=None, timeout_seconds=10, output_widget=None, headless=False, devmode=False
):
    """Save the figure to an image file.

    :param str filename: must have extension .png, .jpeg or .svg
    :param int width: the width of the image in pixels
    :param int height: the height of the image in pixels
    :type fig: ipyvolume.widgets.Figure or None
    :param fig: if None use the current figure
    :param float timeout_seconds: maximum time to wait for image data to return
    :param ipywidgets.Output output_widget: a widget to use as a context manager for capturing the data
    :param bool headless: if True, use headless chrome to save figure
    :param bool devmode: if True, attempt to get index.js from local js/dist folder
    """
    __, ext = os.path.splitext(filename)
    format = ext[1:]
    assert format in ['png', 'jpeg', 'svg'], "image format must be png, jpeg or svg"
    with open(filename, "wb") as f:
        f.write(
            _screenshot_data(
                timeout_seconds=timeout_seconds,
                output_widget=output_widget,
                format=format,
                width=width,
                height=height,
                fig=fig,
                headless=headless,
                devmode=devmode,
            )
        )


def xlabel(label):
    """Set the labels for the x-axis."""
    fig = gcf()
    fig.xlabel = label


def ylabel(label):
    """Set the labels for the y-axis."""
    fig = gcf()
    fig.ylabel = label


def zlabel(label):
    """Set the labels for the z-axis."""
    fig = gcf()
    fig.zlabel = label


def xyzlabel(labelx, labely, labelz):
    """Set all labels at once."""
    xlabel(labelx)
    ylabel(labely)
    zlabel(labelz)


def view(azimuth=None, elevation=None, distance=None):
    """Set camera angles and distance and return the current.

    :param float azimuth: rotation around the axis pointing up in degrees
    :param float elevation: rotation where +90 means 'up', -90 means 'down', in degrees
    :param float distance: radial distance from the center to the camera.
    """
    fig = gcf()
    # first calculate the current values
    x, y, z = fig.camera.position
    r = np.sqrt(x ** 2 + y ** 2 + z ** 2)
    az = np.degrees(np.arctan2(x, z))
    el = np.degrees(np.arcsin(y / r))
    if azimuth is None:
        azimuth = az
    if elevation is None:
        elevation = el
    if distance is None:
        distance = r
    cosaz = np.cos(np.radians(azimuth))
    sinaz = np.sin(np.radians(azimuth))
    sine = np.sin(np.radians(elevation))
    cose = np.cos(np.radians(elevation))
    fig.camera.position = (distance * sinaz * cose, distance * sine, distance * cosaz * cose)
    return azimuth, elevation, distance


# mimic matplotlib namesace
class style:
    """Static class that mimics a matplotlib module.

    Example:

    >>> import ipyvolume as ipv
    >>> ipv.style.use('light'])
    >>> ipv.style.use('seaborn-darkgrid'])
    >>> ipv.style.use(['seaborn-darkgrid', {'axes.x.color':'orange'}])

    Possible style values:
     * figure.facecolor: background color
     * axes.color: color of the box around the volume/viewport
     * xaxis.color: color of xaxis
     * yaxis.color: color of xaxis
     * zaxis.color: color of xaxis

    """

    @staticmethod
    def use(style):
        """Set the style of the current figure/visualization.

        :param style: matplotlib style name, or dict with values, or a sequence of these, where the last value overrides previous
        :return:
        """
        def valid(value):  # checks if json'able
            return isinstance(value, six.string_types)

        def translate(mplstyle):
            style = {}
            mapping = [
                ['figure.facecolor', 'background-color'],
                ['xtick.color', 'axes.x.color'],  # TODO: is this the right thing?
                ['xtick.color', 'axes.z.color'],  # map x to z as well
                ['ytick.color', 'axes.y.color'],
                ['axes.labelcolor', 'axes.label.color'],
                ['text.color', 'color'],
                ['axes.edgecolor', 'axes.color'],
            ]
            for from_name, to_name in mapping:
                if from_name in mplstyle:
                    value = mplstyle[from_name]
                    if "color" in from_name:
                        try:  # threejs doesn't like a color like '.13', so try to convert to proper format
                            value = float(value) * 255
                            value = "rgb(%d, %d, %d)" % (value, value, value)
                        except:
                            pass

