ó  ‰\c@sddlZddlZddlZddlmZddlmZejd kr_ej Z n ej Z dddde ed„Zd „Zejd dgddgdd gd d gd dgddgdd gd d gd d gddgddgd d gg d ƒZejd d gd dgddgdd gd d gd dgddgdd gd d gd d gddgddgg d ƒZejd d gd d gd d gd d gddgddgddgddgd dgd dgd dgd dgg d ƒZd „ZdS(iÿÿÿÿNi(t_marching_cubes_lewiner_luts(t_marching_cubes_lewiner_cyigð?tdescentcCsgt|tjƒ s"|jdkr1tdƒ‚n|jddksj|jddksj|jddkrytdƒ‚ntj|tjƒ}|dkr·d|j ƒ|j ƒ}n?t |ƒ}||j ƒksç||j ƒkrötdƒ‚nt |ƒdkrtd ƒ‚nt |ƒ}|dkr>td ƒ‚nt|ƒ}tƒ}tj}||||||ƒ\} } } } t | ƒs›td ƒ‚ntj| ƒ} tj| ƒ} d| _|d kràtj| ƒ} n|dksÿtd|ƒ‚ntj|dƒs%| tj|} n|r;| | | | fStj} | | jtjƒ| | | ƒSdS(s¡ Lewiner marching cubes algorithm to find surfaces in 3d volumetric data. In contrast to ``marching_cubes_classic()``, this algorithm is faster, resolves ambiguities, and guarantees topologically correct results. Therefore, this algorithm generally a better choice, unless there is a specific need for the classic algorithm. Parameters ---------- volume : (M, N, P) array Input data volume to find isosurfaces. Will internally be converted to float32 if necessary. level : float Contour value to search for isosurfaces in `volume`. If not given or None, the average of the min and max of vol is used. spacing : length-3 tuple of floats Voxel spacing in spatial dimensions corresponding to numpy array indexing dimensions (M, N, P) as in `volume`. gradient_direction : string Controls if the mesh was generated from an isosurface with gradient descent toward objects of interest (the default), or the opposite, considering the *left-hand* rule. The two options are: * descent : Object was greater than exterior * ascent : Exterior was greater than object step_size : int Step size in voxels. Default 1. Larger steps yield faster but coarser results. The result will always be topologically correct though. allow_degenerate : bool Whether to allow degenerate (i.e. zero-area) triangles in the end-result. Default True. If False, degenerate triangles are removed, at the cost of making the algorithm slower. use_classic : bool If given and True, the classic marching cubes by Lorensen (1987) is used. This option is included for reference purposes. Note that this algorithm has ambiguities and is not guaranteed to produce a topologically correct result. The results with using this option are *not* generally the same as the ``marching_cubes_classic()`` function. Returns ------- verts : (V, 3) array Spatial coordinates for V unique mesh vertices. Coordinate order matches input `volume` (M, N, P). faces : (F, 3) array Define triangular faces via referencing vertex indices from ``verts``. This algorithm specifically outputs triangles, so each face has exactly three indices. normals : (V, 3) array The normal direction at each vertex, as calculated from the data. values : (V, ) array Gives a measure for the maximum value of the data in the local region near each vertex. This can be used by visualization tools to apply a colormap to the mesh. Notes ----- The algorithm [1] is an improved version of Chernyaev's Marching Cubes 33 algorithm. It is an efficient algorithm that relies on heavy use of lookup tables to handle the many different cases, keeping the algorithm relatively easy. This implementation is written in Cython, ported from Lewiner's C++ implementation. To quantify the area of an isosurface generated by this algorithm, pass