__init__.py

"""Affine transformation matrices

The 3x3 augmented affine transformation matrix for transformations in two
dimensions is illustrated below.

  | x' |   | a  b  c | | x |
  | y' | = | d  e  f | | y |
  | 1  |   | 0  0  1 | | 1 |

The Affine package is derived from Casey Duncan's Planar package. See the
copyright statement below.
"""

#############################################################################
# Copyright (c) 2010 by Casey Duncan
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are met:
#
# * Redistributions of source code must retain the above copyright notice,
#   this list of conditions and the following disclaimer.
# * Redistributions in binary form must reproduce the above copyright notice,
#   this list of conditions and the following disclaimer in the documentation
#   and/or other materials provided with the distribution.
# * Neither the name(s) of the copyright holders nor the names of its
#   contributors may be used to endorse or promote products derived from this
#   software without specific prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AS IS AND ANY EXPRESS OR
# IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
# MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO
# EVENT SHALL THE COPYRIGHT HOLDERS BE LIABLE FOR ANY DIRECT, INDIRECT,
# INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
# LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
# OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
# LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
# NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE,
# EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
#############################################################################

from __future__ import division

from collections import namedtuple
import math


__all__ = ['Affine']
__author__ = "Sean Gillies"
__version__ = "1.1.0"

EPSILON = 1e-5
EPSILON2 = EPSILON ** 2


def set_epsilon(epsilon):
    """Set the global absolute error value and rounding limit for approximate
    floating point comparison operations. This value is accessible via the
    :attr:`planar.EPSILON` global variable.

    The default value of ``0.00001`` is suitable for values
    that are in the "countable range". You may need a larger
    epsilon when using large absolute values, and a smaller value
    for very small values close to zero. Otherwise approximate
    comparison operations will not behave as expected.
    """
    global EPSILON, EPSILON2
    EPSILON = float(epsilon)
    EPSILON2 = EPSILON ** 2


class TransformNotInvertibleError(Exception):
    """The transform could not be inverted"""

# Define assert_unorderable() depending on the language
# implicit ordering rules. This keeps things consistent
# across major Python versions
try:
    3 > ""
except TypeError:  # pragma: no cover
    # No implicit ordering (newer Python)
    def assert_unorderable(a, b):
        """Assert that a and b are unorderable"""
        return NotImplemented
else:  # pragma: no cover
    # Implicit ordering by default (older Python)
    # We must raise an exception ourselves
    # To prevent nonsensical ordering
    def assert_unorderable(a, b):
        """Assert that a and b are unorderable"""
        raise TypeError("unorderable types: %s and %s"
            % (type(a).__name__, type(b).__name__))


def cached_property(func):
    """Special property decorator that caches the computed
    property value in the object's instance dict the first
    time it is accessed.
    """
    name = func.__name__
    doc = func.__doc__

    def getter(self, name=name):
        try:
            return self.__dict__[name]
        except KeyError:
            self.__dict__[name] = value = func(self)
            return value
    getter.func_name = name
    return property(getter, doc=doc)


def cos_sin_deg(deg):
    """Return the cosine and sin for the given angle
    in degrees, with special-case handling of multiples
    of 90 for perfect right angles
    """
    deg = deg % 360.0
    if deg == 90.0:
        return 0.0, 1.0
    elif deg == 180.0:
        return -1.0, 0
    elif deg == 270.0:
        return 0, -1.0
    rad = math.radians(deg)
    return math.cos(rad), math.sin(rad)


class Affine(
        namedtuple('Affine', ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i'))):
    """Two dimensional affine transform for linear mapping from 2D coordinates
    to other 2D coordinates. Parallel lines are preserved by these
    transforms. Affine transforms can perform any combination of translations,
    scales/flips, shears, and rotations.  Class methods are provided to
    conveniently compose transforms from these operations.

    Internally the transform is stored as a 3x3 transformation matrix.  The
    transform may be constructed directly by specifying the first two rows of
    matrix values as 6 floats. Since the matrix is an affine transform, the
    last row is always ``(0, 0, 1)``.

