def _graphics(self, plot_curve, ambient_coords, thickness=1, aspect_ratio='automatic', color='red', style='-', label_axes=True): r""" Plot a 2D or 3D curve in a Cartesian graph with axes labeled by the ambient coordinates; it is invoked by the methods :meth:`plot` of :class:`~sage.manifolds.differentiable.curve.DifferentiableCurve`, and its subclasses (:class:`~sage.manifolds.differentiable.integrated_curve.IntegratedCurve`, :class:`~sage.manifolds.differentiable.integrated_curve.IntegratedAutoparallelCurve`, and :class:`~sage.manifolds.differentiable.integrated_curve.IntegratedGeodesic`). TESTS:: sage: M = Manifold(2, 'R^2') sage: X.<x,y> = M.chart() sage: R.<t> = RealLine() sage: c = M.curve([cos(t), sin(t)], (t, 0, 2*pi), name='c') sage: graph = c._graphics([[1,2], [3,4]], [x,y]) sage: graph._objects[0].xdata == [1,3] True sage: graph._objects[0].ydata == [2,4] True sage: graph._objects[0]._options['thickness'] == 1 True sage: graph._extra_kwds['aspect_ratio'] == 'automatic' True sage: graph._objects[0]._options['rgbcolor'] == 'red' True sage: graph._objects[0]._options['linestyle'] == '-' True sage: l = [r'$'+latex(x)+r'$', r'$'+latex(y)+r'$'] sage: graph._extra_kwds['axes_labels'] == l True """ from sage.plot.graphics import Graphics from sage.plot.line import line from sage.manifolds.utilities import set_axes_labels # # The plot # n_pc = len(ambient_coords) resu = Graphics() resu += line(plot_curve, color=color, linestyle=style, thickness=thickness) if n_pc == 2: # 2D graphic resu.set_aspect_ratio(aspect_ratio) if label_axes: # We update the dictionary _extra_kwds (options to be passed # to show()), instead of using the method # Graphics.axes_labels() since the latter is not robust w.r.t. # graph addition resu._extra_kwds['axes_labels'] = [r'$'+latex(pc)+r'$' for pc in ambient_coords] else: # 3D graphic if aspect_ratio == 'automatic': aspect_ratio = 1 resu.aspect_ratio(aspect_ratio) if label_axes: labels = [str(pc) for pc in ambient_coords] resu = set_axes_labels(resu, *labels) return resu
def plot(self, chart=None, ambient_coords=None, mapping=None, prange=None, include_end_point=(True, True), end_point_offset=(0.001, 0.001), max_value=8, parameters=None, color='red', style='-', thickness=1, plot_points=75, label_axes=True, aspect_ratio='automatic'): r""" Plot the current curve (``self``) in a Cartesian graph based on the coordinates of some ambient chart. The curve is drawn in terms of two (2D graphics) or three (3D graphics) coordinates of a given chart, called hereafter the *ambient chart*. The ambient chart's domain must overlap with the curve's codomain or with the codomain of the composite curve `\Phi\circ c`, where `c` is ``self`` and `\Phi` some manifold differential mapping (argument ``mapping`` below). INPUT: - ``chart`` -- (default: ``None``) the ambient chart (see above); if ``None``, the default chart of the codomain of the curve (or of the curve composed with `\Phi`) is used - ``ambient_coords`` -- (default: ``None``) tuple containing the 2 or 3 coordinates of the ambient chart in terms of which the plot is performed; if ``None``, all the coordinates of the ambient chart are considered - ``mapping`` -- (default: ``None``) differentiable mapping `\Phi` (instance of :class:`~sage.geometry.manifolds.diffmapping.DiffMapping`) providing the link between ``self`` and the ambient chart ``chart`` (cf. above); if ``None``, the ambient chart is supposed to be defined on the codomain of the curve ``self``. - ``prange`` -- (default: ``None``) range of the curve parameter for the plot; if ``None``, the entire parameter range declared during the curve construction is considered (with -Infinity replaced