Python triangulation.Triangulation类代码示例

    def plot_trisurf(self, *args, **kwargs):
        '''
        plot_trisurf(x, y, z,  **wrargs)
        plot_trisurf(x, y, z,  triangles = triangle,,,)
        plot_trisurf(tri, z,  **kwargs, cz = cz, cdata = cdata)


        '''
        from art3d_gl import poly_collection_3d_to_gl
        from matplotlib.tri.triangulation import Triangulation

        cz = kwargs.pop('cz', False)
        cdata = kwargs.pop('cdata', None)
        expanddata = kwargs.pop('expanddata', False)
        
        tri, args, kwargs = Triangulation.get_from_args_and_kwargs(*args, **kwargs)
        if 'Z' in kwargs:
            z = np.asarray(kwargs.pop('Z'))
        else:
            z = np.asarray(args[0])
            # We do this so Z doesn't get passed as an arg to PolyCollection
            args = args[1:]

        triangles = tri.get_masked_triangles()
        X3D = tri.x
        Y3D = tri.y
        Z3D = z
        idxset = tri.get_masked_triangles()

        if expanddata:
            verts = np.dstack((X3D[idxset], 
                           Y3D[idxset],
                           Z3D[idxset]))
            if cz:
                if cdata is not None:
                    cdata = cdata[idxset]
                else:
                    cdata = Z3D[idxset]
                shade = kwargs.pop('shade', 'linear')
                if shade != 'linear':
                    cdata = np.mean(cdata, -1)
                kwargs['facecolordata'] = np.real(cdata)
                kwargs.pop('facecolor', None) # get rid of this keyword
            kwargs['cz'] = cz
            o =  self.plot_solid(verts, **kwargs)
            o._idxset = (None, None, idxset)   # this is used for phasor
        else:
            verts = np.vstack((X3D, Y3D, Z3D)).transpose()
            if cz:
                if cdata is not None:
                    cdata = cdata
                else:
                    cdata = Z3D
                kwargs['facecolordata'] = np.real(cdata)
                kwargs.pop('facecolor', None) # get rid of this keyword
            kwargs['cz'] = cz
            o =  self.plot_solid(verts, idxset, **kwargs)
            o._idxset = (None, None, None)   # this is used for phasor            
        return o

 def _contour_args(self, args, kwargs):
     if self.filled: fn = 'contourf'
     else:           fn = 'contour'
     tri, args, kwargs = \
         Triangulation.get_from_args_and_kwargs(*args, **kwargs)
     z = np.asarray(args[0])
     if z.shape != tri.x.shape:
         raise ValueError('z array must have same length as triangulation x'
                          'and y arrays')
     self.zmax = z.max()
     self.zmin = z.min()
     if self.logscale and self.zmin <= 0:
         raise ValueError('Cannot %s log of negative values.' % fn)
     self._contour_level_args(z, args[1:])
     return (tri, z)

def meshDelaunay(settings,heights):
    '''
    Convert coordinates to mesh using Delaunay triangulation. Also returns
    colormap for writing the mesh in IDTF format, surface triangles from
    triangulation (as opposed to tetrahedra), and the top surface area of
    the mesh.
    '''
    # Get coordinates of all height points (omitting zeros)
    coordinates = np.where(heights != 0)
    x_3D = coordinates[0]
    y_3D = coordinates[1]

    # Generate 3D mesh from heights using meshgrid and griddata
    dx = (max(x_3D) - min(x_3D)) / settings['grid_size']
    dy = (max(y_3D) - min(y_3D)) / settings['grid_size']

    x_grid = np.linspace(min(x_3D),max(x_3D),max(dx,dy))
    y_grid = np.linspace(min(y_3D),max(y_3D),max(dx,dy))

    X,Y = np.meshgrid(x_grid,y_grid)
    z = np.array([heights[x_3D[i],y_3D[i]] for i in range(len(coordinates[0]))])
    Z = griddata((x_3D,y_3D),z,(X,Y))