    :param members: 6 floats for the first two matrix rows.
    :type members: float
    """

    def __new__(self, *members):
        if len(members) == 6:
            mat3x3 = [x * 1.0 for x in members] + [0.0, 0.0, 1.0]
            return tuple.__new__(Affine, mat3x3)
        else:
            raise TypeError(
                "Expected 6 coefficients, found %d" % len(members))

    @classmethod
    def from_gdal(cls, c, a, b, f, d, e):
        """Use same coefficient order as GDAL's GetGeoTransform().

        :param c, a, b, f, d, e: 6 floats ordered by GDAL.
        :rtype: Affine
        """
        members = [a, b, c, d, e, f]
        mat3x3 = [x * 1.0 for x in members] + [0.0, 0.0, 1.0]
        return tuple.__new__(cls, mat3x3)

    @classmethod
    def identity(cls):
        """Return the identity transform.

        :rtype: Affine
        """
        return identity

    @classmethod
    def translation(cls, xoff, yoff):
        """Create a translation transform from an offset vector.

        :param xoff: Translation x offset.
        :type xoff: float
        :param yoff: Translation y offset.
        :type yoff: float
        :rtype: Affine
        """
        return tuple.__new__(cls,
            (1.0, 0.0, xoff,
             0.0, 1.0, yoff,
             0.0, 0.0, 1.0))

    @classmethod
    def scale(cls, *scaling):
        """Create a scaling transform from a scalar or vector.

        :param scaling: The scaling factor. A scalar value will
            scale in both dimensions equally. A vector scaling
            value scales the dimensions independently.
        :type scaling: float or sequence
        :rtype: Affine
        """
        if len(scaling) == 1:
            sx = sy = float(scaling[0])
        else:
            sx, sy = scaling
        return tuple.__new__(cls,
            (sx, 0.0, 0.0,
             0.0, sy, 0.0,
             0.0, 0.0, 1.0))

    @classmethod
    def shear(cls, x_angle=0, y_angle=0):
        """Create a shear transform along one or both axes.

        :param x_angle: Angle in degrees to shear along the x-axis.
        :type x_angle: float
        :param y_angle: Angle in degrees to shear along the y-axis.
        :type y_angle: float
        :rtype: Affine
        """
        sx = math.tan(math.radians(x_angle))
        sy = math.tan(math.radians(y_angle))
        return tuple.__new__(cls,
            (1.0, sy, 0.0,
             sx, 1.0, 0.0,
             0.0, 0.0, 1.0))

    @classmethod
    def rotation(cls, angle, pivot=None):
        """Create a rotation transform at the specified angle,
        optionally about the specified pivot point.

        :param angle: Rotation angle in degrees
        :type angle: float
        :param pivot: Point to rotate about, if omitted the
            rotation is about the origin.
        :type pivot: sequence
        :rtype: Affine
        """
        ca, sa = cos_sin_deg(angle)
        if pivot is None:
            return tuple.__new__(cls,
                (ca, sa, 0.0,
                -sa, ca, 0.0,
                 0.0, 0.0, 1.0))
        else:
            px, py = pivot
            return tuple.__new__(cls,
                (ca, sa, px - px * ca + py * sa,
                -sa, ca, py - px * sa - py * ca,
                 0.0, 0.0, 1.0))

    def __str__(self):
        """Concise string representation."""
        return ("|% .2f,% .2f,% .2f|\n"
                "|% .2f,% .2f,% .2f|\n"
                "|% .2f,% .2f,% .2f|") % self

    def __repr__(self):
        """Precise string representation."""
        return ("Affine(%r, %r, %r,\n"
                "       %r, %r, %r)") % self[:6]

    def to_gdal(self):
        """Return same coefficient order as GDAL's SetGeoTransform().