                    utils.nested_setitem(style, to_name, value)
            return style

        if isinstance(style, six.string_types + (dict,)):
            styles = [style]
        else:
            styles = style
        fig = gcf()
        totalstyle = utils.dict_deep_update({}, fig.style)
        for style in styles:
            if isinstance(style, six.string_types):
                if hasattr(ipyvolume.styles, style):
                    style = getattr(ipyvolume.styles, style)
                else:
                    # lets see if we can copy matplotlib's style
                    # we assume now it's a matplotlib style, get all properties that we understand
                    cleaned_style = {
                        key: value for key, value in dict(matplotlib.style.library[style]).items() if valid(value)
                    }
                    style = translate(cleaned_style)
                    # totalstyle.update(cleaned_style)
            else:
                # otherwise assume it's a dict
                pass
            totalstyle = utils.dict_deep_update(totalstyle, style)

        fig = gcf()
        fig.style = totalstyle

    @staticmethod
    def axes_off():
        """Do not draw the axes."""
        style.use({'axes': {'visible': False}})

    @staticmethod
    def axes_on():
        """Draw the axes."""
        style.use({'axes': {'visible': True}})

    @staticmethod
    def box_off():
        """Do not draw the box around the visible volume."""
        style.use({'box': {'visible': False}})

    @staticmethod
    def box_on():
        """Draw a box around the visible volume."""
        style.use({'box': {'visible': True}})

    @staticmethod
    def background_color(color):
        """Set the background color."""
        style.use({'background-color': color})


for style_name, __ in ipv.styles.styles.items():

    def closure(style_name=style_name):
        def quick_set():
            style.use(style_name)

        attr_name = 'set_style_' + style_name
        attr = staticmethod(quick_set)
        setattr(style, attr_name, attr)
        getattr(style, attr_name).__doc__ = """Short for style.use(%r)""" % style_name

    closure()


@_docsubst
def plot_plane(where="back", texture=None):
    """Plot a plane at a particular location in the viewbox.

    :param str where: 'back', 'front', 'left', 'right', 'top', 'bottom'
    :param texture: {texture}
    :return: :any:`Mesh`
    """
    fig = gcf()
    xmin, xmax = fig.xlim
    ymin, ymax = fig.ylim
    zmin, zmax = fig.zlim
    if where == "back":
        x = [xmin, xmax, xmax, xmin]
        y = [ymin, ymin, ymax, ymax]
        z = [zmin, zmin, zmin, zmin]
    if where == "front":
        x = [xmin, xmax, xmax, xmin][::-1]
        y = [ymin, ymin, ymax, ymax]
        z = [zmax, zmax, zmax, zmax]
    if where == "left":
        x = [xmin, xmin, xmin, xmin]
        y = [ymin, ymin, ymax, ymax]
        z = [zmin, zmax, zmax, zmin]
    if where == "right":
        x = [xmax, xmax, xmax, xmax]
        y = [ymin, ymin, ymax, ymax]
        z = [zmin, zmax, zmax, zmin][::-1]
    if where == "top":
        x = [xmin, xmax, xmax, xmin]
        y = [ymax, ymax, ymax, ymax]
        z = [zmax, zmax, zmin, zmin]
    if where == "bottom":
        x = [xmax, xmin, xmin, xmax]
        y = [ymin, ymin, ymin, ymin]
        z = [zmin, zmin, zmax, zmax]
    triangles = [(0, 1, 2), (0, 2, 3)]
    u = v = None
    if texture is not None:
        u = [0.0, 1.0, 1.0, 0.0]
        v = [0.0, 0.0, 1.0, 1.0]
    mesh = plot_trisurf(x, y, z, triangles, texture=texture, u=u, v=v)
    return mesh


def selector_default(output_widget=None):
    """Capture selection events from the current figure, and apply the selections to Scatter objects.

    Example:

    >>> import ipyvolume as ipv
    >>> ipv.figure()
    >>> ipv.examples.gaussian()
    >>> ipv.selector_default()
    >>> ipv.show()

    Now hold the control key to do selections, type

      * 'C' for circle
      * 'R' for rectangle
      * 'L' for lasso
      * '=' for replace mode
      * '&' for logically and mode
      * '|' for logically or mode
      * '-' for subtract mode

    """
    fig = gcf()
    if output_widget is None:
        output_widget = ipywidgets.Output()
        display(output_widget)

    def lasso(data, other=None, fig=fig):
        with output_widget:
            inside = None
            if data['device'] and data['type'] == 'lasso':
                region = shapely.geometry.Polygon(data['device'])