    # Convert NaNs to zeros and find non-zero coordinates
    Z[np.isnan(Z)] = 0
    nonZero = np.where(Z > 0) # Indices of non-zero points
    # Subset X,Y, and Z to contain only non-zero points
    Z_nz = Z[nonZero[0],nonZero[1]]
    X_nz= np.array([X[0][xi] for xi in nonZero[0]])
    Y_nz = np.array([Y[:,0][yi] for yi in nonZero[1]])

    xyz_points = np.column_stack((X_nz,Y_nz,Z_nz))
    triangulation = Delaunay(xyz_points)

    # Get surface triangles
    triang,args,kwargs = Triangulation.get_from_args_and_kwargs(X_nz,Y_nz,Z_nz,triangles=triangulation.simplices)
    triangles = triang.get_masked_triangles() # From matplotlib.tri.triangulation

    # Get color values for mesh triangle faces
    fig = plt.figure()
    ax = fig.add_subplot(111, projection='3d')
    surf = ax.plot_trisurf(X_nz,Y_nz,Z_nz,triangles=triangles,cmap=plt.cm.viridis)
    m = plt.cm.ScalarMappable(cmap=surf.cmap,norm=surf.norm)
    colors = m.to_rgba(Z_nz)

    return z,triangulation,triangles,colors

#.........这里部分代码省略.........
        # hint: each apex is shared by 2 masked_triangles except the borders.
        borders = np.sum(neighbors == -1)
        added_pts = (3*ntri + borders) / 2
        refi_npts = npts + added_pts
        refi_x = np.zeros(refi_npts)
        refi_y = np.zeros(refi_npts)

        # First part of refi_x, refi_y is just the initial points
        refi_x[:npts] = x
        refi_y[:npts] = y

        # Second part contains the edge midside nodes.
        # Each edge belongs to 1 triangle (if border edge) or is shared by 2
        # masked_triangles (interior edge).
        # We first build 2 * ntri arrays of edge starting nodes (edge_elems,
        # edge_apexes) ; we then extract only the masters to avoid overlaps.
        # The so-called 'master' is the triangle with biggest index
        # The 'slave' is the triangle with lower index
        # (can be -1 if border edge)
        # For slave and master we will identify the apex pointing to the edge
        # start
        edge_elems = np.ravel(np.vstack([np.arange(ntri, dtype=np.int32),
                                         np.arange(ntri, dtype=np.int32),
                                         np.arange(ntri, dtype=np.int32)]))
        edge_apexes = np.ravel(np.vstack([np.zeros(ntri, dtype=np.int32),
                                          np.ones(ntri, dtype=np.int32),
                                          np.ones(ntri, dtype=np.int32)*2]))
        edge_neighbors = neighbors[edge_elems, edge_apexes]
        mask_masters = (edge_elems > edge_neighbors)

        # Identifying the "masters" and adding to refi_x, refi_y vec
        masters = edge_elems[mask_masters]
        apex_masters = edge_apexes[mask_masters]
        x_add = (x[triangles[masters, apex_masters]] +
                 x[triangles[masters, (apex_masters+1) % 3]]) * 0.5
        y_add = (y[triangles[masters, apex_masters]] +
                 y[triangles[masters, (apex_masters+1) % 3]]) * 0.5
        refi_x[npts:] = x_add
        refi_y[npts:] = y_add

        # Building the new masked_triangles ; each old masked_triangles hosts
        # 4 new masked_triangles
        # there are 6 pts to identify per 'old' triangle, 3 new_pt_corner and
        # 3 new_pt_midside
        new_pt_corner = triangles

        # What is the index in refi_x, refi_y of point at middle of apex iapex
        #  of elem ielem ?
        # If ielem is the apex master: simple count, given the way refi_x was
        #  built.
        # If ielem is the apex slave: yet we do not know ; but we will soon
        # using the neighbors table.
        new_pt_midside = np.empty([ntri, 3], dtype=np.int32)
        cum_sum = npts
        for imid in range(3):
            mask_st_loc = (imid == apex_masters)
            n_masters_loc = np.sum(mask_st_loc)
            elem_masters_loc = masters[mask_st_loc]
            new_pt_midside[:, imid][elem_masters_loc] = np.arange(
                n_masters_loc, dtype=np.int32) + cum_sum
            cum_sum += n_masters_loc