verts and faces to `skimage.measure.mesh_surface_area`. Regarding visualization of algorithm output, to contour a volume named `myvolume` about the level 0.0, using the ``mayavi`` package:: >>> from mayavi import mlab # doctest: +SKIP >>> verts, faces, normals, values = marching_cubes_lewiner(myvolume, 0.0) # doctest: +SKIP >>> mlab.triangular_mesh([vert[0] for vert in verts], ... [vert[1] for vert in verts], ... [vert[2] for vert in verts], ... faces) # doctest: +SKIP >>> mlab.show() # doctest: +SKIP Similarly using the ``visvis`` package:: >>> import visvis as vv # doctest: +SKIP >>> verts, faces, normals, values = marching_cubes_lewiner(myvolume, 0.0) # doctest: +SKIP >>> vv.mesh(np.fliplr(verts), faces, normals, values) # doctest: +SKIP >>> vv.use().Run() # doctest: +SKIP References ---------- .. [1] Thomas Lewiner, Helio Lopes, Antonio Wilson Vieira and Geovan Tavares. Efficient implementation of Marching Cubes' cases with topological guarantees. Journal of Graphics Tools 8(2) pp. 1-15 (december 2003). DOI: 10.1080/10867651.2003.10487582 See Also -------- skimage.measure.marching_cubes_classic skimage.measure.mesh_surface_area is(Input volume should be a 3D numpy array.iiis#Input array must be at least 2x2x2.gà?s/Surface level must be within volume data range.s'`spacing` must consist of three floats.sstep_size must be at least one.s(No surface found at the given iso value.iÿÿÿÿRtascents:Incorrect input %s in `gradient_direction`, see docstring.N(iÿÿÿÿi(iii(t isinstancetnptndarraytndimt ValueErrortshapetascontiguousarraytfloat32tNonetmintmaxtfloattlentinttboolt _get_mc_lutsRtmarching_cubest RuntimeErrortfliplrt array_equaltr_tremove_degenerate_facestastype(tvolumetleveltspacingtgradient_directiont step_sizetallow_degeneratet use_classictLtfunctverticestfacestnormalstvaluestfun((sFlib/python2.7/site-packages/skimage/measure/_marching_cubes_lewiner.pytmarching_cubes_lewinersFj"9  $     $      cCsC|\}}t|jdƒƒ}tj|ddƒ}||_|S(Nsutf-8tdtypetint8(t base64decodetencodeRt frombufferR (targsR ttexttbytstar((sFlib/python2.7/site-packages/skimage/measure/_marching_cubes_lewiner.pyt _to_array²s   iR+c5Csqttdƒsjtjtttttjƒttj ƒttj ƒttj ƒttj ƒttj ƒttjƒttjƒttjƒttjƒttjƒttjƒttjƒttjƒttjƒttjƒttjƒttjƒttjƒttjƒttjƒttjƒttjƒttjƒttj ƒttj!ƒttj"ƒttj#ƒttj$ƒttj%ƒttj&ƒttj'ƒttj(ƒttj)ƒttj*ƒttj+ƒttj,ƒttj-ƒttj.ƒttj/ƒttj0ƒttj1ƒttj2ƒttj3ƒttj4ƒttj5ƒttj6ƒttj7ƒƒ3t_8ntj8S(s) Kind of lazy obtaining of the luts. tTHE_LUTS(9thasattrtmclutsRt LutProvidertEDGETORELATIVEPOSXtEDGETORELATIVEPOSYtEDGETORELATIVEPOSZR3t CASESCLASSICtCASEStTILING1tTILING2t TILING3_1t TILING3_2t TILING4_1t TILING4_2tTILING5t TILING6_1_1t TILING6_1_2t TILING6_2t TILING7_1t TILING7_2t TILING7_3t TILING7_4_1t TILING7_4_2tTILING8tTILING9t TILING10_1_1t TILING10_1_1_t TILING10_1_2t TILING10_2t TILING10_2_tTILING11t TILING12_1_1t TILING12_1_1_t TILING12_1_2t TILING12_2t TILING12_2_t TILING13_1t TILING13_1_t TILING13_2t TILING13_2_t TILING13_3t TILING13_3_t TILING13_4t TILING13_5_1t TILING13_5_2tTILING14tTEST3tTEST4tTEST6tTEST7tTEST10tTEST12tTEST13t SUBCONFIG13R4(((sFlib/python2.7/site-packages/skimage/measure/_marching_cubes_lewiner.pyRÅs( 00$$$$$$$$$$$$$(i(gð?gð?gð?(tsystbase64tnumpyRtRR6Rt version_infot decodebytesR,t decodestringR tTruetFalseR)R3tarrayR8R9R:R(((sFlib/python2.7/site-packages/skimage/measure/_marching_cubes_lewiner.pyts       ~~~