U ?h@1@sbddlZddlZddlmZddlmZdddddddd d d Zd d ZddZ e ddgddgddgddgddgddgddgddgddgddgddgddgg dZ e ddgddgddgddgddgddgddgddgddgddgddgddgg dZ e ddgddgddgddgddgddgddgddgddgddgddgddgg dZ ddZddZdS)N)_marching_cubes_lewiner_luts)_marching_cubes_lewiner_cy)?rrdescentTlewiner)spacinggradient_direction step_sizeallow_degeneratemethodmaskc Cs:d}|dkrd}n|dkr"tdt||||||||dS)aMarching cubes algorithm to find surfaces in 3d volumetric data. In contrast with Lorensen et al. approach [2]_, Lewiner et al. algorithm is faster, resolves ambiguities, and guarantees topologically correct results. Therefore, this algorithm generally a better choice. Parameters ---------- volume : (M, N, P) array Input data volume to find isosurfaces. Will internally be converted to float32 if necessary. level : float, optional 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, optional Voxel spacing in spatial dimensions corresponding to numpy array indexing dimensions (M, N, P) as in `volume`. gradient_direction : string, optional 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, optional Step size in voxels. Default 1. Larger steps yield faster but coarser results. The result will always be topologically correct though. allow_degenerate : bool, optional 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. method: {'lewiner', 'lorensen'}, optional Whether the method of Lewiner et al. or Lorensen et al. will be used. mask : (M, N, P) array, optional Boolean array. The marching cube algorithm will be computed only on True elements. This will save computational time when interfaces are located within certain region of the volume M, N, P-e.g. the top half of the cube-and also allow to compute finite surfaces-i.e. open surfaces that do not end at the border of the cube. Returns ------- verts : (V, 3) array Spatial coordinates for V unique mesh vertices. Coordinate order matches input `volume` (M, N, P). If ``allow_degenerate`` is set to True, then the presence of degenerate triangles in the mesh can make this array have duplicate vertices. 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. See Also -------- skimage.measure.mesh_surface_area skimage.measure.find_contours 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 >> verts, faces, _, _ = marching_cubes(myvolume, 0.0) >> mlab.triangular_mesh([vert[0] for vert in verts], [vert[1] for vert in verts], [vert[2] for vert in verts], faces) >> mlab.show() Similarly using the ``visvis`` package:: >>> >> import visvis as vv >> verts, faces, normals, values = marching_cubes(myvolume, 0.0) >> vv.mesh(np.fliplr(verts), faces, normals, values) >> vv.use().Run() To reduce the number of triangles in the mesh for better performance, see this `example `_ using the ``mayavi`` package. 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` .. [2] Lorensen, William and Harvey E. Cline. Marching Cubes: A High Resolution 3D Surface Construction Algorithm. Computer Graphics (SIGGRAPH 87 Proceedings) 21(4) July 1987, p. 163-170). :DOI:`10.1145/37401.37422` FZlorensenTrz/method should be either 'lewiner' or 'lorensen') use_classicr ) ValueError_marching_cubes_lewiner) volumelevelrr r r r r rrY/var/www/html/venv/lib/python3.8/site-packages/skimage/measure/_marching_cubes_lewiner.pymarching_cubes surcCst|tjr|jdkrtd|jddksH|jddksH|jddkrPtdt|tj}|dkr|d|| }n(t |}||ks|| krtd t |dkrtd t |}|dkrtd t |}t}|dk r|j|jkstd tj} | ||||||\} } } } t | s,td t| } t| } d| _|dkr\t| } n|dksvtd|dt|ds| tj|} |r| | | | fStj}|| tj| | | SdS)zdLewiner et al. algorithm for marching cubes. See marching_cubes_lewiner for documentation. z(Input volume should be a 3D numpy array.rrz#Input array must be at least 2x2x2.N?z/Surface level must be within volume data range.z'`spacing` must consist of three floats.zstep_size must be at least one.z)volume and mask must have the same shape.z(No surface found at the given iso value.)rrZascentzIncorrect input z( in `gradient_direction`, see docstring.)rrr) isinstancenpZndarrayndimrshapeZascontiguousarrayZfloat32minmaxfloatlenintbool _get_mc_lutsrr RuntimeErrorZfliplrZ array_equalZr_Zremove_degenerate_facesZastype)rrrr r r rr LfuncZverticesfacesZnormalsvaluesZfunrrrrsZ*           rcCs0|\}}t|d}tj|dd}||_|S)Nzutf-8int8)Zdtype)base64 decodebytesencoderZ frombufferr)argsrtextZbytsarrrr _to_arrays r1r*c6Csttdsttttttjttj ttj ttj ttj ttj ttjttjttjttjttjttjttjttjttjttjttjttjttjttjttjttjttjttjttj ttj!ttj"ttj#ttj$ttj%ttj&ttj'ttj(ttj)ttj*ttj+ttj,ttj-ttj.ttj/ttj0ttj1ttj2ttj3ttj4ttj5ttj6ttj73t_8tj8S)z) Kind of lazy obtaining of the luts. THE_LUTS)9hasattrmclutsrZ LutProviderEDGETORELATIVEPOSXEDGETORELATIVEPOSYEDGETORELATIVEPOSZr1Z CASESCLASSICZCASESZTILING1ZTILING2Z TILING3_1Z TILING3_2Z TILING4_1Z TILING4_2ZTILING5Z TILING6_1_1Z TILING6_1_2Z TILING6_2Z TILING7_1Z TILING7_2Z TILING7_3Z TILING7_4_1Z TILING7_4_2ZTILING8ZTILING9Z TILING10_1_1Z TILING10_1_1_Z TILING10_1_2Z TILING10_2Z TILING10_2_ZTILING11Z TILING12_1_1Z TILING12_1_1_Z TILING12_1_2Z TILING12_2Z TILING12_2_Z TILING13_1Z TILING13_1_Z TILING13_2Z TILING13_2_Z TILING13_3Z TILING13_3_Z TILING13_4Z TILING13_5_1Z TILING13_5_2ZTILING14ZTEST3ZTEST4ZTEST6ZTEST7ZTEST10ZTEST12ZTEST13Z SUBCONFIG13r2rrrrr$sn r$cCs||}|dddddf|dddddf}|dddddf|dddddf}~t||djddddS)aGCompute surface area, given vertices and triangular faces. Parameters ---------- verts : (V, 3) array of floats Array containing (x, y, z) coordinates for V unique mesh vertices. faces : (F, 3) array of ints List of length-3 lists of integers, referencing vertex coordinates as provided in `verts`. Returns ------- area : float Surface area of mesh. Units now [coordinate units] ** 2. Notes ----- The arguments expected by this function are the first two outputs from `skimage.measure.marching_cubes`. For unit correct output, ensure correct `spacing` was passed to `skimage.measure.marching_cubes`. This algorithm works properly only if the ``faces`` provided are all triangles. See Also -------- skimage.measure.marching_cubes Nrrr)Zaxisrg@)rcrosssum)Zvertsr(Z actual_vertsabrrrmesh_surface_areas ,,r<)N)r+numpyrrr4rrrr1arrayr5r6r7r$r<rrrrs$   JTTT