by ``-max_value`` and +Infinity by ``max_value``) - ``include_end_point`` -- (default: ``(True, True)``) determines whether the end points of ``prange`` are included in the plot - ``end_point_offset`` -- (default: ``(0.001, 0.001)``) offsets from the end points when they are not included in the plot: if ``include_end_point[0] == False``, the minimal value of the curve parameter used for the plot is ``prange[0] + end_point_offset[0]``, while if ``include_end_point[1] == False``, the maximal value is ``prange[1] - end_point_offset[1]``. - ``max_value`` -- (default: 8) numerical value substituted to +Infinity if the latter is the upper bound of the parameter range; similarly ``-max_value`` is the numerical valued substituted for -Infinity - ``parameters`` -- (default: ``None``) dictionary giving the numerical values of the parameters that may appear in the coordinate expression of ``self`` - ``color`` -- (default: 'red') color of the drawn curve - ``style`` -- (default: '-') color of the drawn curve; NB: ``style`` is effective only for 2D plots - ``thickness`` -- (default: 1) thickness of the drawn curve - ``plot_points`` -- (default: 75) number of points to plot the curve - ``label_axes`` -- (default: ``True``) boolean determining whether the labels of the coordinate axes of ``chart`` shall be added to the graph; can be set to ``False`` if the graph is 3D and must be superposed with another graph. - ``aspect_ratio`` -- (default: 'automatic') aspect ratio of the plot; the default value ('automatic') applies only for 2D plots; for 3D plots, the default value is ``1`` instead. OUTPUT: - a graphic object, either an instance of :class:`~sage.plot.graphics.Graphics` for a 2D plot (i.e. based on 2 coordinates of ``chart``) or an instance of :class:`~sage.plot.plot3d.base.Graphics3d` for a 3D plot (i.e. based on 3 coordinates of ``chart``) EXAMPLES: Plot of the lemniscate of Gerono:: sage: R2 = Manifold(2, 'R^2') sage: X.<x,y> = R2.chart() sage: R.<t> = RealLine() sage: c = R2.curve([sin(t), sin(2*t)/2], (t, 0, 2*pi), name='c') sage: c.plot() # 2D plot Graphics object consisting of 1 graphics primitive Plot for a subinterval of the curve's domain:: sage: c.plot(prange=(0,pi)) Graphics object consisting of 1 graphics primitive Plot with various options:: sage: c.plot(color='green', style=':', thickness=3, aspect_ratio=1) Graphics object consisting of 1 graphics primitive Plot via a mapping to another manifold: loxodrome of a sphere viewed in `\RR^3`:: sage: S2 = Manifold(2, 'S^2') sage: U = S2.open_subset('U') sage: XS.<th,ph> = U.chart(r'th:(0,pi):\theta ph:(0,2*pi):\phi') sage: R3 = Manifold(3, 'R^3') sage: X3.<x,y,z> = R3.chart() sage: F = S2.diff_mapping(R3, {(XS, X3): [sin(th)*cos(ph), ....: sin(th)*sin(ph), cos(th)]}, name='F') sage: F.display() F: S^2 --> R^3 on U: (th, ph) |--> (x, y, z) = (cos(ph)*sin(th), sin(ph)*sin(th), cos(th)) sage: c = S2.curve([2*atan(exp(-t/10)), t], (t, -oo, +oo), name='c') sage: graph_c = c.plot(mapping=F, max_value=40, ....: plot_points=200, thickness=2, label_axes=False) # 3D plot sage: graph_S2 = XS.plot(X3, mapping=F, nb_values=11, color='black') # plot of the sphere sage: show(graph_c + graph_S2) # the loxodrome + the sphere Example of use of the argument ``parameters``: we define a curve with some symbolic parameters ``a`` and ``b``:: sage: a, b = var('a b') sage: c = R2.curve([a*cos(t) + b, a*sin(t)], (t, 0, 2*pi), name='c') To make a plot, we set spectific values for ``a`` and ``b`` by means of the Python dictionary ``parameters``:: sage: c.plot(parameters={a: 2, b: -3}, aspect_ratio=1) Graphics object consisting of 1 graphics primitive """ from sage.rings.infinity import Infinity