python3-matplotlib 1.3.1-1ubuntu5 / usr / lib / python3 / dist-packages / mpl_toolkits / mplot3d / art3d.py

#!/usr/bin/python
# art3d.py, original mplot3d version by John Porter
# Parts rewritten by Reinier Heeres <reinier@heeres.eu>
# Minor additions by Ben Axelrod <baxelrod@coroware.com>

'''
Module containing 3D artist code and functions to convert 2D
artists into 3D versions which can be added to an Axes3D.
'''

from matplotlib import lines, text as mtext, path as mpath, colors as mcolors
from matplotlib.collections import Collection, LineCollection, \
        PolyCollection, PatchCollection
from matplotlib.cm import ScalarMappable
from matplotlib.patches import Patch
from matplotlib.colors import Normalize
from matplotlib.cbook import iterable

import warnings
import numpy as np
import math
from . import proj3d

def norm_angle(a):
    """Return angle between -180 and +180"""
    a = (a + 360) % 360
    if a > 180:
        a = a - 360
    return a

def norm_text_angle(a):
    """Return angle between -90 and +90"""
    a = (a + 180) % 180
    if a > 90:
        a = a - 180
    return a

def get_dir_vector(zdir):
    if zdir == 'x':
        return np.array((1, 0, 0))
    elif zdir == 'y':
        return np.array((0, 1, 0))
    elif zdir == 'z':
        return np.array((0, 0, 1))
    elif zdir is None:
        return np.array((0, 0, 0))
    elif iterable(zdir) and len(zdir) == 3:
        return zdir
    else:
        raise ValueError("'x', 'y', 'z', None or vector of length 3 expected")

class Text3D(mtext.Text):
    '''
    Text object with 3D position and (in the future) direction.
    '''

    def __init__(self, x=0, y=0, z=0, text='', zdir='z', **kwargs):
        '''
        *x*, *y*, *z*  Position of text
        *text*         Text string to display
        *zdir*         Direction of text

        Keyword arguments are passed onto :func:`~matplotlib.text.Text`.
        '''
        mtext.Text.__init__(self, x, y, text, **kwargs)
        self.set_3d_properties(z, zdir)

    def set_3d_properties(self, z=0, zdir='z'):
        x, y = self.get_position()
        self._position3d = np.array((x, y, z))
        self._dir_vec = get_dir_vector(zdir)

    def draw(self, renderer):
        proj = proj3d.proj_trans_points([self._position3d, \
                self._position3d + self._dir_vec], renderer.M)
        dx = proj[0][1] - proj[0][0]
        dy = proj[1][1] - proj[1][0]
        if dx==0. and dy==0.:
            # atan2 raises ValueError: math domain error on 0,0
            angle = 0.
        else:
            angle = math.degrees(math.atan2(dy, dx))
        self.set_position((proj[0][0], proj[1][0]))
        self.set_rotation(norm_text_angle(angle))
        mtext.Text.draw(self, renderer)

def text_2d_to_3d(obj, z=0, zdir='z'):
    """Convert a Text to a Text3D object."""
    obj.__class__ = Text3D
    obj.set_3d_properties(z, zdir)

class Line3D(lines.Line2D):
    '''
    3D line object.
    '''

    def __init__(self, xs, ys, zs, *args, **kwargs):
        '''
        Keyword arguments are passed onto :func:`~matplotlib.lines.Line2D`.
        '''
        lines.Line2D.__init__(self, [], [], *args, **kwargs)
        self._verts3d = xs, ys, zs

    def set_3d_properties(self, zs=0, zdir='z'):
        xs = self.get_xdata()
        ys = self.get_ydata()

        try:
            zs = float(zs)
            zs = [zs for x in xs]
        except:
            pass
        self._verts3d = juggle_axes(xs, ys, zs, zdir)

    def draw(self, renderer):
        xs3d, ys3d, zs3d = self._verts3d
        xs, ys, zs = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)
        self.set_data(xs, ys)
        lines.Line2D.draw(self, renderer)

def line_2d_to_3d(line, zs=0, zdir='z'):
    '''
    Convert a 2D line to 3D.
    '''
    line.__class__ = Line3D
    line.set_3d_properties(zs, zdir)

def path_to_3d_segment(path, zs=0, zdir='z'):
    '''Convert a path to a 3D segment.'''

