This file is indexed.

/usr/lib/python2.7/dist-packages/shapely/affinity.py is in python-shapely 1.4.3-1.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below.

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
"""Affine transforms, both in general and specific, named transforms."""

from math import sin, cos, tan, pi

__all__ = ['affine_transform', 'rotate', 'scale', 'skew', 'translate']


def affine_transform(geom, matrix):
    """Returns a transformed geometry using an affine transformation matrix.

    The coefficient matrix is provided as a list or tuple with 6 or 12 items
    for 2D or 3D transformations, respectively.

    For 2D affine transformations, the 6 parameter matrix is:

        [a, b, d, e, xoff, yoff]

    which represents the augmented matrix:

                            / a  b xoff \ 
        [x' y' 1] = [x y 1] | d  e yoff |
                            \ 0  0   1  /

    or the equations for the transformed coordinates:

        x' = a * x + b * y + xoff
        y' = d * x + e * y + yoff

    For 3D affine transformations, the 12 parameter matrix is:

        [a, b, c, d, e, f, g, h, i, xoff, yoff, zoff]

    which represents the augmented matrix:

                                 / a  b  c xoff \ 
        [x' y' z' 1] = [x y z 1] | d  e  f yoff |
                                 | g  h  i zoff |
                                 \ 0  0  0   1  /

    or the equations for the transformed coordinates:

        x' = a * x + b * y + c * z + xoff
        y' = d * x + e * y + f * z + yoff
        z' = g * x + h * y + i * z + zoff
    """
    if geom.is_empty:
        return geom
    if len(matrix) == 6:
        ndim = 2
        a, b, d, e, xoff, yoff = matrix
        if geom.has_z:
            ndim = 3
            i = 1.0
            c = f = g = h = zoff = 0.0
            matrix = a, b, c, d, e, f, g, h, i, xoff, yoff, zoff
    elif len(matrix) == 12:
        ndim = 3
        a, b, c, d, e, f, g, h, i, xoff, yoff, zoff = matrix
        if not geom.has_z:
            ndim = 2
            matrix = a, b, d, e, xoff, yoff
    else:
        raise ValueError("'matrix' expects either 6 or 12 coefficients")

    def affine_pts(pts):
        """Internal function to yield affine transform of coordinate tuples"""
        if ndim == 2:
            for x, y in pts:
                xp = a * x + b * y + xoff
                yp = d * x + e * y + yoff
                yield (xp, yp)
        elif ndim == 3:
            for x, y, z in pts:
                xp = a * x + b * y + c * z + xoff
                yp = d * x + e * y + f * z + yoff
                zp = g * x + h * y + i * z + zoff
                yield (xp, yp, zp)

    # Process coordinates from each supported geometry type
    if geom.type in ('Point', 'LineString', 'LinearRing'):
        return type(geom)(list(affine_pts(geom.coords)))
    elif geom.type == 'Polygon':
        ring = geom.exterior
        shell = type(ring)(list(affine_pts(ring.coords)))
        holes = list(geom.interiors)
        for pos, ring in enumerate(holes):
            holes[pos] = type(ring)(list(affine_pts(ring.coords)))
        return type(geom)(shell, holes)
    elif geom.type.startswith('Multi') or geom.type == 'GeometryCollection':
        # Recursive call
        # TODO: fix GeometryCollection constructor
        return type(geom)([affine_transform(part, matrix)
                           for part in geom.geoms])
    else:
        raise ValueError('Type %r not recognized' % geom.type)


def interpret_origin(geom, origin, ndim):
    """Returns interpreted coordinate tuple for origin parameter.

    This is a helper function for other transform functions.

    The point of origin can be a keyword 'center' for the 2D bounding box
    center, 'centroid' for the geometry's 2D centroid, a Point object or a
    coordinate tuple (x0, y0, z0).
    """
    # get coordinate tuple from 'origin' from keyword or Point type
    if origin == 'center':
        # bounding box center
        minx, miny, maxx, maxy = geom.bounds
        origin = ((maxx + minx)/2.0, (maxy + miny)/2.0)
    elif origin == 'centroid':
        origin = geom.centroid.coords[0]
    elif isinstance(origin, str):
        raise ValueError("'origin' keyword %r is not recognized" % origin)
    elif hasattr(origin, 'type') and origin.type == 'Point':
        origin = origin.coords[0]

    # origin should now be tuple-like
    if len(origin) not in (2, 3):
        raise ValueError("Expected number of items in 'origin' to be "
                         "either 2 or 3")
    if ndim == 2:
        return origin[0:2]
    else:  # 3D coordinate
        if len(origin) == 2:
            return origin + (0.0,)
        else:
            return origin


def rotate(geom, angle, origin='center', use_radians=False):
    """Returns a rotated geometry on a 2D plane.

