python-matplotlib 1.3.1-1ubuntu5 / usr / share / pyshared / matplotlib / delaunay / triangulate.py

from __future__ import print_function
import warnings
# 2.3 compatibility
try:
    set
except NameError:
    import sets
    set = sets.Set
from itertools import izip

import numpy as np

from matplotlib._delaunay import delaunay
from interpolate import LinearInterpolator, NNInterpolator

__all__ = ['Triangulation', 'DuplicatePointWarning']


class DuplicatePointWarning(RuntimeWarning):
    """Duplicate points were passed in to the triangulation routine.
    """


class Triangulation(object):
    """A Delaunay triangulation of points in a plane.

    Triangulation(x, y)
    x, y -- the coordinates of the points as 1-D arrays of floats

    Let us make the following definitions:
        npoints = number of points input
        nedges = number of edges in the triangulation
        ntriangles = number of triangles in the triangulation

        point_id = an integer identifying a particular point (specifically, an
            index into x and y), range(0, npoints)
        edge_id = an integer identifying a particular edge, range(0, nedges)
        triangle_id = an integer identifying a particular triangle
            range(0, ntriangles)

    Attributes: (all should be treated as read-only to maintain consistency)
      x, y -- the coordinates of the points as 1-D arrays of floats.

      circumcenters -- (ntriangles, 2) array of floats giving the (x,y)
        coordinates of the circumcenters of each triangle (indexed by a
        triangle_id).

      edge_db -- (nedges, 2) array of point_id's giving the points forming
        each edge in no particular order; indexed by an edge_id.

      triangle_nodes -- (ntriangles, 3) array of point_id's giving the points
        forming each triangle in counter-clockwise order; indexed by a
        triangle_id.

      triangle_neighbors -- (ntriangles, 3) array of triangle_id's giving the
        neighboring triangle; indexed by a triangle_id.

        The value can also be -1 meaning that that edge is on the convex hull
        of the points and there is no neighbor on that edge. The values are
        ordered such that triangle_neighbors[tri, i] corresponds with the edge
        *opposite* triangle_nodes[tri, i]. As such, these neighbors are also
        in counter-clockwise order.

      hull -- list of point_id's giving the nodes which form the convex hull
        of the point set. This list is sorted in counter-clockwise order.

    Duplicate points.
      If there are no duplicate points, Triangulation stores the specified
      x and y arrays and there is no difference between the client's and
      Triangulation's understanding of point indices used in edge_db,
      triangle_nodes and hull.

      If there are duplicate points, they are removed from the stored
      self.x and self.y as the underlying delaunay code cannot deal with
      duplicates.  len(self.x) is therefore equal to len(x) minus the
      number of duplicate points.  Triangulation's edge_db, triangle_nodes
      and hull refer to point indices in self.x and self.y, for internal
      consistency within Triangulation and the corresponding Interpolator
      classes.  Client code must take care to deal with this in one of
      two ways:

      1. Ignore the x,y it specified in Triangulation's constructor and
         use triangulation.x and triangulation.y instead, as these are
         consistent with edge_db, triangle_nodes and hull.

      2. If using the x,y the client specified then edge_db,
         triangle_nodes and hull should be passed through the function
         to_client_point_indices() first.
    """
    def __init__(self, x, y):
        self.x = np.asarray(x, dtype=np.float64)
        self.y = np.asarray(y, dtype=np.float64)

        if self.x.shape != self.y.shape or len(self.x.shape) != 1:
            raise ValueError("x,y must be equal-length 1-D arrays")

        self.old_shape = self.x.shape
        duplicates = self._get_duplicate_point_indices()

        if len(duplicates) > 0:
            warnings.warn(
                "Input data contains duplicate x,y points; some values are "
                "ignored.",
                DuplicatePointWarning,
            )

            # self.j_unique is the array of non-duplicate indices, in
            # increasing order.
            self.j_unique = np.delete(np.arange(len(self.x)), duplicates)
            self.x = self.x[self.j_unique]
            self.y = self.y[self.j_unique]
        else:
            self.j_unique = None

        # If there are duplicate points, need a map of point indices used
        # by delaunay to those used by client.  If there are no duplicate
        # points then the map is not needed.  Either way, the map is
        # conveniently the same as j_unique, so share it.
        self._client_point_index_map = self.j_unique

        self.circumcenters, self.edge_db, self.triangle_nodes, \
            self.triangle_neighbors = delaunay(self.x, self.y)

        self.hull = self._compute_convex_hull()

    def _get_duplicate_point_indices(self):
        """Return array of indices of x,y points that are duplicates of
        previous points. Indices are in no particular order.
        """
        # Indices of sorted x,y points.
        j_sorted = np.lexsort(keys=(self.x, self.y))
        mask_duplicates = np.hstack([
            False,
            (np.diff(self.x[j_sorted]) == 0) &
            (np.diff(self.y[j_sorted]) == 0),
        ])

        # Array of duplicate point indices, in no particular order.
        return j_sorted[mask_duplicates]

    def _compute_convex_hull(self):
        """Extract the convex hull from the triangulation information.