    if not iterable(zs):
        zs = np.ones(len(path)) * zs

    seg = []
    pathsegs = path.iter_segments(simplify=False, curves=False)
    for (((x, y), code), z) in zip(pathsegs, zs):
        seg.append((x, y, z))
    seg3d = [juggle_axes(x, y, z, zdir) for (x, y, z) in seg]
    return seg3d

def paths_to_3d_segments(paths, zs=0, zdir='z'):
    '''
    Convert paths from a collection object to 3D segments.
    '''

    if not iterable(zs):
        zs = np.ones(len(paths)) * zs

    segments = []
    for path, pathz in zip(paths, zs):
        segments.append(path_to_3d_segment(path, pathz, zdir))
    return segments

class Line3DCollection(LineCollection):
    '''
    A collection of 3D lines.
    '''

    def __init__(self, segments, *args, **kwargs):
        '''
        Keyword arguments are passed onto :func:`~matplotlib.collections.LineCollection`.
        '''
        LineCollection.__init__(self, segments, *args, **kwargs)

    def set_sort_zpos(self,val):
        '''Set the position to use for z-sorting.'''
        self._sort_zpos = val

    def set_segments(self, segments):
        '''
        Set 3D segments
        '''
        self._segments3d = segments
        LineCollection.set_segments(self, [])

    def do_3d_projection(self, renderer):
        '''
        Project the points according to renderer matrix.
        '''
        xyslist = [
            proj3d.proj_trans_points(points, renderer.M) for points in
            self._segments3d]
        segments_2d = [list(zip(xs, ys)) for (xs, ys, zs) in xyslist]
        LineCollection.set_segments(self, segments_2d)

        # FIXME
        minz = 1e9
        for (xs, ys, zs) in xyslist:
            minz = min(minz, min(zs))
        return minz

    def draw(self, renderer, project=False):
        if project:
            self.do_3d_projection(renderer)
        LineCollection.draw(self, renderer)

def line_collection_2d_to_3d(col, zs=0, zdir='z'):
    """Convert a LineCollection to a Line3DCollection object."""
    segments3d = paths_to_3d_segments(col.get_paths(), zs, zdir)
    col.__class__ = Line3DCollection
    col.set_segments(segments3d)

class Patch3D(Patch):
    '''
    3D patch object.
    '''

    def __init__(self, *args, **kwargs):
        zs = kwargs.pop('zs', [])
        zdir = kwargs.pop('zdir', 'z')
        Patch.__init__(self, *args, **kwargs)
        self.set_3d_properties(zs, zdir)

    def set_3d_properties(self, verts, zs=0, zdir='z'):
        if not iterable(zs):
            zs = np.ones(len(verts)) * zs

        self._segment3d = [juggle_axes(x, y, z, zdir) \
                for ((x, y), z) in zip(verts, zs)]
        self._facecolor3d = Patch.get_facecolor(self)

    def get_path(self):
        return self._path2d

    def get_facecolor(self):
        return self._facecolor2d

    def do_3d_projection(self, renderer):
        s = self._segment3d
        xs, ys, zs = list(zip(*s))
        vxs, vys,vzs, vis = proj3d.proj_transform_clip(xs, ys, zs, renderer.M)
        self._path2d = mpath.Path(list(zip(vxs, vys)))
        # FIXME: coloring
        self._facecolor2d = self._facecolor3d
        return min(vzs)

    def draw(self, renderer):
        Patch.draw(self, renderer)


class PathPatch3D(Patch3D):
    '''
    3D PathPatch object.
    '''