        # Now dealing with slave elems.
        # for each slave element we identify the master and then the inode
        # onces slave_masters is indentified, slave_masters_apex is such that:
        # neighbors[slaves_masters, slave_masters_apex] == slaves
        mask_slaves = np.logical_not(mask_masters)
        slaves = edge_elems[mask_slaves]
        slaves_masters = edge_neighbors[mask_slaves]
        diff_table = np.abs(neighbors[slaves_masters, :] -
                            np.outer(slaves, np.ones(3, dtype=np.int32)))
        slave_masters_apex = np.argmin(diff_table, axis=1)
        slaves_apex = edge_apexes[mask_slaves]
        new_pt_midside[slaves, slaves_apex] = new_pt_midside[
            slaves_masters, slave_masters_apex]

        # Builds the 4 child masked_triangles
        child_triangles = np.empty([ntri*4, 3], dtype=np.int32)
        child_triangles[0::4, :] = np.vstack([
            new_pt_corner[:, 0], new_pt_midside[:, 0],
            new_pt_midside[:, 2]]).T
        child_triangles[1::4, :] = np.vstack([
            new_pt_corner[:, 1], new_pt_midside[:, 1],
            new_pt_midside[:, 0]]).T
        child_triangles[2::4, :] = np.vstack([
            new_pt_corner[:, 2], new_pt_midside[:, 2],
            new_pt_midside[:, 1]]).T
        child_triangles[3::4, :] = np.vstack([
            new_pt_midside[:, 0], new_pt_midside[:, 1],
            new_pt_midside[:, 2]]).T
        child_triangulation = Triangulation(refi_x, refi_y, child_triangles)

        # Builds the child mask
        if triangulation.mask is not None:
            child_triangulation.set_mask(np.repeat(triangulation.mask, 4))

        if ancestors is None:
            return child_triangulation
        else:
            return child_triangulation, np.repeat(ancestors, 4)

def tripcolor(ax, *args, **kwargs):
    """
    Create a pseudocolor plot of an unstructured triangular grid.

    The triangulation can be specified in one of two ways; either::

      tripcolor(triangulation, ...)

    where triangulation is a :class:`matplotlib.tri.Triangulation`
    object, or

    ::

      tripcolor(x, y, ...)
      tripcolor(x, y, triangles, ...)
      tripcolor(x, y, triangles=triangles, ...)
      tripcolor(x, y, mask=mask, ...)
      tripcolor(x, y, triangles, mask=mask, ...)

    in which case a Triangulation object will be created.  See
    :class:`~matplotlib.tri.Triangulation` for a explanation of these
    possibilities.

    The next argument must be *C*, the array of color values, either
    one per point in the triangulation if color values are defined at
    points, or one per triangle in the triangulation if color values
    are defined at triangles. If there are the same number of points
    and triangles in the triangulation it is assumed that color
    values are defined at points; to force the use of color values at
    triangles use the kwarg *facecolors*=C instead of just *C*.

    *shading* may be 'flat' (the default) or 'gouraud'. If *shading*
    is 'flat' and C values are defined at points, the color values
    used for each triangle are from the mean C of the triangle's
    three points. If *shading* is 'gouraud' then color values must be
    defined at points.

    The remaining kwargs are the same as for
    :meth:`~matplotlib.axes.Axes.pcolor`.

    **Example:**

        .. plot:: mpl_examples/pylab_examples/tripcolor_demo.py
    """
    if not ax._hold:
        ax.cla()

    alpha = kwargs.pop('alpha', 1.0)
    norm = kwargs.pop('norm', None)
    cmap = kwargs.pop('cmap', None)
    vmin = kwargs.pop('vmin', None)
    vmax = kwargs.pop('vmax', None)
    shading = kwargs.pop('shading', 'flat')
    facecolors = kwargs.pop('facecolors', None)

    if shading not in ['flat', 'gouraud']:
        raise ValueError("shading must be one of ['flat', 'gouraud'] "
                         "not {0}".format(shading))

    tri, args, kwargs = Triangulation.get_from_args_and_kwargs(*args, **kwargs)

    # C is the colors array defined at either points or faces (i.e. triangles).
    # If facecolors is None, C are defined at points.
    # If facecolors is not None, C are defined at faces.
    if facecolors is not None:
        C = facecolors
    else:
        C = np.asarray(args[0])

