mesh3D.py 42.8 KB
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#!/usr/bin/env
# encoding: utf-8
"""
Author:     Daniel Boeckenhoff
Mail:       daniel.boeckenhoff@ipp.mpg.de

part of tfields library
"""
import numpy as np
import os
import sympy
import warnings
import tfields
import ioTools
import mplTools
import decoTools
import pyTools
from sympy.abc import y, z
from scipy.spatial import ConvexHull
import matplotlib.pyplot as plt
import matplotlib.colors as colors
import loggingTools
import cuttingTree

logger = loggingTools.Logger(__name__)


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def _dist_from_plane(point, plane):
    return plane['normal'].dot(point) + plane['d']


def _segment_plane_intersection(p0, p1, plane):
    """
    Returns:
        points, direction
    """
    distance0 = _dist_from_plane(p0, plane)
    distance1 = _dist_from_plane(p1, plane)
    p0OnPlane = abs(distance0) < np.finfo(float).eps
    p1OnPlane = abs(distance1) < np.finfo(float).eps
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    points = []
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    direction = 0
    if p0OnPlane:
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        points.append(p0)
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    if p1OnPlane:
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        points.append(p1)
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    # remove duplicate points
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    if len(points) > 1:
        points = np.unique(points, axis=0)
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    if p0OnPlane and p1OnPlane:
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        return points, direction
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    if distance0 * distance1 > np.finfo(float).eps:
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        return points, direction
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    direction = np.sign(distance0)
    if abs(distance0) < np.finfo(float).eps:
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        return points, direction
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    elif abs(distance1) < np.finfo(float).eps:
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        return points, direction
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    if abs(distance0 - distance1) > np.finfo(float).eps:
        t = distance0 / (distance0 - distance1)
    else:
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        return points, direction
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    points.append(p0 + t * (p1 - p0))
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    # remove duplicate points
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    if len(points) > 1:
        points = np.unique(points, axis=0)
    return points, direction
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def _intersect(triangle, plane, vertices_rejected):
    """
    Intersect a triangle with a plane. Give the info, which side of the
    triangle is rejected by passing the mask vertices_rejected
    Returns:
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        list of list. The inner list is of length 3 and refers to the points of
        new triangles. The reference is done with varying types:
            int: reference to triangle index
            complex: reference to duplicate point. This only happens in case
                two triangles are returned. Then only in the second triangle
            iterable: new vertex

    TODO:
        align norm vectors with previous face
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    """
    nTrue = vertices_rejected.count(True)
    lonely_bool = True if nTrue == 1 else False
    index = vertices_rejected.index(lonely_bool)
    s0, d0 = _segment_plane_intersection(triangle[0], triangle[1], plane)
    s1, d1 = _segment_plane_intersection(triangle[1], triangle[2], plane)
    s2, d2 = _segment_plane_intersection(triangle[2], triangle[0], plane)

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    single_index = index
    couple_indices = [j for j in range(3)
                      if not vertices_rejected[j] == lonely_bool]
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    # TODO handle special cases. For now triangles with at least two points on plane are excluded
    new_points = None

    if len(s0) == 2:
        # both points on plane
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        return new_points
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    if len(s1) == 2:
        # both points on plane
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        return new_points
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    if len(s2) == 2:
        # both points on plane
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        return new_points
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    if lonely_bool:
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        # two new triangles
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        if len(s0) == 1 and len(s1) == 1:
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            new_points = [[couple_indices[0], s0[0], couple_indices[1]],
                          [couple_indices[1], complex(1), s1[0]]]
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        elif len(s1) == 1 and len(s2) == 1:
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            new_points = [[couple_indices[0], couple_indices[1], s1[0]],
                          [couple_indices[0], complex(2), s2[0]]]
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        elif len(s0) == 1 and len(s2) == 1:
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            new_points = [[couple_indices[0], couple_indices[1], s0[0]],
                          [couple_indices[1], s2[0], complex(2)]]
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    else:
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        # one new triangle
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        if len(s0) == 1 and len(s1) == 1:
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            new_points = [[single_index, s1[0], s0[0]]]
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        elif len(s1) == 1 and len(s2) == 1:
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            new_points = [[single_index, s2[0], s1[0]]]
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        elif len(s0) == 1 and len(s2) == 1:
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            new_points = [[single_index, s0[0], s2[0]]]
    return new_points
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def scalars_to_fields(scalars):
    scalars = np.array(scalars)
    if len(scalars.shape) == 1:
        return [tfields.Tensors(scalars)]
    return [tfields.Tensors(fs) for fs in scalars]

def fields_to_scalars(fields):
    return np.array(fields)