    def __init__(self, path, **kwargs):
        zs = kwargs.pop('zs', [])
        zdir = kwargs.pop('zdir', 'z')
        Patch.__init__(self, **kwargs)
        self.set_3d_properties(path, zs, zdir)

    def set_3d_properties(self, path, zs=0, zdir='z'):
        Patch3D.set_3d_properties(self, path.vertices, zs=zs, zdir=zdir)
        self._code3d = path.codes

    def do_3d_projection(self, renderer):
        s = self._segment3d
        xs, ys, zs = list(zip(*s))
        vxs, vys,vzs, vis = proj3d.proj_transform_clip(xs, ys, zs, renderer.M)
        self._path2d = mpath.Path(list(zip(vxs, vys)), self._code3d)
        # FIXME: coloring
        self._facecolor2d = self._facecolor3d
        return min(vzs)

def get_patch_verts(patch):
    """Return a list of vertices for the path of a patch."""
    trans = patch.get_patch_transform()
    path =  patch.get_path()
    polygons = path.to_polygons(trans)
    if len(polygons):
        return polygons[0]
    else:
        return []

def patch_2d_to_3d(patch, z=0, zdir='z'):
    """Convert a Patch to a Patch3D object."""
    verts = get_patch_verts(patch)
    patch.__class__ = Patch3D
    patch.set_3d_properties(verts, z, zdir)

def pathpatch_2d_to_3d(pathpatch, z=0, zdir='z'):
    """Convert a PathPatch to a PathPatch3D object."""
    path = pathpatch.get_path()
    trans = pathpatch.get_patch_transform()

    mpath = trans.transform_path(path)
    pathpatch.__class__ = PathPatch3D
    pathpatch.set_3d_properties(mpath, z, zdir)

class Patch3DCollection(PatchCollection):
    '''
    A collection of 3D patches.
    '''

    def __init__(self, *args, **kwargs):
        PatchCollection.__init__(self, *args, **kwargs)
        self._old_draw = lambda x: PatchCollection.draw(self, x)

    def set_sort_zpos(self,val):
        '''Set the position to use for z-sorting.'''
        self._sort_zpos = val

    def set_3d_properties(self, zs, zdir):
        # Force the collection to initialize the face and edgecolors
        # just in case it is a scalarmappable with a colormap.
        self.update_scalarmappable()
        offsets = self.get_offsets()
        if len(offsets) > 0:
            xs, ys = list(zip(*self.get_offsets()))
        else:
            xs = [0] * len(zs)
            ys = [0] * len(zs)
        self._offsets3d = juggle_axes(xs, ys, zs, zdir)
        self._facecolor3d = self.get_facecolor()
        self._edgecolor3d = self.get_edgecolor()

    def do_3d_projection(self, renderer):
        xs, ys, zs = self._offsets3d
        vxs, vys, vzs, vis = proj3d.proj_transform_clip(xs, ys, zs, renderer.M)
        #FIXME: mpl allows us no way to unset the collection alpha value
        self._alpha = None
        self.set_facecolors(zalpha(self._facecolor3d, vzs))
        self.set_edgecolors(zalpha(self._edgecolor3d, vzs))
        PatchCollection.set_offsets(self, list(zip(vxs, vys)))

        if vzs.size > 0 :
            return min(vzs)
        else :
            return np.nan

    def draw(self, renderer):
        self._old_draw(renderer)

def patch_collection_2d_to_3d(col, zs=0, zdir='z'):
    """Convert a PatchCollection to a Patch3DCollection object."""

    # The tricky part here is that there are several classes that are
    # derived from PatchCollection. We need to use the right draw method.
    col._old_draw = col.draw

    col.__class__ = Patch3DCollection
    col.set_3d_properties(zs, zdir)

class Poly3DCollection(PolyCollection):
    '''
    A collection of 3D polygons.
    '''

    def __init__(self, verts, *args, **kwargs):
        '''
        Create a Poly3DCollection.

