Rc@sddlmZddlZyeWn&ek rLddlZejZnXddlmZddl Z ddl m Z ddl mZmZddgZdefdYZdefd YZdS( i(tprint_functionN(tizip(tdelaunay(tLinearInterpolatortNNInterpolatort TriangulationtDuplicatePointWarningcBseZdZRS(sBDuplicate points were passed in to the triangulation routine. (t__name__t __module__t__doc__(((sY/opt/xtal/ccp4-6.5-linux32/lib/python2.7/site-packages/matplotlib/delaunay/triangulate.pyRscBseZdZdZdZdZdZejdZ ejdZ d dZ d ejdZ d ejd Zd ZRS( s 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. cCsWtj|dtj|_tj|dtj|_|jj|jjksft|jjdkrutdn|jj|_|j }t|dkrt j dt tj tjt|j||_|j|j|_|j|j|_n d|_|j|_t|j|j\|_|_|_|_|j|_dS(Ntdtypeis#x,y must be equal-length 1-D arraysisBInput data contains duplicate x,y points; some values are ignored.(tnptasarraytfloat64txtytshapetlent ValueErrort old_shapet_get_duplicate_point_indicestwarningstwarnRtdeletetarangetj_uniquetNonet_client_point_index_mapRt circumcenterstedge_dbttriangle_nodesttriangle_neighborst_compute_convex_hullthull(tselfRRt duplicates((sY/opt/xtal/ccp4-6.5-linux32/lib/python2.7/site-packages/matplotlib/delaunay/triangulate.pyt__init__Zs"0 '  -cCsktjd|j|jf}tjttj|j|dktj|j|dk@g}||S(sReturn array of indices of x,y points that are duplicates of previous points. Indices are in no particular order. tkeysi(R tlexsortRRthstacktFalsetdiff(R"tj_sortedtmask_duplicates((sY/opt/xtal/ccp4-6.5-linux32/lib/python2.7/site-packages/matplotlib/delaunay/triangulate.pyR~s #cCs|jdk}i}|jtt|j|dddfdddf|j|dddfdddf|jtt|j|dddfdddf|j|dddfdddf|jtt|j|dddfdddf|j|dddfdddft|j}x$|r|j|j|dqhW|j|S(sExtract 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. iNiii( RtupdatetdictRRtlisttpopitemtappendtpop(R"tbordertedgesR!((sY/opt/xtal/ccp4-6.5-linux32/lib/python2.7/site-packages/matplotlib/delaunay/triangulate.pyR s646464  cCs"|jdk r|j|S|SdS(sConverts 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. N(RR(R"tarray((sY/opt/xtal/ccp4-6.5-linux32/lib/python2.7/site-packages/matplotlib/delaunay/triangulate.pytto_client_point_indicess cCshtj|dtj}|j|jkr9tdn|jdk rX||j}nt|||S(sGet 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. R s#z must be the same shape as x and yN( R R R RRRRRR(R"tzt default_value((sY/opt/xtal/ccp4-6.5-linux32/lib/python2.7/site-packages/matplotlib/delaunay/triangulate.pytlinear_interpolators cCshtj|dtj}|j|jkr9tdn|jdk rX||j}nt|||S(sGet 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. R s#z must be the same shape as x and yN( R R R RRRRRR(R"R6R7((sY/opt/xtal/ccp4-6.5-linux32/lib/python2.7/site-packages/matplotlib/delaunay/triangulate.pytnn_interpolators cCs\|dkr=|jd|jd|jd|jdf}ntj|tj\}}}}t|tjj|j}t|tjj|j}t |tj j|j}t |tj j|j}t ||d||d}||d}||d} tj |d|||d|g| | d|| d|gg\} } tj |j| f} tj |j| f} |j | | }tjt|jdftj}|j|dddf<|j|dddfs