import os
from spb.defaults import cfg
from spb.backends.base_backend import Plot
from spb.backends.k3d.renderers import (
Line3DRenderer, Vector3DRenderer,
ComplexRenderer, SurfaceRenderer, Implicit3DRenderer,
GeometryRenderer, Arrow3DRenderer
)
from spb.series import (
Parametric3DLineSeries, ComplexParametric3DLineSeries,
List3DSeries, Vector3DSeries, SliceVector3DSeries,
RiemannSphereSeries, Implicit3DSeries,
ComplexDomainColoringSeries, ComplexSurfaceSeries,
SurfaceOver2DRangeSeries, ParametricSurfaceSeries,
PlaneSeries, GeometrySeries, Arrow3DSeries
)
from sympy.external import import_module
import warnings
[docs]
class K3DBackend(Plot):
"""A backend for plotting SymPy's symbolic expressions using K3D-Jupyter.
Parameters
==========
camera : list, optional
A list of 9 numbers, namely:
* ``x_cam, y_cam, z_cam``: the position of the camera in the scene
* ``x_tar, y_tar, z_tar``: the position of the target of the camera
* ``x_up, y_up, z_up``: components of the up vector
rendering_kw : dict, optional
A dictionary of keywords/values which is passed to Matplotlib's plot
functions to customize the appearance of lines, surfaces, images,
contours, quivers, streamlines...
To learn more about customization:
* Default options for line plots:
``dict(width=0.1, shader="mesh")``.
Set ``use_cm=False`` to switch to a solid color.
* Default options for quiver plots:
``dict(scale = 1, pivot = "mid")``. The keys to this
dictionary are:
- ``scale``: a float number acting as a scale multiplier.
- ``pivot``: indicates the part of the arrow that is anchored to the
X, Y, Z grid. It can be ``"tail", "mid", "middle", "tip"``.
- ``color``: set a solid color by specifying an integer color, or
a colormap by specifying one of k3d's colormaps.
If this key is not provided, a default color or colormap is used,
depending on the value of ``use_cm``.
Set ``use_cm=False`` to switch to a default solid color.
* Default options for streamline plots:
``dict( width=0.1, shader='mesh' )``.
Refer to k3d.line for more options.
Set ``use_cm=False`` to switch to a solid color.
* To customize surface plots, refers to:
- k3d.mesh function for 3D surface and parametric surface plots.
- k3d.marching_cubes function for 3D implicit plots.
show_label : boolean, optional
Show/hide labels of the expressions. Default to False (labels not
visible).
use_cm : boolean, optional
If True, apply a color map to the meshes/surface. If False, solid
colors will be used instead. Default to True.
Notes
=====
After the installation of this plotting module, try one of the examples
of ``plot3d`` with this backend. If no figure is visible in the output
cell, follow this procedure:
1. Save the Notebook.
2. Close Jupyter server.
3. Run the following commands, which are going to install the Jupyter
extension for K3D:
* jupyter nbextension install --user --py k3d
* jupyter nbextension enable --user --py k3d
4. Restart `jupyter notebook`
5. Open the previous notebook and execute the plot command.
See also
========
Plot, MatplotlibBackend, PlotlyBackend, BokehBackend, plot3d
"""
_library = "k3d"
wireframe_color = 0x000000
colormaps = []
cyclic_colormaps = []
skip_notebook_check = False
# quivers-pivot offsets
_qp_offset = {"tail": 0, "mid": 0.5, "middle": 0.5, "tip": 1}
_allowed_keys = Plot._allowed_keys + ["show_label", "camera"]
renderers_map = {
Parametric3DLineSeries: Line3DRenderer,
ComplexParametric3DLineSeries: Line3DRenderer,
List3DSeries: Line3DRenderer,
Vector3DSeries: Vector3DRenderer,
SliceVector3DSeries: Vector3DRenderer,
Implicit3DSeries: Implicit3DRenderer,
ComplexDomainColoringSeries: ComplexRenderer,
ComplexSurfaceSeries: ComplexRenderer,
RiemannSphereSeries: ComplexRenderer,
SurfaceOver2DRangeSeries: SurfaceRenderer,
ParametricSurfaceSeries: SurfaceRenderer,
PlaneSeries: SurfaceRenderer,
GeometrySeries: GeometryRenderer,
Arrow3DSeries: Arrow3DRenderer
}
def __init__(self, *args, **kwargs):
self.np = import_module('numpy')
self.k3d = k3d = import_module(
'k3d',
import_kwargs={'fromlist': ['helpers', 'objects']},
warn_not_installed=True,
min_module_version='2.9.7')
cc = import_module(
'colorcet',
warn_not_installed=True,
min_module_version='3.0.0')
self.matplotlib = import_module(
'matplotlib',
import_kwargs={'fromlist': ['tri', 'cm']},
min_module_version='1.1.0',
warn_not_installed=True,
catch=(RuntimeError,))
cm = self.matplotlib.cm
self.colorloop = cm.tab10.colors
self.colormaps = [
k3d.basic_color_maps.CoolWarm,
k3d.matplotlib_color_maps.Plasma,
k3d.matplotlib_color_maps.Winter,
k3d.matplotlib_color_maps.Viridis,
k3d.paraview_color_maps.Haze,
k3d.matplotlib_color_maps.Summer,
k3d.paraview_color_maps.Blue_to_Yellow,
]
self.cyclic_colormaps = [
cc.colorwheel, k3d.paraview_color_maps.Erdc_iceFire_H]
self._init_cyclers()
super().__init__(*args, **kwargs)
if (not self.skip_notebook_check) and (self._get_mode() != 0):
warnings.warn(
"K3DBackend only works properly within Jupyter Notebook")
self._use_latex = kwargs.get("use_latex", cfg["k3d"]["use_latex"])
self._set_labels("%s")
self._set_title("%s")
self._show_label = kwargs.get("show_label", False)
self._bounds = []
self._clipping = []
self._title_handle = None
self.grid = kwargs.get("grid", cfg["k3d"]["grid"])
kw = dict(
grid_visible=self.grid,
menu_visibility=True,
)
if cfg["k3d"]["bg_color"]:
kw["background_color"] = int(cfg["k3d"]["bg_color"])
if cfg["k3d"]["grid_color"]:
kw["grid_color"] = int(cfg["k3d"]["grid_color"])
if cfg["k3d"]["label_color"]:
kw["label_color"] = int(cfg["k3d"]["label_color"])
if cfg["k3d"]["camera_mode"]:
kw["camera_mode"] = cfg["k3d"]["camera_mode"]
self._use_existing_figure = kwargs.get("fig", False)
if self._use_existing_figure:
self._fig = kwargs["fig"]
self._use_existing_figure = True
else:
self._fig = k3d.plot(**kw)
if (self.xscale == "log") or (self.yscale == "log"):
warnings.warn(
"K3D-Jupyter doesn't support log scales. We will "
+ "continue with linear scales."
)
self._create_renderers()
@property
def fig(self):
"""Returns the figure."""
if (
(len(self.renderers) > 0) and
(
(self.renderers[0] and len(self.renderers[0].handles) == 0)
or (self.renderers[0] is None)
)
):
# if the backend was created without showing it
self._process_renderers()
return self._fig
def draw(self):
""" Loop over data renderers, generates numerical data and add it to
the figure. Note that this method doesn't show the plot.