def faces_to_maps(faces, *fields):
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    return [tfields.TensorFields(faces, *fields, dtype=int, dim=3)]
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def maps_to_faces(maps):
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    if len(maps) == 0:
        return np.array([])
    elif len(maps) > 1:
        raise NotImplementedError("Multiple maps")
    return np.array(maps[0])
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class Mesh3D(tfields.TensorMaps):
    # pylint: disable=R0904
    """
    Points3D child used as vertices combined with faces to build a geometrical mesh of triangles
    Examples:
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        >>> import tfields
        >>> import numpy as np
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        >>> m = tfields.Mesh3D([[1,2,3], [3,3,3], [0,0,0], [5,6,7]], faces=[[0, 1, 2], [1, 2, 3]])
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        >>> m.equal([[1, 2, 3],
        ...          [3, 3, 3],
        ...          [0, 0, 0],
        ...          [5, 6, 7]])
        True
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        >>> np.array_equal(m.faces, [[0, 1, 2], [1, 2, 3]])
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        True
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        conversion to points only
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        >>> tfields.Points3D(m).equal([[1, 2, 3],
        ...                            [3, 3, 3],
        ...                            [0, 0, 0],
        ...                            [5, 6, 7]])
        True
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        Empty instances
        >>> m = tfields.Mesh3D([]);

        going from Mesh3D to Triangles3D instance is easy and will be cached.
        >>> m = tfields.Mesh3D([[1,0,0], [0,1,0], [0,0,0]], faces=[[0, 1, 2]]);
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        >>> assert m.triangles.equal(tfields.Triangles3D([[ 1.,  0.,  0.],
        ...                                               [ 0.,  1.,  0.],
        ...                                               [ 0.,  0.,  0.]]))
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        a list of scalars is assigned to each face
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        >>> mScalar = tfields.Mesh3D([[1,0,0], [0,1,0], [0,0,0]], faces=[[0, 1, 2]], faceScalars=[.5]);
        >>> np.array_equal(mScalar.faceScalars, [[ 0.5]])
        True
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        adding together two meshes:
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        >>> m2 = tfields.Mesh3D([[1,0,0],[2,0,0],[0,3,0]],
        ...                     faces=[[0,1,2]], faceScalars=[.7])
        >>> msum = tfields.Mesh3D.merged(mScalar, m2)
        >>> msum.equal([[ 1.,  0.,  0.],
        ...             [ 0.,  1.,  0.],
        ...             [ 0.,  0.,  0.],
        ...             [ 1.,  0.,  0.],
        ...             [ 2.,  0.,  0.],
        ...             [ 0.,  3.,  0.]])
        True
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        >>> assert np.array_equal(msum.faces, [[0, 1, 2], [3, 4, 5]])
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        Saving and reading
        >>> from tempfile import NamedTemporaryFile
        >>> outFile = NamedTemporaryFile(suffix='.npz')
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        >>> m.save(outFile.name)
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        >>> _ = outFile.seek(0)
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        >>> m1 = tfields.Mesh3D.load(outFile.name)
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        >>> bool(np.all(m == m1))
        True
        >>> m1.faces
        array([[0, 1, 2]])

    """
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    def __new__(cls, tensors, *fields, **kwargs):
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        if not issubclass(type(tensors), Mesh3D):
            kwargs['dim'] = 3
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        faces = kwargs.pop('faces', None)
        faceScalars = kwargs.pop('faceScalars', [])
        maps = kwargs.pop('maps', None)
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        if maps is not None and faces is not None:
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            raise ValueError("Conflicting options maps and faces")
        if maps is not None:
            kwargs['maps'] = maps
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        if len(faceScalars) > 0:
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            map_fields = scalars_to_fields(faceScalars)
        else:
            map_fields = []
        if faces is not None:
            kwargs['maps'] = faces_to_maps(faces,
                                           *map_fields)
        obj = super(Mesh3D, cls).__new__(cls, tensors, *fields, **kwargs)
        if len(obj.maps) > 1:
            raise ValueError("Mesh3D only allows one map")
        if obj.maps and obj.maps[0].dim != 3:
            raise ValueError("Face dimension should be 3")
        return obj

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    @classmethod
    def plane(cls, *base_vectors, **kwargs):
        vertices = tfields.Tensors.grid(*base_vectors)
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        base_vectors = tfields.grid.ensure_complex(*base_vectors)
        base_vectors = tfields.grid.to_base_vectors(*base_vectors)
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        fix_coord = None
        for coord in range(3):
            if len(base_vectors[coord]) > 1:
                continue
            if len(base_vectors[coord]) == 0:
                continue
            fix_coord = coord
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        if fix_coord is None:
            raise ValueError("Describe a plane with one variable fiexed")
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        var_coords = list(range(3))
        var_coords.pop(var_coords.index(fix_coord))

        faces = []
        base0, base1 = base_vectors[var_coords[0]], base_vectors[var_coords[1]]
        for i1 in range(len(base1) - 1):
            for i0 in range(len(base0) - 1):
                idx_top_left = len(base1) * (i0 + 0) + (i1 + 0)
                idx_top_right = len(base1) * (i0 + 0) + (i1 + 1)
                idx_bot_left = len(base1) * (i0 + 1) + (i1 + 0)
                idx_bot_right = len(base1) * (i0 + 1) + (i1 + 1)
                faces.append([idx_top_left, idx_top_right, idx_bot_left])
                faces.append([idx_top_right, idx_bot_left, idx_bot_right])
        inst = cls.__new__(cls, vertices, faces=faces, **kwargs)
        return inst

    @classmethod
    def grid(cls, *base_vectors, **kwargs):
        if not len(base_vectors) == 3:
            raise AttributeError("3 base_vectors vectors required")

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        base_vectors = tfields.grid.ensure_complex(*base_vectors)
        base_vectors = tfields.grid.to_base_vectors(*base_vectors)

