def __spacetime_diagram_o_prime_frame(self):
# from (x,t) to (x',t')
def tr(x_prime, t_prime):
x_prime, t_prime = np.asarray(x_prime), np.asarray(t_prime)
return self.lorentz_transformations.transform(
x_prime, t_prime, self.velocity)
# form (x',t') to (x,t)
def inv_tr(x, t):
x, t = np.asarray(x), np.asarray(t)
return self.lorentz_transformations.transform(x, t, -self.velocity)
grid_helper = GridHelperCurveLinear((tr, inv_tr))
ax = SubplotHost(self.fig, 1, 2, 2, grid_helper=grid_helper)
self.fig.add_subplot(ax)
ax.set_xlabel("x'", loc="center")
ax.set_ylabel("t'", loc="center")
# O x axis
ax.axis["x1"] = x1 = ax.new_floating_axis(0, 0)
x1.label.set_text("x")
# O t axis
ax.axis["t1"] = t1 = ax.new_floating_axis(1, 0)
t1.label.set_text("t")
self.__add_x_and_y_axis(ax)
ax.format_coord = self.__format_coord_o_prime_frame
self.__remove_ticks(ax, x1, t1)
self.world_lines_plotter.transform_and_plot(plt, ax, self.velocity)
def curvelinear_test2(fig):
"""
polar projection, but in a rectangular box.
"""
global ax1
import numpy as np
import mpl_toolkits.axisartist.angle_helper as angle_helper
from matplotlib.projections import PolarAxes
from matplotlib.transforms import Affine2D
from mpl_toolkits.axisartist import SubplotHost
from mpl_toolkits.axisartist import GridHelperCurveLinear
# see demo_curvelinear_grid.py for details
tr = Affine2D().scale(np.pi/180., 1.) + PolarAxes.PolarTransform()
extreme_finder = angle_helper.ExtremeFinderCycle(20, 20,
lon_cycle = 360,
lat_cycle = None,
lon_minmax = None,
lat_minmax = (0, np.inf),
)
grid_locator1 = angle_helper.LocatorDMS(12)
tick_formatter1 = angle_helper.FormatterDMS()
grid_helper = GridHelperCurveLinear(tr,
extreme_finder=extreme_finder,
grid_locator1=grid_locator1,
tick_formatter1=tick_formatter1
)
ax1 = SubplotHost(fig, 1, 1, 1, grid_helper=grid_helper)
fig.add_subplot(ax1)
# Now creates floating axis
#grid_helper = ax1.get_grid_helper()
# floating axis whose first coordinate (theta) is fixed at 60
ax1.axis["lat"] = axis = ax1.new_floating_axis(0, 60)
axis.label.set_text(r"$\theta = 60^{\circ}$")
axis.label.set_visible(True)
# floating axis whose second coordinate (r) is fixed at 6
ax1.axis["lon"] = axis = ax1.new_floating_axis(1, 6)
axis.label.set_text(r"$r = 6$")
ax1.set_aspect(1.)
ax1.set_xlim(-5, 12)
ax1.set_ylim(-5, 10)
ax1.grid(True)
def curvelinear_test(fig):
"""Polar projection, but in a rectangular box.
"""
# 创建一个极坐标变换。PolarAxes.PolarTransform使用弧度，但本例
# 要设置的坐标系中角度的单位为度
tr = Affine2D().scale(np.pi / 180., 1.) + PolarAxes.PolarTransform()
# 极坐标投影涉及到周期，在坐标上也有限制，需要一种特殊的方法来找到
# 坐标的最小值和最大值
extreme_finder = angle_helper.ExtremeFinderCycle(
20,
20,
lon_cycle=360,
lat_cycle=None,
lon_minmax=None,
lat_minmax=(0, np.inf),
)
# 找到适合坐标的网格值（度、分、秒）
grid_locator1 = angle_helper.LocatorDMS(12)
# 使用适当的Formatter。请注意，可接受的Locator和Formatter类
# 与Matplotlib中的相应类稍有不同，后者目前还不能直接在这里使用
tick_formatter1 = angle_helper.FormatterDMS()
grid_helper = GridHelperCurveLinear(tr,
extreme_finder=extreme_finder,
grid_locator1=grid_locator1,
tick_formatter1=tick_formatter1)
ax1 = SubplotHost(fig, 1, 1, 1, grid_helper=grid_helper)
fig.add_subplot(ax1)
# 创建浮动坐标轴
# 浮动坐标轴的第一个坐标（theta）指定为60度
ax1.axis["lat"] = axis = ax1.new_floating_axis(0, 60)
axis.label.set_text(r"$\theta = 60^{\circ}$")
axis.label.set_visible(True)
# 浮动坐标轴的第二个坐标（r）指定为6
ax1.axis["lon"] = axis = ax1.new_floating_axis(1, 6)
axis.label.set_text(r"$r = 6$")
ax1.set_aspect(1.)