"""
# this is necessary in order for the series to be added even if
# show=False
self._process_renderers()
# process_series = draw
@staticmethod
def _do_sum_kwargs(p1, p2):
kw = p1._copy_kwargs()
sl1 = False if not hasattr(p1, "_show_label") else p1._show_label
sl2 = False if not hasattr(p2, "_show_label") else p2._show_label
kw["show_label"] = sl1 or sl2
return kw
@staticmethod
def _int_to_rgb(RGBint):
"""Convert an integer number to an RGB tuple with components from 0
to 255.
https://stackoverflow.com/a/2262152/2329968
"""
B = RGBint & 255
G = (RGBint >> 8) & 255
R = (RGBint >> 16) & 255
return R, G, B
@staticmethod
def _rgb_to_int(RGB):
"""Convert an RGB tuple to an integer number.
https://stackoverflow.com/q/2262100/2329968
"""
R, G, B = RGB
return R * 256 ** 2 + G * 256 + B
@classmethod
def _convert_to_int(cls, color):
"""Convert the provided RGB tuple with values from 0 to 1 to an
integer number.
"""
color = [int(c * 255) for c in color]
return cls._rgb_to_int(color)
def _process_renderers(self):
self._init_cyclers()
self._fig.auto_rendering = False
if not self._use_existing_figure:
# clear data
for o in self._fig.objects:
self._fig.remove_class(o)
for r, s in zip(self.renderers, self.series):
self._check_supported_series(r, s)
r.draw()
self._set_axes_texts()
self._new_camera_position()
self._add_clipping_planes()
self._fig.auto_rendering = True
def _set_axes_texts(self):
title, xlabel, ylabel, zlabel = self._get_title_and_labels()
xl = xlabel if xlabel else "x"
yl = ylabel if ylabel else "y"
zl = zlabel if zlabel else "z"
self._fig.axes = [xl, yl, zl]
if title:
if not self._title_handle:
self._fig += self.k3d.text2d(
title, position=[0.025, 0.015], color=0, size=1,
label_box=False)
self._title_handle = len(self._fig.objects) - 1
else:
self._fig.objects[self._title_handle].text = title
def _build_k3d_vector_data(
self, xx, yy, zz, uu, vv, ww, qkw, colormap, normalize, series
):
"""Assemble the origins, vectors and colors (if possible) matrices.
"""
np = import_module('numpy')
xx, yy, zz, uu, vv, ww = [
t.flatten().astype(np.float32) for t in [xx, yy, zz, uu, vv, ww]
]
scale = qkw["scale"]
magnitude = np.sqrt(uu ** 2 + vv ** 2 + ww ** 2)
if normalize:
uu, vv, ww = [t / magnitude for t in [uu, vv, ww]]
vectors = np.array((uu, vv, ww)).T * scale
origins = np.array((xx, yy, zz)).T
color_val = magnitude
if series.color_func is not None:
color_val = series.eval_color_func(xx, yy, zz, uu, vv, ww)
# if color_func was a symbolic expression, than color_val is
# a matrix. Need to flatten.
color_val = color_val.flatten()
colors = None
if colormap is not None:
colors = self.k3d.helpers.map_colors(color_val, colormap, [])
return origins, vectors, colors
def _create_vector_colors(self, colors):
"""Create a color matrix. Each vector requires one color for the tail
and one for the head.
"""
np = import_module('numpy')
vec_colors = np.zeros(2 * len(colors))
for i, c in enumerate(colors):
vec_colors[2 * i] = c
vec_colors[2 * i + 1] = c
vec_colors = vec_colors.astype(np.uint32)
return vec_colors
def _high_aspect_ratio(self, x, y, z):
"""Look for high aspect ratio meshes, where (dz >> dx, dy) and
eventually set the bounds around the mid point of the mesh in order
to improve visibility. Bounds will be used to set the camera position.