    The angle of rotation can be specified in either degrees (default) or
    radians by setting ``use_radians=True``. Positive angles are
    counter-clockwise and negative are clockwise rotations.

    The point of origin can be a keyword 'center' for the bounding box
    center (default), 'centroid' for the geometry's centroid, a Point object
    or a coordinate tuple (x0, y0).

    The affine transformation matrix for 2D rotation is:

      / cos(r) -sin(r) xoff \ 
      | sin(r)  cos(r) yoff |
      \   0       0      1  /

    where the offsets are calculated from the origin Point(x0, y0):

        xoff = x0 - x0 * cos(r) + y0 * sin(r)
        yoff = y0 - x0 * sin(r) - y0 * cos(r)
    """
    if not use_radians:  # convert from degrees
        angle *= pi/180.0
    cosp = cos(angle)
    sinp = sin(angle)
    if abs(cosp) < 2.5e-16:
        cosp = 0.0
    if abs(sinp) < 2.5e-16:
        sinp = 0.0
    x0, y0 = interpret_origin(geom, origin, 2)

    matrix = (cosp, -sinp, 0.0,
              sinp,  cosp, 0.0,
              0.0,    0.0, 1.0,
              x0 - x0 * cosp + y0 * sinp, y0 - x0 * sinp - y0 * cosp, 0.0)
    return affine_transform(geom, matrix)


def scale(geom, xfact=1.0, yfact=1.0, zfact=1.0, origin='center'):
    """Returns a scaled geometry, scaled by factors along each dimension.

    The point of origin can be a keyword 'center' for the 2D bounding box
    center (default), 'centroid' for the geometry's 2D centroid, a Point
    object or a coordinate tuple (x0, y0, z0).

    Negative scale factors will mirror or reflect coordinates.

    The general 3D affine transformation matrix for scaling is:

        / xfact  0    0   xoff \ 
        |   0  yfact  0   yoff |
        |   0    0  zfact zoff |
        \   0    0    0     1  /

    where the offsets are calculated from the origin Point(x0, y0, z0):

        xoff = x0 - x0 * xfact
        yoff = y0 - y0 * yfact
        zoff = z0 - z0 * zfact
    """
    x0, y0, z0 = interpret_origin(geom, origin, 3)

    matrix = (xfact, 0.0, 0.0,
              0.0, yfact, 0.0,
              0.0, 0.0, zfact,
              x0 - x0 * xfact, y0 - y0 * yfact, z0 - z0 * zfact)
    return affine_transform(geom, matrix)


def skew(geom, xs=0.0, ys=0.0, origin='center', use_radians=False):
    """Returns a skewed geometry, sheared by angles along x and y dimensions.

    The shear angle can be specified in either degrees (default) or radians
    by setting ``use_radians=True``.

    The point of origin can be a keyword 'center' for the bounding box
    center (default), 'centroid' for the geometry's centroid, a Point object
    or a coordinate tuple (x0, y0).

    The general 2D affine transformation matrix for skewing is:

        /   1    tan(xs) xoff \ 
        | tan(ys)  1     yoff |
        \   0      0       1  /

    where the offsets are calculated from the origin Point(x0, y0):

        xoff = -y0 * tan(xs)
        yoff = -x0 * tan(ys)
    """
    if not use_radians:  # convert from degrees
        xs *= pi/180.0
        ys *= pi/180.0
    tanx = tan(xs)
    tany = tan(ys)
    if abs(tanx) < 2.5e-16:
        tanx = 0.0
    if abs(tany) < 2.5e-16:
        tany = 0.0
    x0, y0 = interpret_origin(geom, origin, 2)

    matrix = (1.0, tanx, 0.0,
              tany, 1.0, 0.0,
              0.0,  0.0, 1.0,
              -y0 * tanx, -x0 * tany, 0.0)
    return affine_transform(geom, matrix)


def translate(geom, xoff=0.0, yoff=0.0, zoff=0.0):
    """Returns a translated geometry shifted by offsets along each dimension.

    The general 3D affine transformation matrix for translation is:

        / 1  0  0 xoff \ 
        | 0  1  0 yoff |
        | 0  0  1 zoff |
        \ 0  0  0   1  /
    """
    matrix = (1.0, 0.0, 0.0,
              0.0, 1.0, 0.0,
              0.0, 0.0, 1.0,
              xoff, yoff, zoff)
    return affine_transform(geom, matrix)