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grid_helper_curvelinear.py
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""" An experimental support for curvelinear grid. """ from itertools import chain from grid_finder import GridFinder from axislines import \ AxisArtistHelper, GridHelperBase from axis_artist import AxisArtist from matplotlib.transforms import Affine2D, IdentityTransform import numpy as np class FixedAxisArtistHelper(AxisArtistHelper.Fixed): """ Helper class for a fixed axis. """ def __init__(self, grid_helper, side, nth_coord_ticks=None): """ nth_coord = along which coordinate value varies. nth_coord = 0 -> x axis, nth_coord = 1 -> y axis """ super(FixedAxisArtistHelper, self).__init__( \ loc=side, ) self.grid_helper = grid_helper if nth_coord_ticks is None: nth_coord_ticks = self.nth_coord self.nth_coord_ticks = nth_coord_ticks self.side = side def update_lim(self, axes): self.grid_helper.update_lim(axes) def change_tick_coord(self, coord_number=None): if coord_number is None: self.nth_coord_ticks = 1 - self.nth_coord_ticks elif coord_number in [0, 1]: self.nth_coord_ticks = coord_number else: raise Exception("wrong coord number") def get_tick_transform(self, axes): return axes.transData def get_tick_iterators(self, axes): """tick_loc, tick_angle, tick_label""" g = self.grid_helper ti1 = g.get_tick_iterator(self.nth_coord_ticks, self.side) ti2 = g.get_tick_iterator(1-self.nth_coord_ticks, self.side, minor=True) #ti2 = g.get_tick_iterator(1-self.nth_coord_ticks, self.side, minor=True) return chain(ti1, ti2), iter([]) class FloatingAxisArtistHelper(AxisArtistHelper.Floating): def __init__(self, grid_helper, nth_coord, value, axis_direction=None): """ nth_coord = along which coordinate value varies. nth_coord = 0 -> x axis, nth_coord = 1 -> y axis """ super(FloatingAxisArtistHelper, self).__init__(nth_coord, value, ) self.value = value self.grid_helper = grid_helper self._extremes = None, None def set_extremes(self, e1, e2): self._extremes = e1, e2 def update_lim(self, axes): self.grid_helper.update_lim(axes) x1, x2 = axes.get_xlim() y1, y2 = axes.get_ylim() grid_finder = self.grid_helper.grid_finder extremes = grid_finder.extreme_finder(grid_finder.inv_transform_xy, x1, y1, x2, y2) extremes = list(extremes) e1, e2 = self._extremes # ranges of other coordinates if self.nth_coord == 0: if e1 is not None: extremes[2] = max(e1, extremes[2]) if e2 is not None: extremes[3] = min(e2, extremes[3]) elif self.nth_coord == 1: if e1 is not None: extremes[0] = max(e1, extremes[0]) if e2 is not None: extremes[1] = min(e2, extremes[1]) grid_info = dict() lon_min, lon_max, lat_min, lat_max = extremes lon_levs, lon_n, lon_factor = \ grid_finder.grid_locator1(lon_min, lon_max) lat_levs, lat_n, lat_factor = \ grid_finder.grid_locator2(lat_min, lat_max) grid_info["extremes"] = extremes grid_info["lon_info"] = lon_levs, lon_n, lon_factor grid_info["lat_info"] = lat_levs, lat_n, lat_factor grid_info["lon_labels"] = grid_finder.tick_formatter1("bottom", lon_factor, lon_levs) grid_info["lat_labels"] = grid_finder.tick_formatter2("bottom", lat_factor, lat_levs) grid_finder = self.grid_helper.grid_finder #e1, e2 = self._extremes # ranges of other coordinates if self.nth_coord == 0: xx0 = np.linspace(self.value, self.value, 100) yy0 = np.linspace(extremes[2], extremes[3], 100) xx, yy = grid_finder.transform_xy(xx0, yy0) elif self.nth_coord == 1: xx0 = np.linspace(extremes[0], extremes[1], 100) yy0 = np.linspace(self.value, self.value, 