ax1.set_xlim(-5, 12)
ax1.set_ylim(-5, 10)
ax1.grid(True)
def SemiPolarPlot(fig):
# see demo_curvelinear_grid.py for details
tr = Affine2D().scale(pi/180., 1.) + PolarAxes.PolarTransform()
extreme_finder = angle_helper.ExtremeFinderCycle(20, 20,
lon_cycle = 360,
lat_cycle = None,
lon_minmax = None,
lat_minmax = (0, 1),
)
grid_locator1 = angle_helper.LocatorDMS(11)
grid_locator2 = FixedLocator([0.25, 0.5, 1., 0.75])
tick_formatter1 = angle_helper.FormatterDMS()
grid_helper = GridHelperCurveLinear(tr,
extreme_finder=extreme_finder,
grid_locator1=grid_locator1,
grid_locator2=grid_locator2,
tick_formatter1=tick_formatter1,
tick_formatter2=None
)
ax1 = SubplotHost(fig, 1, 1, 1, grid_helper=grid_helper)
fig.add_subplot(ax1)
ax1.axis["top"].set_visible(False)
ax1.axis["right"].set_visible(False)
ax1.axis["bottom"].set_visible(False)
ax1.axis["lon"] = ax1.new_floating_axis(1, 1)
ax1.set_aspect(1)
ax1.set_xlim(0, 2)
ax1.set_ylim(-1., 1.)
ax1.grid(True)
curved_ax = ax1.get_aux_axes(tr)
curved_ax.patch = ax1.patch # for aux_ax to have a clip path as in ax
ax1.patch.zorder=0.9
return ax1, curved_ax
def sgrid():
# From matplotlib demos:
# https://matplotlib.org/gallery/axisartist/demo_curvelinear_grid.html
# https://matplotlib.org/gallery/axisartist/demo_floating_axis.html
# PolarAxes.PolarTransform takes radian. However, we want our coordinate
# system in degree
tr = Affine2D().scale(np.pi/180., 1.) + PolarAxes.PolarTransform()
# polar projection, which involves cycle, and also has limits in
# its coordinates, needs a special method to find the extremes
# (min, max of the coordinate within the view).
# 20, 20 : number of sampling points along x, y direction
sampling_points = 20
extreme_finder = ModifiedExtremeFinderCycle(sampling_points, sampling_points,
lon_cycle=360,
lat_cycle=None,
lon_minmax=(90,270),
lat_minmax=(0, np.inf),)
grid_locator1 = angle_helper.LocatorDMS(15)
tick_formatter1 = FormatterDMS()
grid_helper = GridHelperCurveLinear(tr,
extreme_finder=extreme_finder,
grid_locator1=grid_locator1,
tick_formatter1=tick_formatter1
)
fig = plt.figure()
ax = SubplotHost(fig, 1, 1, 1, grid_helper=grid_helper)