"""
mz, Mz, meanz = z.min(), z.max(), z.mean()
mx, Mx = x.min(), x.max()
my, My = y.min(), y.max()
dx, dy, dz = (Mx - mx), (My - my), (Mz - mz)
# thresholds
t1, t2 = 10, 3
if (dz / dx >= t1) and (dz / dy >= t1) and (self.zlim is None):
if abs(Mz / meanz) > t1:
Mz = meanz + t2 * max(dx, dy)
if abs(mz / meanz) > t1:
mz = meanz - t2 * max(dx, dy)
self._bounds.append([mx, Mx, my, My, mz, Mz])
elif self.zlim:
self._bounds.append([mx, Mx, my, My, self.zlim[0], self.zlim[1]])
def update_interactive(self, params):
"""Implement the logic to update the data generated by
interactive-widget plots.
Parameters
==========
params : dict
Map parameter-symbols to numeric values.
"""
self._bounds = []
# Because InteractivePlot doesn't call the show method, the following
# line of code will add the numerical data (if not already present).
if len(self.renderers) > 0 and len(self.renderers[0].handles) == 0:
self.draw()
for r in self.renderers:
if r.series.is_interactive:
r.update(params)
self._set_axes_texts()
self._new_camera_position()
self._add_clipping_planes()
# self._fig.auto_rendering = True
def _new_camera_position(self):
if self.camera is None:
np = import_module('numpy')
if len(self._bounds) > 0:
# when there are very high aspect ratio meshes, or when zlim has
# been set, we compute a new camera position to improve user
# experience
self._fig.camera_auto_fit = False
bounds = np.array(self._bounds)
bounds = np.dstack([
np.min(bounds[:, 0::2], axis=0),
np.max(bounds[:, 1::2], axis=0)
]).flatten()
self._fig.camera = self._fig.get_auto_camera(
1.5, 40, 60, bounds
)
else:
# TODO: why on Earth doesn't it work?
self._fig.camera = self.camera
def show(self):
"""Visualize the plot on the screen."""
if len(self.renderers) > 0 and len(self.renderers[0].handles) == 0:
self._process_renderers()
self._fig.display()
def _add_clipping_planes(self):
if len(self._fig.clipping_planes) == 0:
clipping_planes = []
if self.zlim:
clipping_planes += [
[0, 0, 1, -self.zlim[0]],
[0, 0, -1, self.zlim[1]],
]
if self.xlim:
clipping_planes += [
[1, 0, 0, -self.xlim[0]],
[-1, 0, 0, self.xlim[1]],
]
if self.ylim:
clipping_planes += [
[0, 1, 0, -self.ylim[0]],
[0, -1, 0, self.ylim[1]],
]
self._fig.clipping_planes = clipping_planes
def save(self, path, **kwargs):
"""Export the plot to a static picture or to an interactive html file.
Notes
=====
K3D-Jupyter is only capable of exporting:
1. '.png' pictures: refer to [#fn1]_ to visualize the available
keyword arguments.
2. '.html' files: this requires the ``msgpack`` [#fn2]_ python module
to be installed.
When exporting a fully portable html file, by default the required
Javascript libraries will be loaded with a CDN. Set
``include_js=True`` to include all the javascript code in the html
file: this will create a bigger file size, but can be
run without internet connection.
References
==========
.. [#fn1] https://k3d-jupyter.org/k3d.html#k3d.plot.Plot.fetch_screenshot
.. [#fn2] https://github.com/msgpack/msgpack-python
"""
ext = os.path.splitext(path)[1]
if not ext:
path += ".png"
if ext in [".html", ".htm"]:
with open(path, 'w') as f:
include_js = kwargs.pop("include_js", False)
self.fig.snapshot_include_js = include_js
f.write(self.fig.get_snapshot(**kwargs))
elif ext == ".png":
if self._get_mode() != 0:
raise ValueError(
"K3D-Jupyter requires the plot to be shown on the screen "
+ "before saving a png file.")
@self._fig.yield_screenshots
def _func():
self._fig.fetch_screenshot(**kwargs)
screenshot = yield
with open(path, "wb") as f:
f.write(screenshot)
_func()
else:
raise ValueError(
"K3D-Jupyter can only export '.png' images or " +
"html files.")
KB = K3DBackend