    # If there are a different number of points and triangles in the
    # triangulation, can omit facecolors kwarg as it is obvious from
    # length of C whether it refers to points or faces.
    # Do not do this for gouraud shading.
    if (facecolors is None and len(C) == len(tri.triangles) and
            len(C) != len(tri.x) and shading != 'gouraud'):
        facecolors = C

    # Check length of C is OK.
    if ((facecolors is None and len(C) != len(tri.x)) or
            (facecolors is not None and len(C) != len(tri.triangles))):
        raise ValueError('Length of color values array must be the same '
                         'as either the number of triangulation points '
                         'or triangles')

    # Handling of linewidths, shading, edgecolors and antialiased as
    # in Axes.pcolor
    linewidths = (0.25,)
    if 'linewidth' in kwargs:
        kwargs['linewidths'] = kwargs.pop('linewidth')
    kwargs.setdefault('linewidths', linewidths)

    edgecolors = 'none'
    if 'edgecolor' in kwargs:
        kwargs['edgecolors'] = kwargs.pop('edgecolor')
    ec = kwargs.setdefault('edgecolors', edgecolors)

    if 'antialiased' in kwargs:
        kwargs['antialiaseds'] = kwargs.pop('antialiased')
    if 'antialiaseds' not in kwargs and ec.lower() == "none":
        kwargs['antialiaseds'] = False
#.........这里部分代码省略.........

def triplot(ax, *args, **kwargs):
    """
    Draw a unstructured triangular grid as lines and/or markers to
    the :class:`~matplotlib.axes.Axes`.

    The triangulation to plot can be specified in one of two ways;
    either::

      triplot(triangulation, ...)

    where triangulation is a :class:`~matplotlib.tri.Triangulation`
    object, or

    ::

      triplot(x, y, ...)
      triplot(x, y, triangles, ...)
      triplot(x, y, triangles=triangles, ...)
      triplot(x, y, mask=mask, ...)
      triplot(x, y, triangles, mask=mask, ...)

    in which case a Triangulation object will be created.  See
    :class:`~matplotlib.tri.Triangulation` for a explanation of these
    possibilities.

    The remaining args and kwargs are the same as for
    :meth:`~matplotlib.axes.Axes.plot`.

    **Example:**

        .. plot:: mpl_examples/pylab_examples/triplot_demo.py
    """
    import matplotlib.axes
    tri, args, kwargs = Triangulation.get_from_args_and_kwargs(*args, **kwargs)

    x = tri.x
    y = tri.y
    edges = tri.edges

    # If draw both lines and markers at the same time, e.g.
    #     ax.plot(x[edges].T, y[edges].T, *args, **kwargs)
    # then the markers are drawn more than once which is incorrect if alpha<1.
    # Hence draw lines and markers separately.

    # Decode plot format string, e.g. 'ro-'
    fmt = ''
    if len(args) > 0:
        fmt = args[0]

#   _process_plot_format moves around so I made copy here.
#   not a best solution...;D
#    linestyle, marker, color = matplotlib.axes._process_plot_format(fmt)
    linestyle, marker, color = _process_plot_format(fmt)

    # Draw lines without markers, if lines are required.
    a = []
    if linestyle is not None and linestyle is not 'None':
        kw = kwargs.copy()
        kw.pop('marker', None)     # Ignore marker if set.
        kw['linestyle'] = ls_mapper[linestyle]
        kw['edgecolor'] = color
        kw['facecolor'] = None

        vertices = np.column_stack((x[edges].flatten(), y[edges].flatten()))
        codes = ([Path.MOVETO] + [Path.LINETO])*len(edges)

        path = Path(vertices, codes)
        pathpatch = PathPatch(path, **kw)

        ax.add_patch(pathpatch)
        a.append(pathpatch)

    # Draw markers without lines.
    # Should avoid drawing markers for points that are not in any triangle?
    kwargs['linestyle'] = ''

    # without hiding points explicitly, marker would expose hidden points. 
    idx = np.unique(edges.flatten())
    l = ax.plot(x[idx], y[idx], *args, **kwargs)
    a = l+a
    return a

def tripcolor(ax, *args, **kwargs):
    """
    Create a pseudocolor plot of an unstructured triangular grid to
    the :class:`~matplotlib.axes.Axes`.