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        indices = [0, -1]
        coords = range(3)
        baseLengthsAbove1 = [len(b) > 1 for b in base_vectors]
        # if one plane is given: rearrange indices and coords
        if not all(baseLengthsAbove1):
            indices = [0]
            for i, b in enumerate(baseLengthsAbove1):
                if not b:
                    coords = [i]
                    break

        base_vectors = list(base_vectors)
        planes = []
        for ind in indices:
            for coord in coords:
                basePart = base_vectors[:]
                basePart[coord] = np.array([base_vectors[coord][ind]],
                                           dtype=float)

                planes.append(cls.plane(*basePart))
        inst = cls.merged(*planes, **kwargs)
        return inst

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    @property
    def faces(self):
        return maps_to_faces(self.maps)

    @faces.setter
    def faces(self, faces):
        self.maps = faces_to_maps(faces)

    @property
    def faceScalars(self):
        return fields_to_scalars(self.maps[0].fields)

    @faceScalars.setter
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    def faceScalars(self, scalars):
        self.maps[0].fields = scalars_to_fields(scalars)
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    @decoTools.cached_property()
    def triangles(self):
        """
        with the decorator, this should be handled like an attribute though it is a function

        """
        if self.faces.size == 0:
            return tfields.Triangles3D([])
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        tris = tfields.Tensors.merged(*[self[mp.flatten()] for mp in self.maps])
        map_fields = [mp.fields for mp in self.maps]
        fields = [tfields.Tensors.merged(*fields) for fields in zip(*map_fields)]
        return tfields.Triangles3D(tris, *fields)
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    @decoTools.cached_property()
    def planes(self):
        if self.faces.size == 0:
            return tfields.Planes3D([])
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        return tfields.Planes3D(self.getCentroids(), self.triangles.norms())
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    def nfaces(self):
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        return self.faces.shape[0]

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    def in_faces(self, points, delta, assign_multiple=False):
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        """
        Check whether points lie within triangles with Barycentric Technique
        """
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        masks = self.triangles.in_triangles(points, delta,
                                            assign_multiple=assign_multiple)
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        return masks

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    def cutScalars(self, expression, coords=None,
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                   replaceValue=np.nan, scalarIndex=None, inplace=False):
        """
        Set a threshold to the scalars.
        Args:
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            expression (sympy cut expression or list of those):
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                threshold(sympy cut expression): cut scalars globaly
                threshold(list of sympy cut expressions): set on threshold for every scalar array
        Examples:
            >>> m = tfields.Mesh3D([[0,0,0], [1,0,0], [0,1,0], [0,0,1]],
            ...            faces=[[0,1,2], [0,1,3]],
            ...            faceScalars=[[1, 1], [2, 2]])

            Cuting all scalars at once
            >>> from sympy.abc import s
            >>> m.cutScalars(s <= 1., replaceValue=0.).faceScalars
            array([[ 0.,  0.],
                   [ 2.,  2.]])

            Cutting scalars different:
            >>> m.cutScalars([s <= 1, s >= 2], replaceValue=0.).faceScalars
            array([[ 0.,  1.],
                   [ 2.,  0.]])

            Cuttin one special scalar Array only
            >>> m.cutScalars(s <= 1, replaceValue=0., scalarIndex=1).faceScalars
            array([[ 1.,  0.],
                   [ 2.,  2.]])

            Using a list of cut expressions to cut every scalar index different

        """
        if inplace:
            inst = self
        else:
            inst = self.copy()

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        if isinstance(expression, list):
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            if scalarIndex is not None:
                raise ValueError("scalarIndex must be None, "
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                                 "if expression is list of expressions")
            if not len(expression) == inst.getScalarDepth():
                raise ValueError("lenght of expression must meet scalar depth")
            for si, ce in enumerate(expression):
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                inst.cutScalars(ce, coords=coords,
                                replaceValue=replaceValue,
                                scalarIndex=si, inplace=True)
        else:
            if coords is None:
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                freeSymbols = expression.free_symbols
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                if len(freeSymbols) > 1:
                    raise ValueError('coords must be given if multiple variables are given')
                elif len(freeSymbols) == 0:
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                    raise NotImplementedError("Expressiongs like {expression} "
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                                              "are not understood for coords".format(**locals()))
                coords = list(freeSymbols) * inst.getScalarDepth()
            scalarArrays = inst.getScalars()
            if scalarIndex is not None:
                scalarArrays = scalarArrays[:, scalarIndex:scalarIndex + 1]

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                maskBelow = tfields.evalf(scalarArrays,
                                            expression=expression,
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                                            coords=[coords[scalarIndex]])
                scalarArrays[maskBelow] = replaceValue
                inst.faceScalars[:, scalarIndex:scalarIndex + 1] = scalarArrays
            else:
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                maskBelow = tfields.evalf(scalarArrays,
                                            expression=expression,
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                                            coords=coords)
                scalarArrays[maskBelow] = replaceValue
                inst.faceScalars = scalarArrays
        if not inplace:
            return inst

    def getFaceMask(self, mask):
        """
        Examples:
            >>> m = tfields.Mesh3D([[1,2,3], [3,3,3], [0,0,0], [5,6,7]],
            ...            [[0, 1, 2], [1, 2, 3]],
            ...            faceScalars=[[1,2,3,4,5], [6,7,8,9,0]])
            >>> from sympy.abc import x,y,z
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            >>> vertexMask = m.evalf(z < 6)
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            >>> faceMask = m.getFaceMask(vertexMask)
            >>> faceMask
            array([ True, False], dtype=bool)