        The output will be a list of point_id's in counter-clockwise order
        forming the convex hull of the data set.
        """
        border = (self.triangle_neighbors == -1)

        edges = {}
        edges.update(dict(izip(self.triangle_nodes[border[:, 0]][:, 1],
                               self.triangle_nodes[border[:, 0]][:, 2])))
        edges.update(dict(izip(self.triangle_nodes[border[:, 1]][:, 2],
                               self.triangle_nodes[border[:, 1]][:, 0])))
        edges.update(dict(izip(self.triangle_nodes[border[:, 2]][:, 0],
                               self.triangle_nodes[border[:, 2]][:, 1])))

        # Take an arbitrary starting point and its subsequent node
        hull = list(edges.popitem())
        while edges:
            hull.append(edges.pop(hull[-1]))

        # hull[-1] == hull[0], so remove hull[-1]
        hull.pop()

        return hull

    def to_client_point_indices(self, array):
        """Converts any array of point indices used within this class to
        refer to point indices within the (x,y) arrays specified in the
        constructor before duplicates were removed.
        """
        if self._client_point_index_map is not None:
            return self._client_point_index_map[array]
        else:
            return array

    def linear_interpolator(self, z, default_value=np.nan):
        """Get an object which can interpolate within the convex hull by
        assigning a plane to each triangle.

        z -- an array of floats giving the known function values at each point
          in the triangulation.
        """
        z = np.asarray(z, dtype=np.float64)
        if z.shape != self.old_shape:
            raise ValueError("z must be the same shape as x and y")
        if self.j_unique is not None:
            z = z[self.j_unique]

        return LinearInterpolator(self, z, default_value)

    def nn_interpolator(self, z, default_value=np.nan):
        """Get an object which can interpolate within the convex hull by
        the natural neighbors method.

        z -- an array of floats giving the known function values at each point
          in the triangulation.
        """
        z = np.asarray(z, dtype=np.float64)
        if z.shape != self.old_shape:
            raise ValueError("z must be the same shape as x and y")
        if self.j_unique is not None:
            z = z[self.j_unique]

        return NNInterpolator(self, z, default_value)

    def prep_extrapolator(self, z, bbox=None):
        if bbox is None:
            bbox = (self.x[0], self.x[0], self.y[0], self.y[0])
        minx, maxx, miny, maxy = np.asarray(bbox, np.float64)
        minx = min(minx, np.minimum.reduce(self.x))
        miny = min(miny, np.minimum.reduce(self.y))
        maxx = max(maxx, np.maximum.reduce(self.x))
        maxy = max(maxy, np.maximum.reduce(self.y))
        M = max((maxx - minx) / 2, (maxy - miny) / 2)
        midx = (minx + maxx) / 2.0
        midy = (miny + maxy) / 2.0

        xp, yp = np.array([[midx + 3 * M, midx, midx - 3 * M],
                           [midy, midy + 3 * M, midy - 3 * M]])
        x1 = np.hstack((self.x, xp))
        y1 = np.hstack((self.y, yp))
        newtri = self.__class__(x1, y1)

        # do a least-squares fit to a plane to make pseudo-data
        xy1 = np.ones((len(self.x), 3), np.float64)
        xy1[:, 0] = self.x
        xy1[:, 1] = self.y
        from numpy.dual import lstsq
        c, res, rank, s = lstsq(xy1, z)
        zp = np.hstack((z, xp * c[0] + yp * c[1] + c[2]))

        return newtri, zp

    def nn_extrapolator(self, z, bbox=None, default_value=np.nan):
        newtri, zp = self.prep_extrapolator(z, bbox)
        return newtri.nn_interpolator(zp, default_value)

    def linear_extrapolator(self, z, bbox=None, default_value=np.nan):
        newtri, zp = self.prep_extrapolator(z, bbox)
        return newtri.linear_interpolator(zp, default_value)

    def node_graph(self):
        """Return a graph of node_id's pointing to node_id's.

        The arcs of the graph correspond to the edges in the triangulation.

        {node_id: set([node_id, ...]), ...}
        """
        g = {}
        for i, j in self.edge_db:
            s = g.setdefault(i, set())
            s.add(j)
            s = g.setdefault(j, set())
            s.add(i)
        return g