    The triangulation can be specified in one of two ways; either::

      tripcolor(triangulation, ...)

    where triangulation is a :class:`~matplotlib.tri.Triangulation`
    object, or

    ::

      tripcolor(x, y, ...)
      tripcolor(x, y, triangles, ...)
      tripcolor(x, y, triangles=triangles, ...)
      tripcolor(x, y, mask=mask, ...)
      tripcolor(x, y, triangles, mask=mask, ...)

    in which case a Triangulation object will be created.  See
    :class:`~matplotlib.tri.Triangulation` for a explanation of these
    possibilities.

    The next argument must be *C*, the array of color values, one per
    point in the triangulation.

    *shading* may be 'flat', 'faceted' or 'gouraud'. If *shading* is
    'flat' or 'faceted', the colors used for each triangle are from
    the mean C of the triangle's three points.

    The remaining kwargs are the same as for
    :meth:`~matplotlib.axes.Axes.pcolor`.

    **Example:**

        .. plot:: mpl_examples/pylab_examples/tripcolor_demo.py
    """
    if not ax._hold: ax.cla()

    alpha = kwargs.pop('alpha', 1.0)
    norm = kwargs.pop('norm', None)
    cmap = kwargs.pop('cmap', None)
    vmin = kwargs.pop('vmin', None)
    vmax = kwargs.pop('vmax', None)
    shading = kwargs.pop('shading', 'flat')

    tri, args, kwargs = Triangulation.get_from_args_and_kwargs(*args, **kwargs)
    x = tri.x
    y = tri.y
    triangles = tri.get_masked_triangles()

    C = np.asarray(args[0])
    if C.shape != x.shape:
        raise ValueError('C array must have same length as triangulation x and'
                         ' y arrays')

    if shading == 'gouraud':
        collection = TriMesh(tri, **kwargs)
    else:
        if shading == 'faceted':
            edgecolors = (0,0,0,1),
            linewidths = (0.25,)
        else:
            edgecolors = 'face'
            linewidths = (1.0,)
        kwargs.setdefault('edgecolors', edgecolors)
        kwargs.setdefault('antialiaseds', (0,))
        kwargs.setdefault('linewidths', linewidths)

        # Vertices of triangles.
        verts = np.concatenate((x[triangles][...,np.newaxis],
                                y[triangles][...,np.newaxis]), axis=2)
        # Color values, one per triangle, mean of the 3 vertex color values.
        C = C[triangles].mean(axis=1)
        collection = PolyCollection(verts, **kwargs)

    collection.set_alpha(alpha)
    collection.set_array(C)
    if norm is not None: assert(isinstance(norm, Normalize))
    collection.set_cmap(cmap)
    collection.set_norm(norm)
    if vmin is not None or vmax is not None:
        collection.set_clim(vmin, vmax)
    else:
        collection.autoscale_None()
    ax.grid(False)

    minx = tri.x.min()
    maxx = tri.x.max()
    miny = tri.y.min()
    maxy = tri.y.max()
    corners = (minx, miny), (maxx, maxy)
    ax.update_datalim( corners)
    ax.autoscale_view()
    ax.add_collection(collection)
    return collection

def triplot(ax, *args, **kwargs):
    """
    Draw a unstructured triangular grid as lines and/or markers.

    The triangulation to plot can be specified in one of two ways;
    either::

      triplot(triangulation, ...)

    where triangulation is a :class:`matplotlib.tri.Triangulation`
    object, or

    ::

      triplot(x, y, ...)
      triplot(x, y, triangles, ...)
      triplot(x, y, triangles=triangles, ...)
      triplot(x, y, mask=mask, ...)
      triplot(x, y, triangles, mask=mask, ...)

    in which case a Triangulation object will be created.  See
    :class:`~matplotlib.tri.Triangulation` for a explanation of these
    possibilities.

    The remaining args and kwargs are the same as for
    :meth:`~matplotlib.axes.Axes.plot`.