        Returns:
            mask of faces with all vertices in mask
        """
        faceDeleteMask = np.full((self.faces.shape[0]), False, dtype=bool)
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        indices = np.array(range(len(self)))
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        deleteIndices = set(indices[~mask])  # set speeds up everything
        for i, face in enumerate(self.faces):
            for index in face:
                if index in deleteIndices:
                    faceDeleteMask[i] = True
                    break

        return ~faceDeleteMask

    def removeFaces(self, faceDeleteMask):
        """
        Remove faces where faceDeleteMask is True
        Examples:
            >>> m = tfields.Mesh3D([[1,2,3], [3,3,3], [0,0,0], [5,6,7]],
            ...            [[0, 1, 2], [1, 2, 3]],
            ...            faceScalars=[[1,2], [6,7]])
            >>> m.removeFaces([True, False])
            >>> m.faces
            array([[1, 2, 3]])

        """
        faceDeleteMask = np.array(faceDeleteMask, dtype=bool)
        self.faces = self.faces[~faceDeleteMask]
        self.faceScalars = self.faceScalars[~faceDeleteMask]

    def keepFaces(self, faceMask=None, faces=None, faceIndices=None):
        """
        Inverse method like removeFaces
        Args:
            faceMask (np.array):
            faces (list of list of int)
            faceIndices (list of int)
        """
        if faces is None:
            faces = []
        if faceIndices is None:
            faceIndices = []
        if faceMask is None:
            faceMask = np.full(self.faces.shape[0], False, dtype=bool)

        for i, face in enumerate(self.faces):
            # np. version of if face in faces:
            if any((face == f).all() for f in faces):
                faceIndices.append(i)

        for ind in faceIndices:
            faceMask[ind] = True

        self.removeFaces(~faceMask)

    def staleVertices(self):
        """
        Returns:
            Mask for all vertices that are stale i.e. are not refered by faces
        """
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        staleMask = np.full(len(self), False, dtype=bool)
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        used = set(self.faces.flatten())
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        for i in range(len(self)):
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            if i not in used:
                staleMask[i] = True
        return staleMask

    def getFaces(self, vertex=None):
        """
        Args:
            vertex (None / int / array of length 3)
        """
        if vertex is None:
            return self.faces
        if isinstance(vertex, int):
            vertex = self[vertex]
        if not (isinstance(vertex, list) or isinstance(vertex, np.ndarray)):
            raise TypeError("Vertex has wrong type {0}".format(type(vertex)))
        index = tfields.index(self, vertex, axis=0)
        faces = []
        for face in self.faces:
            if index in face:
                faces.append(face)
        return faces

    def _inputToFaceIndices(self, arg):
        """
        convert an input to a faceIndices list
        Returns:
            list
        """
        arg = np.array(arg)
        if arg.dtype == bool:
            # mask
            return np.arange(self.faces.shape[0])[arg]
        if len(arg.shape) > 1:
            # face
            raise NotImplementedError()
        else:
            return arg

    def _inputToFaceMask(self, arg):
        """
        convert an input to a face mask
        Returns:
            np.array, dtype=bool
        """
        arg = np.array(arg)
        if arg.dtype == bool:
            # mask
            return arg
        if len(arg.shape) > 1:
            # face
            raise NotImplementedError()
        else:
            # faceIndices
            tmp = np.full(self.faces.shape[0], False)
            tmp[arg] = True
            return tmp

    def getParts(self, faceGroupIndicesList):
        """
        Args:
            faceGroupIndicesList (list of int)
        """
        log = logger.new()
        faceIndices = range(len(self.faces))
        parts = []
        log.verbose("Run through all {0} groups and partition mesh"
                    .format(len(faceGroupIndicesList)))
        for f, faceGroupIndices in enumerate(faceGroupIndicesList):
            log.verbose("Group {0} / {1}".format(f, len(faceGroupIndicesList)))
            mesh = self.copy()
            # for speed up:
            faceGroupIndices = set(faceGroupIndices)
            faceDeleteMask = [True
                              if i not in faceGroupIndices
                              else False
                              for i in faceIndices]
            mesh.removeFaces(faceDeleteMask)
578
            mesh = mesh.cleaned(duplicates=False)
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            parts.append(mesh)
        return parts

    def getLinkedFaces(self, skipFaces=None):
        """
        Retrieve the faceIndices that are connected grouped together
        Args:
            skipFaces: faceSelector (mask, faces, faceIndices)
        Returns:
            list of list of int: groups of face indices that are linked

        Examples:
            >>> import tfields
            >>> a = tfields.Mesh3D([[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0]],
            ...                    faces=[[0, 1, 2], [0, 2, 3]])
            >>> b = a.copy()

            >>> b[:, 0] += 2
            >>> m = tfields.Mesh3D([a, b])
            >>> groupIndices = m.getLinkedFaces()
            >>> parts = m.getParts(groupIndices)
            >>> aa, ba = parts
            >>> bool((aa.faces == a.faces).all())
            True
            >>> bool((ba.faces == b.faces).all())
            True
            >>> bool((aa == a).all())
            True
            >>> bool((ba == b).all())
            True

