import numpy as np from matplotlib._delaunay import compute_planes, linear_interpolate_grid, nn_interpolate_grid from matplotlib._delaunay import nn_interpolate_unstructured __all__ = ['LinearInterpolator', 'NNInterpolator'] def slice2gridspec(key): """Convert a 2-tuple of slices to start,stop,steps for x and y. key -- (slice(ystart,ystop,ystep), slice(xtart, xstop, xstep)) For now, the only accepted step values are imaginary integers (interpreted in the same way numpy.mgrid, etc. do). """ if ((len(key) != 2) or (not isinstance(key[0], slice)) or (not isinstance(key[1], slice))): raise ValueError("only 2-D slices, please") x0 = key[1].start x1 = key[1].stop xstep = key[1].step if not isinstance(xstep, complex) or int(xstep.real) != xstep.real: raise ValueError("only the [start:stop:numsteps*1j] form supported") xstep = int(xstep.imag) y0 = key[0].start y1 = key[0].stop ystep = key[0].step if not isinstance(ystep, complex) or int(ystep.real) != ystep.real: raise ValueError("only the [start:stop:numsteps*1j] form supported") ystep = int(ystep.imag) return x0, x1, xstep, y0, y1, ystep 00036 class LinearInterpolator(object): """Interpolate a function defined on the nodes of a triangulation by using the planes defined by the three function values at each corner of the triangles. LinearInterpolator(triangulation, z, default_value=numpy.nan) triangulation -- Triangulation instance z -- the function values at each node of the triangulation default_value -- a float giving the default value should the interpolating point happen to fall outside of the convex hull of the triangulation At the moment, the only regular rectangular grids are supported for interpolation. vals = interp[ystart:ystop:ysteps*1j, xstart:xstop:xsteps*1j] vals would then be a (ysteps, xsteps) array containing the interpolated values. These arguments are interpreted the same way as numpy.mgrid. Attributes: planes -- (ntriangles, 3) array of floats specifying the plane for each triangle. Linear Interpolation -------------------- Given the Delauany triangulation (or indeed *any* complete triangulation) we can interpolate values inside the convex hull by locating the enclosing triangle of the interpolation point and returning the value at that point of the plane defined by the three node values. f = planes[tri,0]*x + planes[tri,1]*y + planes[tri,2] The interpolated function is C0 continuous across the convex hull of the input points. It is C1 continuous across the convex hull except for the nodes and the edges of the triangulation. """ def __init__(self, triangulation, z, default_value=np.nan): self.triangulation = triangulation self.z = np.asarray(z, dtype=np.float64) self.default_value = default_value self.planes = compute_planes(triangulation.x, triangulation.y, self.z, triangulation.triangle_nodes) def __getitem__(self, key): x0, x1, xstep, y0, y1, ystep = slice2gridspec(key) grid = linear_interpolate_grid(x0, x1, xstep, y0, y1, ystep, self.default_value, self.planes, self.triangulation.x, self.triangulation.y, self.triangulation.triangle_nodes, self.triangulation.triangle_neighbors) return grid 00088 class NNInterpolator(object): """Interpolate a function defined on the nodes of a triangulation by the natural neighbors method. NNInterpolator(triangulation, z, default_value=numpy.nan) triangulation -- Triangulation instance z -- the function values at each node of the triangulation default_value -- a float giving the default value should the interpolating point happen to fall outside of the convex hull of the triangulation At the moment, the only regular rectangular grids are supported for interpolation. vals = interp[ystart:ystop:ysteps*1j, xstart:xstop:xsteps*1j] vals would then be a (ysteps, xsteps) array containing the interpolated values. These arguments are interpreted the same way as numpy.mgrid. Natural Neighbors Interpolation ------------------------------- One feature of the Delaunay triangulation is that for each triangle, its circumcircle contains no other point (although in degenerate cases, like squares, other points may be *on* the circumcircle). One can also construct what is called the Voronoi diagram from a Delaunay triangulation by connecting the circumcenters of the triangles to those of their neighbors to form a tesselation of irregular polygons covering the plane and containing only one node from the triangulation. Each point in one node's Voronoi polygon is closer to that node than any other node. To compute the Natural Neighbors interpolant, we consider adding the interpolation point to the triangulation. We define the natural neighbors of this point as the set of nodes participating in Delaunay triangles whose circumcircles contain the point. To restore the Delaunay-ness of the triangulation, one would only have to alter those triangles and Voronoi polygons. The new Voronooi diagram would have a polygon around the inserted point. This polygon would "steal" area from the original Voronoi polygons. For each node i in the natural neighbors set, we compute the area stolen from its original Voronoi polygon, stolen[i]. We define the natural neighbors coordinates phi[i] = stolen[i] / sum(stolen,axis=0) We then use these phi[i] to weight the corresponding function values from the input data z to compute the interpolated value. The interpolated surface is C1-continuous except at the nodes themselves across the convex hull of the input points. One can find the set of points that a given node will affect by computing the union of the areas covered by the circumcircles of each Delaunay triangle that node participates in. """ def __init__(self, triangulation, z, default_value=np.nan): self.triangulation = triangulation self.z = np.asarray(z, dtype=np.float64) self.default_value = default_value def __getitem__(self, key): x0, x1, xstep, y0, y1, ystep = slice2gridspec(key) grid = nn_interpolate_grid(x0, x1, xstep, y0, y1, ystep, self.default_value, self.triangulation.x, self.triangulation.y, self.z, self.triangulation.circumcenters, self.triangulation.triangle_nodes, self.triangulation.triangle_neighbors) return grid def __call__(self, intx, inty): intz = nn_interpolate_unstructured(intx, inty, self.default_value, self.triangulation.x, self.triangulation.y, self.z, self.triangulation.circumcenters, self.triangulation.triangle_nodes, self.triangulation.triangle_neighbors) return intz

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