from sage.misc.functional import numerical_approx from sage.plot.graphics import Graphics from sage.plot.line import line from sage.geometry.manifolds.chart import Chart from sage.geometry.manifolds.utilities import set_axes_labels # # The "effective" curve to be plotted # if mapping is None: eff_curve = self else: eff_curve = mapping.restrict(self.codomain()) * self # # The chart w.r.t. which the curve is plotted # if chart is None: chart = eff_curve._codomain.default_chart() elif not isinstance(chart, Chart): raise TypeError("{} is not a chart".format(chart)) # # Coordinates of the above chart w.r.t. which the curve is plotted # if ambient_coords is None: ambient_coords = chart[:] # all chart coordinates are used n_pc = len(ambient_coords) if n_pc != 2 and n_pc !=3: raise ValueError("The number of coordinates involved in the " + "plot must be either 2 or 3, not {}".format(n_pc)) ind_pc = [chart[:].index(pc) for pc in ambient_coords] # indices of plot # coordinates # # Parameter range for the plot # if prange is None: prange = (self._domain.lower_bound(), self._domain.upper_bound()) elif not isinstance(prange, (tuple, list)): raise TypeError("{} is neither a tuple nor a list".format(prange)) elif len(prange) != 2: raise ValueError("the argument prange must be a tuple/list " + "of 2 elements") tmin = prange[0] tmax = prange[1] if tmin == -Infinity: tmin = -max_value elif not include_end_point[0]: tmin = tmin + end_point_offset[0] if tmax == Infinity: tmax = max_value elif not include_end_point[1]: tmax = tmax - end_point_offset[1] tmin = numerical_approx(tmin) tmax = numerical_approx(tmax) # # The coordinate expression of the effective curve # canon_chart = self._domain.canonical_chart() transf = None for chart_pair in eff_curve._coord_expression: if chart_pair == (canon_chart, chart): transf = eff_curve._coord_expression[chart_pair] break else: # Search for a subchart for chart_pair in eff_curve._coord_expression: for schart in chart._subcharts: if chart_pair == (canon_chart, schart): transf = eff_curve._coord_expression[chart_pair] if transf is None: raise ValueError("No expression has been found for " + "{} in terms of {}".format(self, format)) # # List of points for the plot curve # plot_curve = [] dt = (tmax - tmin) / (plot_points - 1) t = tmin if parameters is None: for i in range(plot_points): x = transf(t, simplify=False) plot_curve.append( [numerical_approx(x[j]) for j in ind_pc] ) t += dt else: for i in range(plot_points): x = transf(t, simplify=False) plot_curve.append( [numerical_approx( x[j].substitute(parameters) ) for j in ind_pc] ) t += dt # # The plot # resu = Graphics() resu += line(plot_curve, color=color, linestyle=style, thickness=thickness) if n_pc==2: # 2D graphic resu.set_aspect_ratio(aspect_ratio) if label_axes: # We update the dictionary _extra_kwds (options to be passed # to show()), instead of using the method # Graphics.axes_labels() since the latter is not robust w.r.t. # graph addition resu._extra_kwds['axes_labels'] = [r'$'+latex(pc)+r'$' for pc in ambient_coords] else: # 3D graphic if aspect_ratio == 'automatic': aspect_ratio = 1 resu.aspect_ratio(aspect_ratio) if label_axes: labels = [str(pc) for pc in ambient_coords] resu = set_axes_labels(resu, *labels) return resu
