o :ήc@sBddlZddlmZddlmZddZddZ  d d d Z dS) N)_marching_cubes_classic_cycCs|jdkr td|durd||}nt|}||ks(||kr,tdt|dkr6tdtj|tjdd}t |t|}t |\}}t |}t |}t ||||||}|tj||fS) zeLorensen et al. algorithm for marching cubes. See marching_cubes_classic for documentation. z$Input volume must have 3 dimensions.N?z/Surface level must be within volume data range.z'`spacing` must consist of three floats.C)dtypeorder)ndim ValueErrorminmaxfloatlennparrayfloat64riterate_and_store_3dunpack_unique_vertsasarray_correct_mesh_orientationr_)volumelevelspacinggradient_direction raw_facesvertsfacesrN/tmp/pip-target-vg8gfxp4/lib/python/skimage/measure/_marching_cubes_classic.py_marching_cubes_classics(    r cCs||}|dddddf|dddddf}|dddddf|dddddf}~t||djddddS)as Compute surface area, given vertices & triangular faces Parameters ---------- verts : (V, 3) array of floats Array containing (x, y, z) coordinates for V unique mesh vertices. faces : (F, 3) array of ints List of length-3 lists of integers, referencing vertex coordinates as provided in `verts` Returns ------- area : float Surface area of mesh. Units now [coordinate units] ** 2. Notes ----- The arguments expected by this function are the first two outputs from `skimage.measure.marching_cubes`. For unit correct output, ensure correct `spacing` was passed to `skimage.measure.marching_cubes`. This algorithm works properly only if the ``faces`` provided are all triangles. See Also -------- skimage.measure.marching_cubes skimage.measure.marching_cubes_classic Nrraxisrg@)rcrosssum)rr actual_vertsabrrrmesh_surface_area1s !,,$r)?r+r+descentcCs~t|\}}}|dddddf|dddddf}|dddddf|dddddf} |jdddj} ~t|| } t|| } t|| } tj| | | f}|tj|ddddddtjf}t|| }|tj|ddddddtjf}||jdd}d|vr|dk d}nd |vr|dk d}nt d || }||ddd f||<|S) aJ Correct orientations of mesh faces. Parameters ---------- volume : (M, N, P) array of doubles Input data volume to find isosurfaces. Will be cast to `np.float64`. actual_verts : (F, 3, 3) array of floats Array with (face, vertex, coords) index coordinates. faces : (F, 3) array of ints List of length-3 lists of integers, referencing vertex coordinates as provided in `verts`. 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. The two options are: * descent : Object was greater than exterior * ascent : Exterior was greater than object Returns ------- faces_corrected (F, 3) array of ints Corrected list of faces referencing vertex coordinates in `verts`. Notes ----- Certain applications and mesh processing algorithms require all faces to be oriented in a consistent way. Generally, this means a normal vector points "out" of the meshed shapes. This algorithm corrects the output from `skimage.measure.marching_cubes_classic` by flipping the orientation of mis-oriented faces. Because marching cubes could be used to find isosurfaces either on gradient descent (where the desired object has greater values than the exterior) or ascent (where the desired object has lower values than the exterior), the ``gradient_direction`` kwarg allows the user to inform this algorithm which is correct. If the resulting mesh appears to be oriented completely incorrectly, try changing this option. The arguments expected by this function are the exact outputs from `skimage.measure.marching_cubes_classic` except `actual_verts`, which is an uncorrected version of the fancy indexing operation `verts[faces]`. Only `faces` is corrected and returned as the vertices do not change, only the order in which they are referenced. This algorithm assumes ``faces`` provided are exclusively triangles. See Also -------- skimage.measure.marching_cubes_classic skimage.measure.mesh_surface_area Nrrr!r"g@rr,ascentz:Incorrect input %s in `gradient_direction`, see docstring.) rgradientr%Tndimap_coordinatesc_newaxisr$nonzeror copy)rr&rrrgrad_xgrad_ygrad_zr'r( centroidsgrad_centroids_xgrad_centroids_ygrad_centroids_zgrad_centroidscrosses dotproductsindicesfaces_correctedrrrr[sB<,,      (r)r*r,) numpyr scipy.ndimagendimager1rr r)rrrrrs  ++