# make ticklabels of right invisible, and top axis visible.
visible = True
ax.axis[:].major_ticklabels.set_visible(visible)
ax.axis[:].major_ticks.set_visible(False)
ax.axis[:].invert_ticklabel_direction()
ax.axis["wnxneg"] = axis = ax.new_floating_axis(0, 180)
axis.set_ticklabel_direction("-")
axis.label.set_visible(False)
ax.axis["wnxpos"] = axis = ax.new_floating_axis(0, 0)
axis.label.set_visible(False)
ax.axis["wnypos"] = axis = ax.new_floating_axis(0, 90)
axis.label.set_visible(False)
axis.set_axis_direction("left")
ax.axis["wnyneg"] = axis = ax.new_floating_axis(0, 270)
axis.label.set_visible(False)
axis.set_axis_direction("left")
axis.invert_ticklabel_direction()
axis.set_ticklabel_direction("-")
# let left axis shows ticklabels for 1st coordinate (angle)
ax.axis["left"].get_helper().nth_coord_ticks = 0
ax.axis["right"].get_helper().nth_coord_ticks = 0
ax.axis["left"].get_helper().nth_coord_ticks = 0
ax.axis["bottom"].get_helper().nth_coord_ticks = 0
fig.add_subplot(ax)
### RECTANGULAR X Y AXES WITH SCALE
#par2 = ax.twiny()
#par2.axis["top"].toggle(all=False)
#par2.axis["right"].toggle(all=False)
#new_fixed_axis = par2.get_grid_helper().new_fixed_axis
#par2.axis["left"] = new_fixed_axis(loc="left",
# axes=par2,
# offset=(0, 0))
#par2.axis["bottom"] = new_fixed_axis(loc="bottom",
# axes=par2,
# offset=(0, 0))
### FINISH RECTANGULAR
ax.grid(True, zorder=0,linestyle='dotted')
_final_setup(ax)
return ax, fig
def sgrid():
# From matplotlib demos:
# https://matplotlib.org/gallery/axisartist/demo_curvelinear_grid.html
# https://matplotlib.org/gallery/axisartist/demo_floating_axis.html
# PolarAxes.PolarTransform takes radian. However, we want our coordinate
# system in degree
tr = Affine2D().scale(np.pi/180., 1.) + PolarAxes.PolarTransform()
# polar projection, which involves cycle, and also has limits in
# its coordinates, needs a special method to find the extremes
# (min, max of the coordinate within the view).
# 20, 20 : number of sampling points along x, y direction
sampling_points = 20
extreme_finder = ModifiedExtremeFinderCycle(sampling_points, sampling_points,
lon_cycle=360,
lat_cycle=None,
lon_minmax=(90,270),
lat_minmax=(0, np.inf),)
grid_locator1 = angle_helper.LocatorDMS(15)
tick_formatter1 = FormatterDMS()
grid_helper = GridHelperCurveLinear(tr,
extreme_finder=extreme_finder,
grid_locator1=grid_locator1,
tick_formatter1=tick_formatter1
)
fig = plt.figure()
ax = SubplotHost(fig, 1, 1, 1, grid_helper=grid_helper)
# make ticklabels of right invisible, and top axis visible.
visible = True
ax.axis[:].major_ticklabels.set_visible(visible)
ax.axis[:].major_ticks.set_visible(False)
ax.axis[:].invert_ticklabel_direction()
ax.axis["wnxneg"] = axis = ax.new_floating_axis(0, 180)
axis.set_ticklabel_direction("-")
axis.label.set_visible(False)
ax.axis["wnxpos"] = axis = ax.new_floating_axis(0, 0)
axis.label.set_visible(False)
ax.axis["wnypos"] = axis = ax.new_floating_axis(0, 90)
axis.label.set_visible(False)
axis.set_axis_direction("left")
ax.axis["wnyneg"] = axis = ax.new_floating_axis(0, 270)
axis.label.set_visible(False)
axis.set_axis_direction("left")
axis.invert_ticklabel_direction()
axis.set_ticklabel_direction("-")
# let left axis shows ticklabels for 1st coordinate (angle)
ax.axis["left"].get_helper().nth_coord_ticks = 0
ax.axis["right"].get_helper().nth_coord_ticks = 0
ax.axis["left"].get_helper().nth_coord_ticks = 0
ax.axis["bottom"].get_helper().nth_coord_ticks = 0
fig.add_subplot(ax)
### RECTANGULAR X Y AXES WITH SCALE
#par2 = ax.twiny()
#par2.axis["top"].toggle(all=False)
#par2.axis["right"].toggle(all=False)
#new_fixed_axis = par2.get_grid_helper().new_fixed_axis
#par2.axis["left"] = new_fixed_axis(loc="left",
# axes=par2,
# offset=(0, 0))
#par2.axis["bottom"] = new_fixed_axis(loc="bottom",
# axes=par2,
# offset=(0, 0))
### FINISH RECTANGULAR
ax.grid(True, zorder=0,linestyle='dotted')
_final_setup(ax)
return ax, fig