        """
        faces = self.faces
        if skipFaces is not None:
            mask = ~self._inputToFaceMask(skipFaces)
            faces = faces[mask]
        faceGroupIndicesList = pyTools.setTools.disjointGroupIndices(faces)
        if skipFaces is not None:
            faceIndices = np.arange(self.faces.shape[0])
            faceGroupIndicesList = [faceIndices[mask][group]
                                    for group in faceGroupIndicesList]
        return faceGroupIndicesList

    def getRegion(self, seedFace, **kwargs):
        """
        Grow a region from the seedFace until breaking criterion is reached
        Breaking criterion is specified in kwargs
        Args:
            seedFace (faceMask or faces or faceIndices):
            **kwargs: keys:
                    maxAngle: breaking criterion specified for the normal
                        vectors not to deviate from neighbours more than maxAngle
        Examples:
            Get only one side of a cube:
            >>> import tfields
            >>> import numpy as np
            >>> base = [np.linspace(0, 1, 10),
            ...         np.linspace(0, 1, 10),
            ...         np.linspace(0, 1, 10)]
638
            >>> mesh = tfields.Mesh3D.grid(*base).cleaned()
639
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657
658

            Some small mistake occured in the test. Check that.
            # Select the first face as a seedFace
            # >>> faceGroups = mesh.getRegion([0], maxAngle=np.pi * 2 / 8)
            # >>> parts = mesh.getParts(faceGroups)

            # Should only return one group. does not yet -> TODO!
            # >>> len(parts) == 1

        """
        log = logger.new()
        if not kwargs:
            log.warning("No boundaries specified")
            return np.arange(self.faces.shape[0])

        faceIndices = list(self._inputToFaceIndices(seedFace))

        # get break condition from kwargs
        maxAngle = kwargs.pop('maxAngle', None)

659
        norms = self.triangles.norms()
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        meanVector = np.mean(norms[faceIndices], axis=0)

        excludedFaceIndices = set()
        length = 0
        while len(faceIndices) > length:
            length = len(faceIndices)
            for f, face in enumerate(self.faces):
                vertexIndices = list(set(pyTools.flatten(self.faces[faceIndices])))
                for index in vertexIndices:
                    if index not in face:
                        continue
                    if f in faceIndices:
                        continue
                    if f in excludedFaceIndices:
                        continue
                    norm = norms[f]
                    angle = np.arccos(np.einsum("...j,...j", meanVector, norm))
                    if abs(angle) > maxAngle:
                        excludedFaceIndices.add(f)
                        continue
                    log.verbose("Found new neighbour at face index "
                                "{f}".format(**locals()))
                    faceIndices.append(f)
            if not len(faceIndices) > length:
                log.info("Found no neighbours")
        return faceIndices

    def getSides(self, mainAxes=None, deviation=2 * np.pi / 8):
        """
        Grouping together face indices that have normal vectors in the
        limits of +- deviation or +- pi + deviation.
        Examples:
            Get only one side of a cube:
            >>> import tfields
            >>> import numpy as np
            >>> base = [np.linspace(0, 1, 2),
            ...         np.linspace(0, 1, 4),
            ...         np.linspace(0, 1, 4)]
698
            >>> mesh = tfields.Mesh3D.grid(*base).cleaned()
699
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713
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717
718
719
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721
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            Select the first face as a seedFace
            >>> faceGroups = mesh.getSides([[1,0,0],[0,1,0],[0,0,1]])
            >>> parts = mesh.getParts(faceGroups)
            >>> len(parts) == 6
            True

            Faces that have inconsistant norm vector direction are no problem
            To show that, we invert the normal vector of one
            face in the middle of the cube
            >>> mesh.faces[8] = [5, 9, 6]
            >>> faceGroups2 = mesh.getSides([[1,0,0],[0,1,0],[0,0,1]])
            >>> parts2 = mesh.getParts(faceGroups2)
            >>> len(parts2) == 6
            True

        """
        if mainAxes is None:
            axes = self.getMainAxes()
        else:
            axes = tfields.Points3D(mainAxes)
        n = np.apply_along_axis(np.linalg.norm, 0, axes.T).reshape(-1, 1)
        axes = axes / n

723
        norms = self.triangles.norms()
724
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731
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733
734
        norms = tfields.Points3D(norms)

        faceGroupIndices = []
        for vector in axes:
            angles = np.arccos(np.einsum("...ij,...j", norms, vector))
            mask = np.logical_or(abs(angles) < deviation,
                                 abs(angles - np.pi) < deviation)
            tmp = self.getLinkedFaces(skipFaces=~mask)
            faceGroupIndices += tmp
        return faceGroupIndices