100) xx, yy = grid_finder.transform_xy(xx0, yy0) grid_info["line_xy"] = xx, yy self.grid_info = grid_info def get_axislabel_transform(self, axes): return Affine2D() #axes.transData def get_axislabel_pos_angle(self, axes): extremes = self.grid_info["extremes"] if self.nth_coord == 0: xx0 = self.value yy0 = (extremes[2]+extremes[3])/2. dxx, dyy = 0., abs(extremes[2]-extremes[3])/1000. elif self.nth_coord == 1: xx0 = (extremes[0]+extremes[1])/2. yy0 = self.value dxx, dyy = abs(extremes[0]-extremes[1])/1000., 0. grid_finder = self.grid_helper.grid_finder xx1, yy1 = grid_finder.transform_xy([xx0], [yy0]) trans_passingthrough_point = axes.transData + axes.transAxes.inverted() p = trans_passingthrough_point.transform_point([xx1[0], yy1[0]]) if (0. <= p[0] <= 1.) and (0. <= p[1] <= 1.): xx1c, yy1c = axes.transData.transform_point([xx1[0], yy1[0]]) xx2, yy2 = grid_finder.transform_xy([xx0+dxx], [yy0+dyy]) xx2c, yy2c = axes.transData.transform_point([xx2[0], yy2[0]]) return (xx1c, yy1c), np.arctan2(yy2c-yy1c, xx2c-xx1c)/np.pi*180. else: return None, None def get_tick_transform(self, axes): return IdentityTransform() #axes.transData def get_tick_iterators(self, axes): """tick_loc, tick_angle, tick_label, (optionally) tick_label""" grid_finder = self.grid_helper.grid_finder lat_levs, lat_n, lat_factor = self.grid_info["lat_info"] lat_levs = np.asarray(lat_levs) if lat_factor is not None: yy0 = lat_levs / lat_factor dy = 0.01 / lat_factor else: yy0 = lat_levs dy = 0.01 lon_levs, lon_n, lon_factor = self.grid_info["lon_info"] lon_levs = np.asarray(lon_levs) if lon_factor is not None: xx0 = lon_levs / lon_factor dx = 0.01 / lon_factor else: xx0 = lon_levs dx = 0.01 e0, e1 = sorted(self._extremes) if e0 is None: e0 = -np.inf if e1 is None: e1 = np.inf if self.nth_coord == 0: mask = (e0 <= yy0) & (yy0 <= e1) #xx0, yy0 = xx0[mask], yy0[mask] yy0 = yy0[mask] elif self.nth_coord == 1: mask = (e0 <= xx0) & (xx0 <= e1) #xx0, yy0 = xx0[mask], yy0[mask] xx0 = xx0[mask] def transform_xy(x, y): x1, y1 = grid_finder.transform_xy(x, y) x2y2 = axes.transData.transform(np.array([x1, y1]).transpose()) x2, y2 = x2y2.transpose() return x2, y2 # find angles if self.nth_coord == 0: xx0 = np.empty_like(yy0) xx0.fill(self.value) xx1, yy1 = transform_xy(xx0, yy0) xx00 = xx0.copy() xx00[xx0+dx>e1] -= dx xx1a, yy1a = transform_xy(xx00, yy0) xx1b, yy1b = transform_xy(xx00+dx, yy0) xx2a, yy2a = transform_xy(xx0, yy0) xx2b, yy2b = transform_xy(xx0, yy0+dy) labels = self.grid_info["lat_labels"] labels = [l for l, m in zip(labels, mask) if m] elif self.nth_coord == 1: yy0 = np.empty_like(xx0) yy0.fill(self.value) xx1, yy1 = transform_xy(xx0, yy0) xx1a, yy1a = transform_xy(xx0, yy0) xx1b, yy1b = transform_xy(xx0, yy0+dy) xx00 = xx0.copy() xx00[xx0+dx>e1] -= dx xx2a, yy2a = transform_xy(xx00, yy0) xx2b, yy2b = transform_xy(xx00+dx, yy0) labels = self.grid_info["lon_labels"] labels = [l for l, m in zip(labels, mask) if m] def f1(): dd = np.arctan2(yy1b-yy1a, xx1b-xx1a) # angle normal dd2 = np.arctan2(yy2b-yy2a, xx2b-xx2a) # angle tangent mm = ((yy1b-yy1a)==0.) & ((xx1b-xx1a)==0.) # mask where dd1 is not defined dd[mm] = dd2[mm]+3.14159/2. #dd = np.arctan2(yy2-yy1, xx2-xx1) # angle normal #dd2 = np.arctan2(yy3-yy1, xx3-xx1) # angle tangent #mm = ((yy2-yy1)==0.) & ((xx2-xx1)==0.) # mask where dd1 is not defined #dd[mm] = dd2[mm]+3.14159/2. #dd += 3.14159 #dd = np.arctan2(xx2-xx1, angle_tangent-yy1) trans_tick = self.get_tick_transform(axes) tr2ax = trans_tick + axes.transAxes.inverted() for x, y, d, d2, lab in zip(xx1, yy1, dd, dd2, labels): c2 = tr2ax.transform_point((x, y)) delta=0.00001 if (0. -delta<= c2[0] <= 1.