    Return a list of 2 :class:`~matplotlib.lines.Line2D` containing
    respectively:

        - the lines plotted for triangles edges
        - the markers plotted for triangles nodes
    """
    import matplotlib.axes

    tri, args, kwargs = Triangulation.get_from_args_and_kwargs(*args, **kwargs)
    x, y, edges = (tri.x, tri.y, tri.edges)

    # Decode plot format string, e.g., 'ro-'
    fmt = ""
    if len(args) > 0:
        fmt = args[0]
    linestyle, marker, color = matplotlib.axes._base._process_plot_format(fmt)

    # Insert plot format string into a copy of kwargs (kwargs values prevail).
    kw = kwargs.copy()
    for key, val in zip(('linestyle', 'marker', 'color'),
                        (linestyle, marker, color)):
        if val is not None:
            kw[key] = kwargs.get(key, val)

    # Draw lines without markers.
    # Note 1: If we drew markers here, most markers would be drawn more than
    #         once as they belong to several edges.
    # Note 2: We insert nan values in the flattened edges arrays rather than
    #         plotting directly (triang.x[edges].T, triang.y[edges].T)
    #         as it considerably speeds-up code execution.
    linestyle = kw['linestyle']
    kw_lines = kw.copy()
    kw_lines['marker'] = 'None'  # No marker to draw.
    kw_lines['zorder'] = kw.get('zorder', 1)  # Path default zorder is used.
    if (linestyle is not None) and (linestyle not in ['None', '', ' ']):
        tri_lines_x = np.insert(x[edges], 2, np.nan, axis=1)
        tri_lines_y = np.insert(y[edges], 2, np.nan, axis=1)
        tri_lines = ax.plot(tri_lines_x.ravel(), tri_lines_y.ravel(),
                            **kw_lines)
    else:
        tri_lines = ax.plot([], [], **kw_lines)

    # Draw markers separately.
    marker = kw['marker']
    kw_markers = kw.copy()
    kw_markers['linestyle'] = 'None'  # No line to draw.
    if (marker is not None) and (marker not in ['None', '', ' ']):
        tri_markers = ax.plot(x, y, **kw_markers)
    else:
        tri_markers = ax.plot([], [], **kw_markers)

    return tri_lines + tri_markers

def triplot(ax, *args, **kwargs):
    """
    Draw a unstructured triangular grid as lines and/or markers.

    The triangulation to plot can be specified in one of two ways;
    either::

      triplot(triangulation, ...)

    where triangulation is a :class:`matplotlib.tri.Triangulation`
    object, or

    ::

      triplot(x, y, ...)
      triplot(x, y, triangles, ...)
      triplot(x, y, triangles=triangles, ...)
      triplot(x, y, mask=mask, ...)
      triplot(x, y, triangles, mask=mask, ...)

    in which case a Triangulation object will be created.  See
    :class:`~matplotlib.tri.Triangulation` for a explanation of these
    possibilities.

    The remaining args and kwargs are the same as for
    :meth:`~matplotlib.axes.Axes.plot`.

    **Example:**

        .. plot:: mpl_examples/pylab_examples/triplot_demo.py
    """
    import matplotlib.axes

    tri, args, kwargs = Triangulation.get_from_args_and_kwargs(*args, **kwargs)

    x = tri.x
    y = tri.y
    edges = tri.edges

    # If draw both lines and markers at the same time, e.g.
    #     ax.plot(x[edges].T, y[edges].T, *args, **kwargs)
    # then the markers are drawn more than once which is incorrect if alpha<1.
    # Hence draw lines and markers separately.

    # Decode plot format string, e.g., 'ro-'
    fmt = ""
    if len(args) > 0:
        fmt = args[0]
    linestyle, marker, color = matplotlib.axes._process_plot_format(fmt)

    # Draw lines without markers, if lines are required.
    if linestyle is not None and linestyle is not "None":
        kw = kwargs.copy()
        kw.pop("marker", None)  # Ignore marker if set.
        kw["linestyle"] = ls_mapper[linestyle]
        kw["edgecolor"] = color
        kw["facecolor"] = None

        vertices = np.column_stack((x[edges].flatten(), y[edges].flatten()))
        codes = ([Path.MOVETO] + [Path.LINETO]) * len(edges)

        path = Path(vertices, codes)
        pathpatch = PathPatch(path, **kw)

        ax.add_patch(pathpatch)

    # Draw markers without lines.
    # Should avoid drawing markers for points that are not in any triangle?
    kwargs["linestyle"] = ""
    ax.plot(x, y, *args, **kwargs)