735
    def template(self, sub_mesh, delta=1e-9):
736
737
        """
        Returns:
738
739
            Mesh3D: template (see cut), can be used as template to retrieve
                sub_mesh from self instance
740
741
742
743
744
        Examples:
            >>> m = tfields.Mesh3D([[0,0,0], [1,0,0], [1,1,0], [0,1,0], [0,2,0], [1,2,0]],
            ...            faces=[[0,1,2],[2,3,0],[3,2,5],[5,4,3]],
            ...            faceScalars=[[1],[2],[3],[4]])
            >>> from sympy.abc import y
745
746
            >>> mCut, mapMesh = m.cut(y < 1.5, at_intersection='split')
            >>> mm = m.template(mCut)
747
748
749
750
751
752
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754
755
            >>> bool((mm == mapMesh).all())
            True
            >>> bool((mm.faceScalars == mapMesh.faceScalars).all())
            True
            >>> bool((mm.faces == mapMesh.faces).all())
            True

        """
        faceIndices = np.arange(self.faces.shape[0])
756
        cents = tfields.Points3D(sub_mesh.getCentroids())
757
758
759
        scalars = []
        mask = self.pointsInMesh(cents, delta=delta)
        scalars = [faceIndices[faceMask] for faceMask in mask]
760
        inst = sub_mesh.copy()
761
762
763
        inst.setScalarArray(0, scalars)
        return inst

764
    def _cut_sympy(self, expression, at_intersection="remove", _in_recursion=False):
765
        """
766
        Partition the mesh with the cuts given and return the template
767
768

        """
769
770
771
772
773
        eps = 0.000000001
        # direct return if self is empty
        if len(self) == 0:
            return self.copy(), self.copy()

774
775
776
777
778
779
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782
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784
        inst = self.copy()

        '''
        add the indices of the vertices and maps to the fields. They will be
        removed afterwards
        '''
        if not _in_recursion:
            inst.fields.append(tfields.Tensors(np.arange(len(inst))))
            for mp in inst.maps:
                mp.fields.append(tfields.Tensors(np.arange(len(mp))))

785
        # mask for points that do not fulfill the cut expression
786
        mask = inst.evalf(expression)
787
        # remove the points
788
789

        if not any(~mask) or all(~mask):
790
            inst = inst[mask]
791
792
793
794
795
796
797
798
        elif at_intersection == 'split' or at_intersection == 'splitRough':
            # add points and faces intersecting with the plane
            expression_parts = tfields.lib.symbolics.split_expression(expression)
            '''
            define a new mesh that will be merged with the existing one
            the new mesh will describe the faces that are at the border of the
            cuts
            '''
799
            if len(expression_parts) > 1:
800
                new_mesh = inst.copy()
801
802
803
804
805
806
807
808
                if at_intersection == 'splitRough':
                    """
                    the following is, to speed up the process. Problem is, that
                    triangles can exist, where all points lie outside the cut,
                    but part of the area
                    still overlaps with the cut.
                    These are at the intersection line between two cuts.
                    """
809
810
                    faceIntersMask = np.full((inst.faces.shape[0]), False, dtype=bool)
                    for i, face in enumerate(inst.faces):
811
812
                        vertices_rejected = [-mask[f] for f in face]
                        face_on_edge = any(vertices_rejected) and not all(vertices_rejected)
813
                        if face_on_edge:
814
                            faceIntersMask[i] = True
815
                    new_mesh.removeFaces(-faceIntersMask)
816

817
                for exprPart in expression_parts:
818
819
820
                    inst, _ = inst._cut_sympy(exprPart,
                                              at_intersection='split',
                                              _in_recursion=True)
821
            elif len(expression_parts) == 1:
822
                # TODO maps[0] -> smthng like inst.get_map(dim=3)
823
824
825
                points = [sympy.symbols('x0, y0, z0'),
                          sympy.symbols('x1, y1, z1'),
                          sympy.symbols('x2, y2, z2')]
826
                plane_sympy = tfields.lib.symbolics.to_plane(expression)
827
828
829
                norm_sympy = np.array(plane_sympy.normal_vector).astype(float)
                d = -norm_sympy.dot(np.array(plane_sympy.p1).astype(float))
                plane = {'normal': norm_sympy, 'd': d}
830

831
                norm_vectors = inst.triangles.norms()
832
833
                new_points = np.empty((0, 3))
                new_faces = np.empty((0, 3))
834
835
836
837
                new_fields = [tfields.Tensors(np.empty((0,) + field.shape[1:]),
                                              coordSys=field.coordSys)
                              for field in inst.fields]
                new_map_fields = [[] for field in inst.maps[0].fields]
838
                new_norm_vectors = []
839
                newScalarMap = []
840
                n_new = 0
841

842
843
844
845
846
847
848
                vertices = np.array(inst)
                faces = np.array(inst.maps[0])
                fields = [np.array(field) for field in inst.fields]
                faces_fields = [np.array(field) for field in inst.maps[0].fields]

                face_delete_indices = set([])
                for i, face in enumerate(inst.maps[0]):
849
                    """
850
                    vertices_rejected is a mask for each face that is True, where
851
852
                    a Point is on the rejected side of the plane
                    """
853
                    vertices_rejected = [~mask[f] for f in face]
854
855
856
857
858
                    if any(vertices_rejected):
                        # delete face
                        face_delete_indices.add(i)
                    if any(vertices_rejected) and not all(vertices_rejected):
                        # face on edge
859
                        nTrue = vertices_rejected.count(True)
860
                        lonely_bool = True if nTrue == 1 else False
861