        *verts* should contain 3D coordinates.

        Keyword arguments:
        zsort, see set_zsort for options.

        Note that this class does a bit of magic with the _facecolors
        and _edgecolors properties.
        '''

        self.set_zsort(kwargs.pop('zsort', True))

        PolyCollection.__init__(self, verts, *args, **kwargs)

    _zsort_functions = {
        'average': np.average,
        'min': np.min,
        'max': np.max,
    }

    def set_zsort(self, zsort):
        '''
        Set z-sorting behaviour:
            boolean: if True use default 'average'
            string: 'average', 'min' or 'max'
        '''

        if zsort is True:
            zsort = 'average'

        if zsort is not False:
            if zsort in self._zsort_functions:
                zsortfunc = self._zsort_functions[zsort]
            else:
                return False
        else:
            zsortfunc = None

        self._zsort = zsort
        self._sort_zpos = None
        self._zsortfunc = zsortfunc

    def get_vector(self, segments3d):
        """Optimize points for projection"""
        si = 0
        ei = 0
        segis = []
        points = []
        for p in segments3d:
            points.extend(p)
            ei = si+len(p)
            segis.append((si, ei))
            si = ei

        if len(segments3d) > 0 :
            xs, ys, zs = list(zip(*points))
        else :
            # We need this so that we can skip the bad unpacking from zip()
            xs, ys, zs = [], [], []

        ones = np.ones(len(xs))
        self._vec = np.array([xs, ys, zs, ones])
        self._segis = segis

    def set_verts(self, verts, closed=True):
        '''Set 3D vertices.'''
        self.get_vector(verts)
        # 2D verts will be updated at draw time
        PolyCollection.set_verts(self, [], closed)

    def set_3d_properties(self):
        # Force the collection to initialize the face and edgecolors
        # just in case it is a scalarmappable with a colormap.
        self.update_scalarmappable()
        self._sort_zpos = None
        self.set_zsort(True)
        self._facecolors3d = PolyCollection.get_facecolors(self)
        self._edgecolors3d = PolyCollection.get_edgecolors(self)

    def set_sort_zpos(self,val):
        '''Set the position to use for z-sorting.'''
        self._sort_zpos = val

    def do_3d_projection(self, renderer):
        '''
        Perform the 3D projection for this object.
        '''
        # FIXME: This may no longer be needed?
        if self._A is not None:
            self.update_scalarmappable()
            self._facecolors3d = self._facecolors

        txs, tys, tzs = proj3d.proj_transform_vec(self._vec, renderer.M)
        xyzlist = [(txs[si:ei], tys[si:ei], tzs[si:ei]) \
                for si, ei in self._segis]

        # This extra fuss is to re-order face / edge colors
        cface = self._facecolors3d
        cedge = self._edgecolors3d
        if len(cface) != len(xyzlist):
            cface = cface.repeat(len(xyzlist), axis=0)
        if len(cedge) != len(xyzlist):
            if len(cedge) == 0:
                cedge = cface
            cedge = cedge.repeat(len(xyzlist), axis=0)

        # if required sort by depth (furthest drawn first)
        if self._zsort:
            z_segments_2d = [(self._zsortfunc(zs), list(zip(xs, ys)), fc, ec) for
                    (xs, ys, zs), fc, ec in zip(xyzlist, cface, cedge)]
            z_segments_2d.sort(key=lambda x: x[0], reverse=True)
        else:
            raise ValueError("whoops")

        segments_2d = [s for z, s, fc, ec in z_segments_2d]
        PolyCollection.set_verts(self, segments_2d)

        self._facecolors2d = [fc for z, s, fc, ec in z_segments_2d]
        if len(self._edgecolors3d) == len(cface):
            self._edgecolors2d = [ec for z, s, fc, ec in z_segments_2d]
        else:
            self._edgecolors2d = self._edgecolors3d