def plot(self, chart=None, ambient_coords=None, mapping=None, prange=None, include_end_point=(True, True), end_point_offset=(0.001, 0.001), parameters=None, color='red', style='-', label_axes=True, **kwds): r""" Plot the current curve in a Cartesian graph based on the coordinates of some ambient chart. The curve is drawn in terms of two (2D graphics) or three (3D graphics) coordinates of a given chart, called hereafter the *ambient chart*. The ambient chart's domain must overlap with the curve's codomain or with the codomain of the composite curve `\Phi\circ c`, where `c` is the current curve and `\Phi` some manifold differential map (argument ``mapping`` below). INPUT: - ``chart`` -- (default: ``None``) the ambient chart (see above); if ``None``, the default chart of the codomain of the curve (or of the curve composed with `\Phi`) is used - ``ambient_coords`` -- (default: ``None``) tuple containing the 2 or 3 coordinates of the ambient chart in terms of which the plot is performed; if ``None``, all the coordinates of the ambient chart are considered - ``mapping`` -- (default: ``None``) differentiable mapping `\Phi` (instance of :class:`~sage.manifolds.differentiable.diff_map.DiffMap`) providing the link between the curve and the ambient chart ``chart`` (cf. above); if ``None``, the ambient chart is supposed to be defined on the codomain of the curve. - ``prange`` -- (default: ``None``) range of the curve parameter for the plot; if ``None``, the entire parameter range declared during the curve construction is considered (with -Infinity replaced by ``-max_range`` and +Infinity by ``max_range``) - ``include_end_point`` -- (default: ``(True, True)``) determines whether the end points of ``prange`` are included in the plot - ``end_point_offset`` -- (default: ``(0.001, 0.001)``) offsets from the end points when they are not included in the plot: if ``include_end_point[0] == False``, the minimal value of the curve parameter used for the plot is ``prange[0] + end_point_offset[0]``, while if ``include_end_point[1] == False``, the maximal value is ``prange[1] - end_point_offset[1]``. - ``max_range`` -- (default: 8) numerical value substituted to +Infinity if the latter is the upper bound of the parameter range; similarly ``-max_range`` is the numerical valued substituted for -Infinity - ``parameters`` -- (default: ``None``) dictionary giving the numerical values of the parameters that may appear in the coordinate expression of the curve - ``color`` -- (default: 'red') color of the drawn curve - ``style`` -- (default: '-') color of the drawn curve; NB: ``style`` is effective only for 2D plots - ``thickness`` -- (default: 1) thickness of the drawn curve - ``plot_points`` -- (default: 75) number of points to plot the curve - ``label_axes`` -- (default: ``True``) boolean determining whether the labels of the coordinate axes of ``chart`` shall be added to the graph; can be set to ``False`` if the graph is 3D and must be superposed with another graph. - ``aspect_ratio`` -- (default: ``'automatic'``) aspect ratio of the plot; the default value (``'automatic'``) applies only for 2D plots; for 3D plots, the default value is ``1`` instead OUTPUT: - a graphic object, either an instance of :class:`~sage.plot.graphics.Graphics` for a 2D plot (i.e. based on 2 coordinates of ``chart``) or an instance of :class:`~sage.plot.plot3d.base.Graphics3d` for a 3D plot (i.e. based on 3 coordinates of ``chart``) EXAMPLES: Plot of the lemniscate of Gerono:: sage: R2 = Manifold(2, 'R^2') sage: X.<x,y> = R2.chart() sage: R.