                @np.vectorize
                def inside_polygon(x, y):
                    return region.contains(shapely.geometry.Point([x, y]))

                inside = inside_polygon

            if data['device'] and data['type'] == 'circle':
                x1, y1 = data['device']['begin']
                x2, y2 = data['device']['end']
                dx = x2 - x1
                dy = y2 - y1
                r = (dx ** 2 + dy ** 2) ** 0.5

                def inside_circle(x, y):
                    return ((x - x1) ** 2 + (y - y1) ** 2) < r ** 2

                inside = inside_circle

            if data['device'] and data['type'] == 'rectangle':
                x1, y1 = data['device']['begin']
                x2, y2 = data['device']['end']
                x = [x1, x2]
                y = [y1, y2]
                xmin, xmax = min(x), max(x)
                ymin, ymax = min(y), max(y)

                def inside_rectangle(x, y):
                    return (x > xmin) & (x < xmax) & (y > ymin) & (y < ymax)

                inside = inside_rectangle

            def join(x, y, mode):
                Nx = 0 if (x is None or len(x[0]) == 0) else np.max(x)
                Ny = 0 if len(y[0]) == 0 else np.max(y)
                N = max(Nx, Ny)
                xmask = np.zeros(N + 1, np.bool)
                ymask = np.zeros(N + 1, np.bool)
                if x is not None:
                    xmask[x] = True
                ymask[y] = True
                if mode == "replace":
                    return np.where(ymask)
                if mode == "and":
                    mask = xmask & ymask
                    return np.where(ymask if x is None else mask)
                if mode == "or":
                    mask = xmask | ymask
                    return np.where(ymask if x is None else mask)
                if mode == "subtract":
                    mask = xmask & ~ymask
                    return np.where(ymask if x is None else mask)

            for scatter in fig.scatters:
                x, y = fig.project(scatter.x, scatter.y, scatter.z)
                mask = inside(x, y)
                scatter.selected = join(scatter.selected, np.where(mask), fig.selection_mode)

    fig.on_selection(lasso)


def _make_triangles_lines(shape, wrapx=False, wrapy=False):
    """Transform rectangular regular grid into triangles.

    :param x: {x2d}
    :param y: {y2d}
    :param z: {z2d}
    :param bool wrapx: when True, the x direction is assumed to wrap, and polygons are drawn between the end end begin points
    :param bool wrapy: simular for the y coordinate
    :return: triangles and lines used to plot Mesh
    """
    nx, ny = shape

    mx = nx if wrapx else nx - 1
    my = ny if wrapy else ny - 1

    """
    create all pair of indices (i,j) of the rectangular grid
    minus last row if wrapx = False => mx
    minus last column if wrapy = False => my
    |  (0,0)   ...   (0,j)    ...   (0,my-1)  |
    |    .      .      .       .       .      |
    |  (i,0)   ...   (i,j)    ...   (i,my-1)  |
    |    .      .      .       .       .      |
    |(mx-1,0)  ...  (mx-1,j)  ... (mx-1,my-1) |
    """
    i, j = np.mgrid[0:mx, 0:my]

    """
    collapsed i and j in one dimensional array, row-major order
    ex :
    array([[0,  1,  2],     =>   array([0, 1, 2, 3, *4*, 5])
           [3, *4*, 5]])
    if we want vertex 4 at (i=1,j=1) we must transform it in i*ny+j = 4
    """
    i, j = np.ravel(i), np.ravel(j)

    """
    Let's go for the triangles :
        (i,j)    -  (i,j+1)   -> y dir
        (i+1,j)  - (i+1,j+1)
          |
          v
        x dir

    in flatten coordinates:
        i*ny+j     -  i*ny+j+1
        (i+1)*ny+j -  (i+1)*ny+j+1
    """

    t1 = (i * ny + j, (i + 1) % nx * ny + j, (i + 1) % nx * ny + (j + 1) % ny)
    t2 = (i * ny + j, (i + 1) % nx * ny + (j + 1) % ny, i * ny + (j + 1) % ny)

    """
        %nx and %ny are used for wrapx and wrapy :
        if (i+1)=nx => (i+1)%nx=0 => close mesh in x direction
        if (j+1)=ny => (j+1)%ny=0 => close mesh in y direction
    """

    nt = len(t1[0])

    triangles = np.zeros((nt * 2, 3), dtype=np.uint32)
    triangles[0::2, 0], triangles[0::2, 1], triangles[0::2, 2] = t1
    triangles[1::2, 0], triangles[1::2, 1], triangles[1::2, 2] = t2

    lines = np.zeros((nt * 4, 2), dtype=np.uint32)
    lines[::4, 0], lines[::4, 1] = t1[:2]
    lines[1::4, 0], lines[1::4, 1] = t1[0], t2[2]
    lines[2::4, 0], lines[2::4, 1] = t2[2:0:-1]
    lines[3::4, 0], lines[3::4, 1] = t1[1], t2[1]

    return triangles, lines