+delta) and \ (0. -delta<= c2[1] <= 1.+delta): d1 = d/3.14159*180. d2 = d2/3.14159*180. yield [x, y], d1, d2, lab return f1(), iter([]) def get_line_transform(self, axes): return axes.transData def get_line(self, axes): self.update_lim(axes) from matplotlib.path import Path xx, yy = self.grid_info["line_xy"] return Path(zip(xx, yy)) class GridHelperCurveLinear(GridHelperBase): def __init__(self, aux_trans, extreme_finder=None, grid_locator1=None, grid_locator2=None, tick_formatter1=None, tick_formatter2=None): """ aux_trans : a transform from the source (curved) coordinate to target (rectlinear) coordinate. An instance of MPL's Transform (inverse transform should be defined) or a tuple of two callable objects which defines the transform and its inverse. The callables need take two arguments of array of source coordinates and should return two target coordinates: e.g. x2, y2 = trans(x1, y1) """ super(GridHelperCurveLinear, self).__init__() self.grid_info = None self._old_values = None #self._grid_params = dict() self._aux_trans = aux_trans self.grid_finder = GridFinder(aux_trans, extreme_finder, grid_locator1, grid_locator2, tick_formatter1, tick_formatter2) def update_grid_finder(self, aux_trans=None, **kw): if aux_trans is not None: self.grid_finder.update_transform(aux_trans) self.grid_finder.update(**kw) self.invalidate() def _update(self, x1, x2, y1, y2): "bbox in 0-based image coordinates" # update wcsgrid if self.valid() and self._old_values == (x1, x2, y1, y2): return self._update_grid(x1, y1, x2, y2) self._old_values = (x1, x2, y1, y2) self._force_update = False def new_fixed_axis(self, loc, nth_coord=None, axis_direction=None, offset=None, axes=None): if axes is None: axes = self.axes if axis_direction is None: axis_direction = loc _helper = FixedAxisArtistHelper(self, loc, #nth_coord, nth_coord_ticks=nth_coord, ) axisline = AxisArtist(axes, _helper, axis_direction=axis_direction) return axisline def new_floating_axis(self, nth_coord, value, axes=None, axis_direction="bottom" ): if axes is None: axes = self.axes _helper = FloatingAxisArtistHelper( \ self, nth_coord, value, axis_direction) axisline = AxisArtist(axes, _helper) #_helper = FloatingAxisArtistHelper(self, nth_coord, # value, # label_direction=label_direction, # ) #axisline = AxisArtistFloating(axes, _helper, # axis_direction=axis_direction) axisline.line.set_clip_on(True) axisline.line.set_clip_box(axisline.axes.bbox) #axisline.major_ticklabels.set_visible(True) #axisline.minor_ticklabels.set_visible(False) #axisline.major_ticklabels.set_rotate_along_line(True) #axisline.set_rotate_label_along_line(True) return axisline def _update_grid(self, x1, y1, x2, y2): self.grid_info = self.grid_finder.get_grid_info(x1, y1, x2, y2) def get_gridlines(self): grid_lines = [] for gl in self.grid_info["lat"]["lines"]: grid_lines.extend(gl) for gl in self.grid_info["lon"]["lines"]: grid_lines.extend(gl) return grid_lines def get_tick_iterator(self, nth_coord, axis_side, minor=False): #axisnr = dict(left=0, bottom=1, right=2, top=3)[axis_side] angle_tangent = dict(left=90, right=90, bottom=0, top=0)[axis_side] #angle = [0, 90, 180, 270][axisnr] lon_or_lat = ["lon", "lat"][nth_coord] if not minor: # major ticks def f(): for (xy, a), l in zip(self.grid_info[lon_or_lat]["tick_locs"][axis_side], self.grid_info[lon_or_lat]["tick_labels"][axis_side]): angle_normal = a yield xy, angle_normal, angle_tangent, l else: def f(): for (xy, a), l in zip(self.grid_info[lon_or_lat]["tick_locs"][axis_side], self.grid_info[lon_or_lat]["tick_labels"][axis_side]): angle_normal = a yield xy, angle_normal, angle_tangent, "" #for xy, a, l in self.grid_info[lon_or_lat]["ticks"][axis_side]: # yield xy, a, "" return f() def test3(): import numpy as np from matplotlib.transforms import Transform from matplotlib.path import Path class MyTransform(Transform): input_dims = 2 output_dims = 2 is_separable = False def __init__(self, resolution): """ Create a new Aitoff transform. Resolution is the number of steps to interpolate between each input line segment to approximate its path in curved Aitoff space. """ Transform.__init__(self) self._resolution = resolution def transform(self, ll): x = ll[:, 0:1] y = ll[:, 1:2] return np.concatenate((x, y-x), 1) transform.__doc__ = Transform.transform.__doc__ transform_non_affine = transform transform_non_affine.__doc__ = Transform.transform_non_affine.__doc__ def transform_path(self, path): vertices = path.vertices ipath = path.interpolated(self._resolution) return Path(self.transform(ipath.vertices), ipath.codes) transform_path.__doc__ = Transform.transform_path.__doc__ transform_path_non_affine = transform_path transform_path_non_affine.__doc__ = Transform.transform_path_non_affine.__doc__ def inverted(self): return MyTransformInv(self._resolution) inverted.__doc__ = Transform.inverted.__doc__ class MyTransformInv(Transform): input_dims = 2 output_dims = 2 is_separable = False def __init__(self, resolution): Transform.__init__(self) self._resolution = resolution def transform(self, ll): x = ll[:, 0:1] y = ll[:, 1:2] return np.concatenate((x, y+x), 1) transform.__doc__ = Transform.transform.__doc__ def inverted(self): return MyTransform(self._resolution) inverted.__doc__ = Transform.inverted.__doc__ import matplotlib.pyplot as plt fig = plt.figure(1) fig.clf() tr = MyTransform(1) grid_helper = GridHelperCurveLinear(tr) from mpl_toolkits.axes_grid1.parasite_axes import host_subplot_class_factory from axislines import Axes SubplotHost = host_subplot_class_factory(Axes) ax1 = SubplotHost(fig, 1, 1, 1, grid_helper=grid_helper) fig.add_subplot(ax1) ax2 = ParasiteAxesAuxTrans(ax1, tr, "equal") ax1.parasites.append(ax2) ax2.plot([3, 6], [5.0, 10.]) ax1.set_aspect(1.) ax1.set_xlim(0, 10) ax1.set_ylim(0, 10) ax1.grid(True) plt.draw() def curvelinear_test2(fig): """ polar projection, but in a rectangular box. """ global ax1 import numpy as np import angle_helper from matplotlib.projections import PolarAxes from matplotlib.transforms import Affine2D from mpl_toolkits.axes_grid.parasite_axes import SubplotHost, \ ParasiteAxesAuxTrans import matplotlib.cbook as cbook # 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 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(5) # Find a grid values appropriate for the coordinate (degree, # minute, second). tick_formatter1 = angle_helper.FormatterDMS() # And also uses an appropriate formatter. Note that,the # acceptable Locator and Formatter class is a bit different than # that of mpl's, and you cannot directly use mpl's Locator and # Formatter here (but may be possible in the future). 