<t> = RealLine() sage: c = R2.curve([sin(t), sin(2*t)/2], (t, 0, 2*pi), name='c') sage: c.plot() # 2D plot Graphics object consisting of 1 graphics primitive .. PLOT:: R2 = Manifold(2, 'R^2') X = R2.chart('x y') t = RealLine().canonical_coordinate() c = R2.curve([sin(t), sin(2*t)/2], (t, 0, 2*pi), name='c') g = c.plot() sphinx_plot(g) Plot for a subinterval of the curve's domain:: sage: c.plot(prange=(0,pi)) Graphics object consisting of 1 graphics primitive .. PLOT:: R2 = Manifold(2, 'R^2') X = R2.chart('x y') t = RealLine().canonical_coordinate() c = R2.curve([sin(t), sin(2*t)/2], (t, 0, 2*pi), name='c') g = c.plot(prange=(0,pi)) sphinx_plot(g) Plot with various options:: sage: c.plot(color='green', style=':', thickness=3, aspect_ratio=1) Graphics object consisting of 1 graphics primitive .. PLOT:: R2 = Manifold(2, 'R^2') X = R2.chart('x y') t = RealLine().canonical_coordinate() c = R2.curve([sin(t), sin(2*t)/2], (t, 0, 2*pi), name='c') g = c.plot(color='green', style=':', thickness=3, aspect_ratio=1) sphinx_plot(g) Plot via a mapping to another manifold: loxodrome of a sphere viewed in `\RR^3`:: sage: S2 = Manifold(2, 'S^2') sage: U = S2.open_subset('U') sage: XS.<th,ph> = U.chart(r'th:(0,pi):\theta ph:(0,2*pi):\phi') sage: R3 = Manifold(3, 'R^3') sage: X3.<x,y,z> = R3.chart() sage: F = S2.diff_map(R3, {(XS, X3): [sin(th)*cos(ph), ....: sin(th)*sin(ph), cos(th)]}, name='F') sage: F.display() F: S^2 --> R^3 on U: (th, ph) |--> (x, y, z) = (cos(ph)*sin(th), sin(ph)*sin(th), cos(th)) sage: c = S2.curve([2*atan(exp(-t/10)), t], (t, -oo, +oo), name='c') sage: graph_c = c.plot(mapping=F, max_range=40, ....: plot_points=200, thickness=2, label_axes=False) # 3D plot sage: graph_S2 = XS.plot(X3, mapping=F, number_values=11, color='black') # plot of the sphere sage: show(graph_c + graph_S2) # the loxodrome + the sphere .. PLOT:: S2 = Manifold(2, 'S^2') U = S2.open_subset('U') XS = U.chart(r'th:(0,pi):\theta ph:(0,2*pi):\phi') th, ph = XS[:] R3 = Manifold(3, 'R^3') X3 = R3.chart('x y z') F = S2.diff_map(R3, {(XS, X3): [sin(th)*cos(ph), sin(th)*sin(ph), cos(th)]}, name='F') t = RealLine().canonical_coordinate() c = S2.curve([2*atan(exp(-t/10)), t], (t, -oo, +oo), name='c') graph_c = c.plot(mapping=F, max_range=40, plot_points=200, thickness=2, label_axes=False) graph_S2 = XS.plot(X3, mapping=F, number_values=11, color='black') sphinx_plot(graph_c + graph_S2) Example of use of the argument ``parameters``: we define a curve with some symbolic parameters ``a`` and ``b``:: sage: a, b = var('a b') sage: c = R2.curve([a*cos(t) + b, a*sin(t)], (t, 0, 2*pi), name='c') To make a plot, we set spectific values for ``a`` and ``b`` by means of the Python dictionary ``parameters``:: sage: c.plot(parameters={a: 2, b: -3}, aspect_ratio=1) Graphics object consisting of 1 graphics primitive .. PLOT:: R2 = Manifold(2, 'R^2') X = R2.chart('x y') t = RealLine().canonical_coordinate() a, b = var('a b') c = R2.curve([a*cos(t) + b, a*sin(t)], (t, 0, 2*pi), name='c') g = c.plot(parameters={a: 2, b: -3}, aspect_ratio=1) sphinx_plot(g) """ from sage.rings.infinity import Infinity from sage.misc.functional import numerical_approx from sage.plot.graphics import Graphics from sage.plot.line import line from sage.manifolds.chart import RealChart from sage.manifolds.utilities import set_axes_labels # # Get the @options from kwds # thickness = kwds.pop('thickness') plot_points = kwds.pop('plot_points') max_range = kwds.pop('max_range') aspect_ratio = kwds.pop('aspect_ratio') # # The "effective" curve to be plotted # if mapping is None: eff_curve = self else: eff_curve = mapping.restrict(self.codomain()) * self # # The chart w.r.t. which the curve is plotted # if chart is None: chart = eff_curve._codomain.default_chart() elif not isinstance(chart, RealChart): raise TypeError("{} is not a real chart".format(chart)) # # Coordinates of the above chart w.r.t. which the curve is plotted # if ambient_coords is None: ambient_coords = chart[:] # all chart coordinates are used n_pc = len(ambient_coords) if n_pc != 2 and n_pc != 3: raise ValueError("the number of coordinates involved in the " + "plot must be either 2 or 3, not {}".format(n_pc)) # indices of plot coordinates ind_pc = [chart[:].index(pc) for pc in ambient_coords] # # Parameter range for the plot # if prange is None: prange = (self._domain.lower_bound(), self._domain.upper_bound()) elif not isinstance(prange, (tuple, list)): raise TypeError("{} is neither a tuple nor a list".format(prange)) elif len(prange) != 2: raise ValueError("the argument prange must be a tuple/list " + "of 2 elements") tmin = prange[0] tmax = prange[1] if tmin == -Infinity: tmin = -max_range elif not include_end_point[0]: tmin = tmin + end_point_offset[0] if tmax == Infinity: tmax = max_range elif not include_end_point[1]: tmax = tmax - end_point_offset[1] tmin = numerical_approx(tmin) tmax = numerical_approx(tmax) # # The coordinate expression of the effective curve # canon_chart = self._domain.canonical_chart() transf = None for chart_pair in eff_curve._coord_expression: if chart_pair == (canon_chart, chart): transf = eff_curve._coord_expression[chart_pair] break else: # Search for a subchart for chart_pair in eff_curve._coord_expression: for schart in chart._subcharts: if chart_pair == (canon_chart, schart): transf = eff_curve._coord_expression[chart_pair] if transf is None: raise ValueError("No expression has been found for " + "{} in terms of {}".format(self, chart)) # # List of points for the plot curve # plot_curve = [] dt = (tmax - tmin) / (plot_points - 1) t = tmin if parameters is None: for i in range(plot_points): x = transf(t, simplify=False) plot_curve.append([numerical_approx(x[j]) for j in ind_pc]) t += dt else: for i in range(plot_points): x = transf(t, simplify=False) plot_curve.append([ numerical_approx(x[j].substitute(parameters)) for j in ind_pc ]) t += dt # # The plot # resu = Graphics() resu += line(plot_curve, color=color, linestyle=style, thickness=thickness) if n_pc == 2: # 2D graphic resu.set_aspect_ratio(aspect_ratio) if label_axes: # We update the dictionary _extra_kwds (options to be passed # to show()), instead of using the method # Graphics.axes_labels() since the latter is not robust w.r.t. # graph addition resu._extra_kwds['axes_labels'] = [ r'$' + latex(pc) + r'$' for pc in ambient_coords ] else: # 3D graphic if aspect_ratio == 'automatic': aspect_ratio = 1 resu.aspect_ratio(aspect_ratio) if label_axes: labels = [str(pc) for pc in ambient_coords] resu = set_axes_labels(resu, *labels) return resu
def finalize(self, G): r""" Finalize a root system plot. INPUT: - ``G`` -- a root system plot or ``0`` This sets the aspect ratio to 1 and remove the axes. This should be called by all the user-level plotting methods of root systems. This will become mostly obsolete when customization options won't be lost anymore upon addition of graphics objects and there will be a proper empty object for 2D and 3D plots. EXAMPLES:: sage: L = RootSystem(["B",2,1]).ambient_space() sage: options = L.plot_parse_options() sage: p = L.plot_roots(plot_options=options) sage: p += L.plot_coroots(plot_options=options) sage: p.axes() True sage: p = options.finalize(p) sage: p.axes() False sage: p.aspect_ratio() 1.0 sage: options = L.plot_parse_options(affine=False) sage: p = L.plot_roots(plot_options=options) sage: p += point([[1,1,0]]) sage: p = options.finalize(p) sage: p.aspect_ratio() [1.0, 1.0, 1.0] If the input is ``0``, this returns an empty graphics object:: sage: type(options.finalize(0)) <class 'sage.plot.plot3d.base.Graphics3dGroup'> sage: options = L.plot_parse_options() sage: type(options.finalize(0)) <class 'sage.plot.graphics.Graphics'> sage: list(options.finalize(0)) [] """ from sage.plot.graphics import Graphics if self.dimension == 2: if G == 0: G = Graphics() G.set_aspect_ratio(1) # TODO: make this customizable G.axes(False) elif self.dimension == 3: if G == 0: from sage.plot.plot3d.base import Graphics3dGroup G = Graphics3dGroup() G.aspect_ratio(1) # TODO: Configuration axes return G