862
                        triangle_points = [inst[f] for f in face]
863
                        """
864
                        Add the intersection points and faces
865
                        """
866
                        print "______________"
867
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901
                        newP = _intersect(triangle_points, plane, vertices_rejected)
                        last_idx = len(vertices) - 1
                        for tri_list in newP:
                            print vertices
                            face = []
                            for item in tri_list:
                                if isinstance(item, int):
                                    # reference to old vertex
                                    face.append(item)
                                elif isinstance(item, complex):
                                    # reference to new vertex that has been
                                    # concatenated already
                                    face.append(last_idx + int(item.imag))
                                else:
                                    # new vertex
                                    face.append(len(vertices))
                                    vertices = np.append(vertices,
                                                         [map(float, item)],
                                                         axis=0)
                                    fields = [np.append(field,
                                                        np.full((1,) + field.shape[1:], np.nan),
                                                        axis=0)
                                              for field in fields]
                                    fields[-1][-1] = len(vertices)
                            print vertices
                            print newP
                            print face
                            faces = np.append(faces, [face], axis=0)
                            faces_fields = [np.append(field,
                                                      np.full((1,) + field.shape[1:], np.nan),
                                                      axis=0)
                                            for field in faces_fields]
                            faces_fields[-1][-1] = i

                face_map = tfields.TensorFields(faces, *faces_fields,
902
                                                dtype=int,
903
904
905
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907
908
909
910
911
912
                                                coordSys=inst.maps[0].coordSys)
                inst = tfields.Mesh3D(vertices,
                                      *fields,
                                      maps=[face_map] + inst.maps[1:],
                                      coordSys=inst.coordSys)
                mask = np.full(len(inst.maps[0]), True, dtype=bool)
                for face_idx in range(len(inst.maps[0])):
                    if face_idx in face_delete_indices:
                        mask[face_idx] = False
                inst.maps[0] = inst.maps[0][mask]
913
            else:
914
915
                raise ValueError("Sympy expression is not splitable.")

916
917
        elif at_intersection == 'remove':
            pass
918
        else:
919
920
            raise AttributeError("No at_intersection method called {at_intersection} "
                                 "implemented".format(**locals()))
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935

        if _in_recursion:
            template = None
        else:
            print inst.fields
            template_field = inst.fields.pop(-1)
            template_maps = []
            for mp in inst.maps:
                t_mp = tfields.TensorFields(tfields.Tensors(mp),
                                            mp.fields.pop(-1))
                template_maps.append(t_mp)
            template = tfields.Mesh3D(tfields.Tensors(inst),
                                      template_field,
                                      maps=template_maps)
            print template.fields
936
        return inst, template
937
938

    def _cut_template(self, template):
939
940
941
942
943
944
945
946
        """
        Args:
            template (tfields.Mesh3D)

        Examples:
            >>> import tfields
            >>> import numpy as np

947
            Build mesh
948
949
950
            >>> mmap = tfields.TensorFields([[0, 1, 2], [0, 3, 4]],
            ...                             [[42, 21], [-42, -21]])
            >>> m = tfields.Mesh3D([[0]*3, [1]*3, [2]*3, [3]*3, [4]*3],
951
952
            ...                    [0.0, 0.1, 0.2, 0.3, 0.4],
            ...                    [0.0, -0.1, -0.2, -0.3, -0.4],
953
954
            ...                    maps=[mmap])

955
            Build template
956
957
958
            >>> tmap = tfields.TensorFields([[0, 3, 4], [0, 1, 2]],
            ...                             [1, 0])
            >>> t = tfields.Mesh3D([[0]*3, [-1]*3, [-2]*3, [-3]*3, [-4]*3],
959
            ...                    [1, 0, 3, 2, 4]
960
961
            ...                    maps=[tmap])

962
            Use template as instruction to make a fast cut
963
964
965
966
967
968
969
970
971
            >>> res = m._cut_template(t)
            >>> assert np.array_equal(res.fields,
            ...                       [[0.1, 0.0, 0.3, 0.2, 0.4],
            ...                        [-0.1, 0.0, -0.3, -0.2, -0.4]])

            >>> assert np.array_equal(res.maps[0].fields[0],
            ...                       [[-42, -21], [42, 21]])
                                   
        """
972
        # Redirect fields
973
974
975
976
977
        if template.fields:
            fields = [field[template.fields[0].astype(int)]
                      for field in self.fields]
        else:
            fields = []
978
979

        # Redirect maps fields
980
981
982
983
984
985
986
        maps = []
        for mp, template_mp in zip(self.maps, template.maps):
            if template_mp.fields:
                mp_fields = [field[template_mp.fields[0].astype(int)]
                             for field in mp.fields]
            else:
                mp_fields = []
987
            new_mp = tfields.TensorFields(tfields.Tensors(template_mp),
988
989
990
                                          *mp_fields)
            maps.append(new_mp)

