264 lines
8.4 KiB
Python
264 lines
8.4 KiB
Python
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"""Affine transforms, both in general and specific, named transforms."""
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from math import sin, cos, tan, pi
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__all__ = ['affine_transform', 'rotate', 'scale', 'skew', 'translate']
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def affine_transform(geom, matrix):
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r"""Returns a transformed geometry using an affine transformation matrix.
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The coefficient matrix is provided as a list or tuple with 6 or 12 items
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for 2D or 3D transformations, respectively.
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For 2D affine transformations, the 6 parameter matrix is::
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[a, b, d, e, xoff, yoff]
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which represents the augmented matrix::
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[x'] / a b xoff \ [x]
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[y'] = | d e yoff | [y]
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[1 ] \ 0 0 1 / [1]
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or the equations for the transformed coordinates::
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x' = a * x + b * y + xoff
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y' = d * x + e * y + yoff
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For 3D affine transformations, the 12 parameter matrix is::
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[a, b, c, d, e, f, g, h, i, xoff, yoff, zoff]
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which represents the augmented matrix::
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[x'] / a b c xoff \ [x]
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[y'] = | d e f yoff | [y]
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[z'] | g h i zoff | [z]
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[1 ] \ 0 0 0 1 / [1]
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or the equations for the transformed coordinates::
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x' = a * x + b * y + c * z + xoff
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y' = d * x + e * y + f * z + yoff
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z' = g * x + h * y + i * z + zoff
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"""
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if geom.is_empty:
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return geom
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if len(matrix) == 6:
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ndim = 2
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a, b, d, e, xoff, yoff = matrix
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if geom.has_z:
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ndim = 3
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i = 1.0
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c = f = g = h = zoff = 0.0
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matrix = a, b, c, d, e, f, g, h, i, xoff, yoff, zoff
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elif len(matrix) == 12:
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ndim = 3
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a, b, c, d, e, f, g, h, i, xoff, yoff, zoff = matrix
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if not geom.has_z:
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ndim = 2
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matrix = a, b, d, e, xoff, yoff
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else:
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raise ValueError("'matrix' expects either 6 or 12 coefficients")
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def affine_pts(pts):
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"""Internal function to yield affine transform of coordinate tuples"""
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if ndim == 2:
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for x, y in pts:
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xp = a * x + b * y + xoff
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yp = d * x + e * y + yoff
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yield (xp, yp)
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elif ndim == 3:
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for x, y, z in pts:
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xp = a * x + b * y + c * z + xoff
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yp = d * x + e * y + f * z + yoff
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zp = g * x + h * y + i * z + zoff
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yield (xp, yp, zp)
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# Process coordinates from each supported geometry type
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if geom.type in ('Point', 'LineString', 'LinearRing'):
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return type(geom)(list(affine_pts(geom.coords)))
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elif geom.type == 'Polygon':
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ring = geom.exterior
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shell = type(ring)(list(affine_pts(ring.coords)))
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holes = list(geom.interiors)
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for pos, ring in enumerate(holes):
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holes[pos] = type(ring)(list(affine_pts(ring.coords)))
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return type(geom)(shell, holes)
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elif geom.type.startswith('Multi') or geom.type == 'GeometryCollection':
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# Recursive call
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# TODO: fix GeometryCollection constructor
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return type(geom)([affine_transform(part, matrix)
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for part in geom.geoms])
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else:
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raise ValueError('Type %r not recognized' % geom.type)
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def interpret_origin(geom, origin, ndim):
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"""Returns interpreted coordinate tuple for origin parameter.
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This is a helper function for other transform functions.
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The point of origin can be a keyword 'center' for the 2D bounding box
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center, 'centroid' for the geometry's 2D centroid, a Point object or a
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coordinate tuple (x0, y0, z0).
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"""
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# get coordinate tuple from 'origin' from keyword or Point type
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if origin == 'center':
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# bounding box center
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minx, miny, maxx, maxy = geom.bounds
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origin = ((maxx + minx)/2.0, (maxy + miny)/2.0)
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elif origin == 'centroid':
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origin = geom.centroid.coords[0]
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elif isinstance(origin, str):
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raise ValueError("'origin' keyword %r is not recognized" % origin)
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elif hasattr(origin, 'type') and origin.type == 'Point':
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origin = origin.coords[0]
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# origin should now be tuple-like
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if len(origin) not in (2, 3):
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raise ValueError("Expected number of items in 'origin' to be "
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"either 2 or 3")
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if ndim == 2:
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return origin[0:2]
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else: # 3D coordinate
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if len(origin) == 2:
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return origin + (0.0,)
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else:
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return origin
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def rotate(geom, angle, origin='center', use_radians=False):
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r"""Returns a rotated geometry on a 2D plane.