def finalize(self, G): r""" Finalize a root system plot. INPUT: - ``G`` -- a root system plot or ``0`` This sets the aspect ratio to 1 and remove the axes. This should be called by all the user-level plotting methods of root systems. This will become mostly obsolete when customization options won't be lost anymore upon addition of graphics objects and there will be a proper empty object for 2D and 3D plots. EXAMPLES:: sage: L = RootSystem(["B",2,1]).ambient_space() sage: options = L.plot_parse_options() sage: p = L.plot_roots(plot_options=options) sage: p += L.plot_coroots(plot_options=options) sage: p.axes() True sage: p = options.finalize(p) sage: p.axes() False sage: p.aspect_ratio() 1.0 sage: options = L.plot_parse_options(affine=False) sage: p = L.plot_roots(plot_options=options) sage: p += point([[1,1,0]]) sage: p = options.finalize(p) sage: p.aspect_ratio() [1.0, 1.0, 1.0] If the input is ``0``, this returns an empty graphics object:: sage: type(options.finalize(0)) <class 'sage.plot.plot3d.base.Graphics3dGroup'> sage: options = L.plot_parse_options() sage: type(options.finalize(0)) <class 'sage.plot.graphics.Graphics'> sage: list(options.finalize(0)) [] """ from sage.plot.graphics import Graphics if self.dimension == 2: if G == 0: G = Graphics() G.set_aspect_ratio(1) # TODO: make this customizable G.axes(False) elif self.dimension == 3: if G == 0: from sage.plot.plot3d.base import Graphics3dGroup G = Graphics3dGroup() G.aspect_ratio(1) # TODO: Configuration axes return G
def _graphics(self, plot_curve, ambient_coords, thickness=1, aspect_ratio='automatic', color='red', style='-', label_axes=True): r""" Plot a 2D or 3D curve in a Cartesian graph with axes labeled by the ambient coordinates; it is invoked by the methods :meth:`plot` of :class:`~sage.manifolds.differentiable.curve.DifferentiableCurve`, and its subclasses (:class:`~sage.manifolds.differentiable.integrated_curve.IntegratedCurve`, :class:`~sage.manifolds.differentiable.integrated_curve.IntegratedAutoparallelCurve`, and :class:`~sage.manifolds.differentiable.integrated_curve.IntegratedGeodesic`). TESTS:: sage: M = Manifold(2, 'R^2') sage: X.<x,y> = M.chart() sage: R.<t> = RealLine() sage: c = M.curve([cos(t), sin(t)], (t, 0, 2*pi), name='c') sage: graph = c._graphics([[1,2], [3,4]], [x,y]) sage: graph._objects[0].xdata == [1,3] True sage: graph._objects[0].ydata == [2,4] True sage: graph._objects[0]._options['thickness'] == 1 True sage: graph._extra_kwds['aspect_ratio'] == 'automatic' True sage: graph._objects[0]._options['rgbcolor'] == 'red' True sage: graph._objects[0]._options['linestyle'] == '-' True sage: l = [r'$'+latex(x)+r'$', r'$'+latex(y)+r'$'] sage: graph._extra_kwds['axes_labels'] == l True """ from sage.plot.graphics import Graphics from sage.plot.line import line from sage.manifolds.utilities import set_axes_labels # # The plot # n_pc = len(ambient_coords) resu = Graphics() resu += line(plot_curve, color=color, linestyle=style, thickness=thickness) if n_pc == 2: # 2D graphic resu.set_aspect_ratio(aspect_ratio) if label_axes: # We update the dictionary _extra_kwds (options to be passed # to show()), instead of using the method # Graphics.axes_labels() since the latter is not robust w.r.t. # graph addition resu._extra_kwds['axes_labels'] = [r'$'+latex(pc)+r'$' for pc in ambient_coords] else: # 3D graphic if aspect_ratio == 'automatic': aspect_ratio = 1 resu.aspect_ratio(aspect_ratio) if label_axes: labels = [str(pc) for pc in ambient_coords] resu = set_axes_labels(resu, *labels) return resu