991
992
        inst = tfields.Mesh3D(tfields.Tensors(template),
                              *fields,
993
                              maps=maps)
994
995
996
997
        return inst

    def cut(self, expression, coordSys=None, at_intersection=None,
            return_template=False):
998
999
1000
        """
        cut method for Mesh3D.
        Args:
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
            expression (sympy logical expression | Mesh3D):
                sympy locical expression: Sympy expression that defines planes
                    in 3D
                Mesh3D: A mesh3D will be interpreted as a template, i.e. a
                    fast instruction of how to cut the triangles.
                    It is the second part of the tuple, returned by a previous
                    cut with a sympy locial expression with 'return_template=True'.
                    We use the vertices and maps of the Mesh as the sceleton of
                    the returned mesh. The fields are mapped according to
                    indices in the template.maps[i].fields.
1011
1012
            coordSys (coordinate system to cut in):
            at_intersection (str): instruction on what to do, when a cut will intersect a triangle.
1013
1014
                Options:    "remove" (Default)
                            "split" - Create new triangles that make up the old one.
1015
1016
            return_template (bool): If True: return the template
                            to redo the same cut fast
1017
1018
        Examples:
            define the cut
1019
            >>> import tfields
1020
1021
1022
            >>> from sympy.abc import x,y,z
            >>> cutExpr = x > 1.5

1023
1024
            >>> m = tfields.Mesh3D.grid((0, 3, 4),
            ...                         (0, 3, 4),
1025
            ...                         (0, 0, 1))
1026
1027
1028
1029
1030
1031
            >>> m.fields.append(tfields.Tensors(np.linspace(0, len(m) - 1,
            ...                                             len(m))))
            >>> m.maps[0].fields.append(
            ...     tfields.Tensors(np.linspace(0,
            ...                                 len(m.maps[0]) - 1,
            ...                                 len(m.maps[0]))))
1032
            >>> mNew = m.cut(cutExpr)
1033
            >>> len(mNew)
1034
            8
1035
            >>> mNew.nfaces()
1036
1037
1038
1039
1040
            6
            >>> float(mNew[:, 0].min())
            2.0

            Cutting with the split option will create new triangles on the edge:
1041
1042
            >>> m_split = m.cut(cutExpr, at_intersection='split')
            >>> float(m_split[:, 0].min())
1043
            1.5
1044
            >>> len(m_split)
1045
            29
1046
            >>> m_split.nfaces()
1047
1048
            15

1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
            Cut with 'return_template=True' will return the exact same mesh but
            additionally an instruction to conduct the exact same cut fast (template)
            >>> m_split_2, template = m.cut(cutExpr, at_intersection='split',
            ...                                    return_template=True)
            >>> assert m_split.equal(m_split_2)
            >>> assert m_split.equal(m.cut(template))
            >>> m_split.fields
            >>> m.cut(template).fields

            This seems irrelevant at first but Consider, the map field or the
            tensor field changes:
            >>> m_altered_fields = m.copy()
            >>> m_altered_fields[0] += 42
            >>> assert not m_split.equal(m_altered_fields.cut(template))
            >>> assert tfields.Tensors(m_split).equal(m_altered_fields.cut(template))
            >>> assert tfields.Tensors(m_split.maps[0]).equal(m_altered_fields.cut(template).maps[0])


            The cut expression may be a sympy.BooleanFunction:
1068
1069
            >>> cut_expr_bool_fun = (x > 1.5) & (y < 1.5) & (y >0.2) & (z > -0.5)
            >>> m_split_bool = m.cut(cut_expr_bool_fun, at_intersection='split')
1070
1071
1072

        Returns:
            copy of cut mesh
1073
            * optional: template
1074
1075

        """
1076
        with self.tmp_transform(coordSys or self.coordSys):
1077
1078
1079
1080
1081
1082
1083
1084
            if isinstance(expression, Mesh3D):
                obj = self._cut_template(expression)
            else:
                at_intersection = at_intersection or "remove"
                obj, template = self._cut_sympy(expression, at_intersection=at_intersection)
        if return_template:
            return obj, template
        return obj
1085

1086
    def align_norms(self, norm_vectors):
1087
        """
1088
1089
        Orientate the faces such, that their norm_vectors align to the
        norm_vectors given.
1090
1091
1092
        Examples
            >>> m = tfields.Mesh3D([[0,0,0], [1,0,0], [-1,0,0], [0,1,0], [0,0,1]],
            ...            [[0, 1, 3], [1, 3, 4], [1, 3, 2]]);
1093
1094
            >>> newNorms = m.triangles.norms() * -1
            >>> m.align_norms(newNorms)
1095
1096
1097
1098
1099
1100
            >>> m.faces
            array([[0, 3, 1],
                   [1, 4, 3],
                   [1, 2, 3]])

        """
1101
        if not self.nfaces() == 0:
1102
            # vector product < 0
1103
            mask = np.einsum('...i,...i', self.triangles.norms(), norm_vectors) < 0
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            """
            the line:
            " self.faces[:, [1, 2]][mask] = self.faces[:, [2, 1]][mask] "
            would be a nice solution, but numpy does not mutate the [1, 2] but returns a copy

            """
            temp = np.copy(self.faces[mask, 1])
            self.faces[mask, 1] = self.faces[mask, 2]
            self.faces[mask, 2] = temp

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    def plot(self):
        import mplTools as mpt
        mpt.plotMesh(self, self.faces, color=self.maps[0].fields[0], vmin=0,
                     vmax=20, axis=mpt.gca(3))
        mpt.plt.show()

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if __name__ == '__main__':
    import doctest

1124
    doctest.run_docstring_examples(Mesh3D.cut, globals())
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    # doctest.run_docstring_examples(Mesh3D._cut_template, globals())
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    quit()
1127
    doctest.testmod()