        # Return zorder value
        if self._sort_zpos is not None:
            zvec = np.array([[0], [0], [self._sort_zpos], [1]])
            ztrans = proj3d.proj_transform_vec(zvec, renderer.M)
            return ztrans[2][0]
        elif tzs.size > 0 :
            # FIXME: Some results still don't look quite right.
            #        In particular, examine contourf3d_demo2.py
            #        with az = -54 and elev = -45.
            return np.min(tzs)
        else :
            return np.nan

    def set_facecolor(self, colors):
        PolyCollection.set_facecolor(self, colors)
        self._facecolors3d = PolyCollection.get_facecolor(self)
    set_facecolors = set_facecolor

    def set_edgecolor(self, colors):
        PolyCollection.set_edgecolor(self, colors)
        self._edgecolors3d = PolyCollection.get_edgecolor(self)
    set_edgecolors = set_edgecolor

    def get_facecolors(self):
        return self._facecolors2d
    get_facecolor = get_facecolors

    def get_edgecolors(self):
        return self._edgecolors2d
    get_edgecolor = get_edgecolors

    def draw(self, renderer):
        return Collection.draw(self, renderer)

def poly_collection_2d_to_3d(col, zs=0, zdir='z'):
    """Convert a PolyCollection to a Poly3DCollection object."""
    segments_3d = paths_to_3d_segments(col.get_paths(), zs, zdir)
    col.__class__ = Poly3DCollection
    col.set_verts(segments_3d)
    col.set_3d_properties()

def juggle_axes(xs, ys, zs, zdir):
    """
    Reorder coordinates so that 2D xs, ys can be plotted in the plane
    orthogonal to zdir. zdir is normally x, y or z. However, if zdir
    starts with a '-' it is interpreted as a compensation for rotate_axes.
    """
    if zdir == 'x':
        return zs, xs, ys
    elif zdir == 'y':
        return xs, zs, ys
    elif zdir[0] == '-':
        return rotate_axes(xs, ys, zs, zdir)
    else:
        return xs, ys, zs

def rotate_axes(xs, ys, zs, zdir):
    """
    Reorder coordinates so that the axes are rotated with zdir along
    the original z axis. Prepending the axis with a '-' does the
    inverse transform, so zdir can be x, -x, y, -y, z or -z
    """
    if zdir == 'x':
        return ys, zs, xs
    elif zdir == '-x':
        return zs, xs, ys

    elif zdir == 'y':
        return zs, xs, ys
    elif zdir == '-y':
        return ys, zs, xs

    else:
        return xs, ys, zs

def iscolor(c):
    try:
        if len(c) == 4 or len(c) == 3:
            if iterable(c[0]):
                return False
            if hasattr(c[0], '__float__'):
                return True
    except:
        return False
    return False

def get_colors(c, num):
    """Stretch the color argument to provide the required number num"""

    if type(c) == type("string"):
        c = mcolors.colorConverter.to_rgba(c)

    if iscolor(c):
        return [c] * num
    if len(c) == num:
        return c
    elif iscolor(c):
        return [c] * num
    elif len(c) == 0: #if edgecolor or facecolor is specified as 'none'
        return [[0,0,0,0]] * num
    elif iscolor(c[0]):
        return [c[0]] * num
    else:
        raise ValueError('unknown color format %s' % c)

def zalpha(colors, zs):
    """Modify the alphas of the color list according to depth"""
    # FIXME: This only works well if the points for *zs* are well-spaced
    #        in all three dimensions. Otherwise, at certain orientations,
    #        the min and max zs are very close together.
    #        Should really normalize against the viewing depth.
    colors = get_colors(colors, len(zs))
    if zs.size > 0 :
        norm = Normalize(min(zs), max(zs))
        sats = 1 - norm(zs) * 0.7
        colors = [(c[0], c[1], c[2], c[3] * s) for c, s in zip(colors, sats)]
    return colors