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) # make ticklabels of right and top axis visible. ax1.axis["right"].major_ticklabels.set_visible(True) ax1.axis["top"].major_ticklabels.set_visible(True) # let right axis shows ticklabels for 1st coordinate (angle) ax1.axis["right"].get_helper().nth_coord_ticks=0 # let bottom axis shows ticklabels for 2nd coordinate (radius) ax1.axis["bottom"].get_helper().nth_coord_ticks=1 fig.add_subplot(ax1) grid_helper = ax1.get_grid_helper() ax1.axis["lat"] = axis = grid_helper.new_floating_axis(0, 60, axes=ax1) axis.label.set_text("Test") axis.label.set_visible(True) #axis._extremes = 2, 10 #axis.label.set_text("Test") #axis.major_ticklabels.set_visible(False) #axis.major_ticks.set_visible(False) axis.get_helper()._extremes=2, 10 ax1.axis["lon"] = axis = grid_helper.new_floating_axis(1, 6, axes=ax1) #axis.major_ticklabels.set_visible(False) #axis.major_ticks.set_visible(False) axis.label.set_text("Test 2") axis.get_helper()._extremes=-180, 90 # A parasite axes with given transform ax2 = ParasiteAxesAuxTrans(ax1, tr, "equal") # note that ax2.transData == tr + ax1.transData # Anthing you draw in ax2 will match the ticks and grids of ax1. ax1.parasites.append(ax2) intp = cbook.simple_linear_interpolation ax2.plot(intp(np.array([0, 30]), 50), intp(np.array([10., 10.]), 50)) ax1.set_aspect(1.) ax1.set_xlim(-5, 12) ax1.set_ylim(-5, 10) ax1.grid(True) def curvelinear_test3(fig): """ polar projection, but in a rectangular box. """ global ax1, axis import numpy as np import angle_helper from matplotlib.projections import PolarAxes from matplotlib.transforms import Affine2D from mpl_toolkits.axes_grid.parasite_axes import SubplotHost # 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 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) # Find a grid values appropriate for the coordinate (degree, # minute, second). tick_formatter1 = angle_helper.FormatterDMS() # And also uses an appropriate formatter. Note that,the # acceptable Locator and Formatter class is a bit different than # that of mpl's, and you cannot directly use mpl's Locator and # Formatter here (but may be possible in the future). 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) for axis in ax1.axis.itervalues(): axis.set_visible(False) fig.add_subplot(ax1) grid_helper = ax1.get_grid_helper() ax1.axis["lat1"] = axis = grid_helper.new_floating_axis(0, 130, axes=ax1, axis_direction="left" ) axis.label.set_text("Test") axis.label.set_visible(True) axis.get_helper()._extremes=0.001, 10 grid_helper = ax1.get_grid_helper() ax1.axis["lat2"] = axis = grid_helper.new_floating_axis(0, 50, axes=ax1, axis_direction="right") axis.label.set_text("Test") axis.label.set_visible(True) axis.get_helper()._extremes=0.001, 10 ax1.axis["lon"] = axis = grid_helper.new_floating_axis(1, 10, axes=ax1, axis_direction="bottom") axis.label.set_text("Test 2") axis.get_helper()._extremes= 50, 130 axis.major_ticklabels.set_axis_direction("top") axis.label.set_axis_direction("top") grid_helper.grid_finder.grid_locator1.den = 5 grid_helper.grid_finder.grid_locator2._nbins = 5 # # A parasite axes with given transform # ax2 = ParasiteAxesAuxTrans(ax1, tr, "equal") # # note that ax2.transData == tr + ax1.transData # # Anthing you draw in ax2 will match the ticks and grids of ax1. # ax1.parasites.append(ax2) # intp = cbook.simple_linear_interpolation # ax2.plot(intp(np.array([0, 30]), 50), # intp(np.array([10., 10.]), 50)) ax1.set_aspect(1.) ax1.set_xlim(-5, 12) ax1.set_ylim(-5, 10) ax1.grid(True) if __name__ == "__main__": import matplotlib.pyplot as plt fig = plt.figure(1, figsize=(5, 5)) fig.clf() #test3() #curvelinear_test2(fig) curvelinear_test3(fig) #plt.draw() plt.show()