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The angle of rotation can be specified in either degrees (default) or
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radians by setting ``use_radians=True``. Positive angles are
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counter-clockwise and negative are clockwise rotations.
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The point of origin can be a keyword 'center' for the bounding box
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center (default), 'centroid' for the geometry's centroid, a Point object
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or a coordinate tuple (x0, y0).
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The affine transformation matrix for 2D rotation is:
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/ cos(r) -sin(r) xoff \
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| sin(r) cos(r) yoff |
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\ 0 0 1 /
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where the offsets are calculated from the origin Point(x0, y0):
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xoff = x0 - x0 * cos(r) + y0 * sin(r)
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yoff = y0 - x0 * sin(r) - y0 * cos(r)
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"""
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if geom.is_empty:
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return geom
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if not use_radians: # convert from degrees
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angle = angle * pi/180.0
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cosp = cos(angle)
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sinp = sin(angle)
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if abs(cosp) < 2.5e-16:
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cosp = 0.0
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if abs(sinp) < 2.5e-16:
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sinp = 0.0
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x0, y0 = interpret_origin(geom, origin, 2)
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matrix = (cosp, -sinp, 0.0,
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sinp, cosp, 0.0,
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0.0, 0.0, 1.0,
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x0 - x0 * cosp + y0 * sinp, y0 - x0 * sinp - y0 * cosp, 0.0)
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return affine_transform(geom, matrix)
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def scale(geom, xfact=1.0, yfact=1.0, zfact=1.0, origin='center'):
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r"""Returns a scaled geometry, scaled by factors along each dimension.
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The point of origin can be a keyword 'center' for the 2D bounding box
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center (default), 'centroid' for the geometry's 2D centroid, a Point
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object or a coordinate tuple (x0, y0, z0).
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Negative scale factors will mirror or reflect coordinates.
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The general 3D affine transformation matrix for scaling is:
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/ xfact 0 0 xoff \
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| 0 yfact 0 yoff |
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| 0 0 zfact zoff |
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\ 0 0 0 1 /
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where the offsets are calculated from the origin Point(x0, y0, z0):
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xoff = x0 - x0 * xfact
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yoff = y0 - y0 * yfact
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zoff = z0 - z0 * zfact
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"""
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if geom.is_empty:
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return geom
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x0, y0, z0 = interpret_origin(geom, origin, 3)
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matrix = (xfact, 0.0, 0.0,
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0.0, yfact, 0.0,
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0.0, 0.0, zfact,
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x0 - x0 * xfact, y0 - y0 * yfact, z0 - z0 * zfact)
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return affine_transform(geom, matrix)
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def skew(geom, xs=0.0, ys=0.0, origin='center', use_radians=False):
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r"""Returns a skewed geometry, sheared by angles along x and y dimensions.
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The shear angle can be specified in either degrees (default) or radians
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by setting ``use_radians=True``.
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The point of origin can be a keyword 'center' for the bounding box
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center (default), 'centroid' for the geometry's centroid, a Point object
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or a coordinate tuple (x0, y0).
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The general 2D affine transformation matrix for skewing is:
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/ 1 tan(xs) xoff \
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| tan(ys) 1 yoff |
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\ 0 0 1 /
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where the offsets are calculated from the origin Point(x0, y0):
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xoff = -y0 * tan(xs)
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yoff = -x0 * tan(ys)
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"""
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if geom.is_empty:
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return geom
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if not use_radians: # convert from degrees
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xs = xs * pi/180.0
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ys = ys * pi/180.0
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tanx = tan(xs)
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tany = tan(ys)
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if abs(tanx) < 2.5e-16:
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tanx = 0.0
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if abs(tany) < 2.5e-16:
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tany = 0.0
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x0, y0 = interpret_origin(geom, origin, 2)
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matrix = (1.0, tanx, 0.0,
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tany, 1.0, 0.0,
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0.0, 0.0, 1.0,
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-y0 * tanx, -x0 * tany, 0.0)
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return affine_transform(geom, matrix)
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def translate(geom, xoff=0.0, yoff=0.0, zoff=0.0):
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r"""Returns a translated geometry shifted by offsets along each dimension.
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The general 3D affine transformation matrix for translation is:
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/ 1 0 0 xoff \
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| 0 1 0 yoff |
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| 0 0 1 zoff |
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\ 0 0 0 1 /
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"""
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if geom.is_empty:
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return geom
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matrix = (1.0, 0.0, 0.0,
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0.0, 1.0, 0.0,
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0.0, 0.0, 1.0,
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xoff, yoff, zoff)
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return affine_transform(geom, matrix)
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