        :rtype: tuple
        """
        return (self.c, self.a, self.b, self.f, self.d, self.e)

    @property
    def xoff(self):
        """Alias for 'c'"""
        return self.c

    @property
    def yoff(self):
        """Alias for 'f'"""
        return self.f

    @cached_property
    def determinant(self):
        """The determinant of the transform matrix. This value
        is equal to the area scaling factor when the transform
        is applied to a shape.
        """
        a, b, c, d, e, f, g, h, i = self
        return a * e - b * d

    @cached_property
    def is_identity(self):
        """True if this transform equals the identity matrix,
        within rounding limits.
        """
        return self is identity or self.almost_equals(identity)

    @cached_property
    def is_rectilinear(self):
        """True if the transform is rectilinear, i.e., whether a shape would
        remain axis-aligned, within rounding limits, after applying the
        transform.
        """
        a, b, c, d, e, f, g, h, i = self
        return ((abs(a) < EPSILON and abs(e) < EPSILON)
            or (abs(d) < EPSILON and abs(b) < EPSILON))

    @cached_property
    def is_conformal(self):
        """True if the transform is conformal, i.e., if angles between points
        are preserved after applying the transform, within rounding limits.
        This implies that the transform has no effective shear.
        """
        a, b, c, d, e, f, g, h, i = self
        return abs(a * b + d * e) < EPSILON

    @cached_property
    def is_orthonormal(self):
        """True if the transform is orthonormal, which means that the
        transform represents a rigid motion, which has no effective scaling or
        shear. Mathematically, this means that the axis vectors of the
        transform matrix are perpendicular and unit-length.  Applying an
        orthonormal transform to a shape always results in a congruent shape.
        """
        a, b, c, d, e, f, g, h, i = self
        return (self.is_conformal
            and abs(1.0 - (a * a + d * d)) < EPSILON
            and abs(1.0 - (b * b + e * e)) < EPSILON)

    @cached_property
    def is_degenerate(self):
        """True if this transform is degenerate, which means that it will
        collapse a shape to an effective area of zero. Degenerate transforms
        cannot be inverted.
        """
        return abs(self.determinant) < EPSILON

    @property
    def column_vectors(self):
        """The values of the transform as three 2D column vectors"""
        a, b, c, d, e, f, _, _, _ = self
        return (a, d), (b, e), (c, f)

    def almost_equals(self, other):
        """Compare transforms for approximate equality.

        :param other: Transform being compared.
        :type other: Affine
        :return: True if absolute difference between each element
            of each respective transform matrix < ``EPSILON``.
        """
        for i in (0, 1, 2, 3, 4, 5):
            if abs(self[i] - other[i]) >= EPSILON:
                return False
        return True

    def __gt__(self, other):
        return assert_unorderable(self, other)

    __ge__ = __lt__ = __le__ = __gt__

    # Override from base class. We do not support entrywise
    # addition, subtraction or scalar multiplication because
    # the result is not an affine transform

    def __add__(self, other):
        raise TypeError("Operation not supported")

    __iadd__ = __add__

    def __mul__(self, other):
        """Apply the transform using matrix multiplication, creating a
        resulting object of the same type.  A transform may be applied to
        another transform, a vector, vector array, or shape.

        :param other: The object to transform.
        :type other: Affine, :class:`~planar.Vec2`,
            :class:`~planar.Vec2Array`, :class:`~planar.Shape`
        :rtype: Same as ``other``
        """
        sa, sb, sc, sd, se, sf, _, _, _ = self
        if isinstance(other, Affine):
            oa, ob, oc, od, oe, of, _, _, _ = other
            return tuple.__new__(Affine,
                (sa * oa + sb * od, sa * ob + sb * oe, sa * oc + sb * of + sc,
                 sd * oa + se * od, sd * ob + se * oe, sd * oc + se * of + sf,
                 0.0, 0.0, 1.0))
        else:
            try:
                vx, vy = other
            except Exception:
                return NotImplemented
            return (vx * sa + vy * sd + sc, vx * sb + vy * se + sf)

    def __rmul__(self, other):
        # We should not be called if other is an affine instance
        # This is just a guarantee, since we would potentially
        # return the wrong answer in that case
        assert not isinstance(other, Affine)
        return self.__mul__(other)

    def __imul__(self, other):
        if isinstance(other, Affine) or isinstance(other, tuple):
            return self.__mul__(other)
        else:
            return NotImplemented

    def itransform(self, seq):
        """Transform a sequence of points or vectors in place.

        :param seq: Mutable sequence of :class:`~planar.Vec2` to be
            transformed.
        :returns: None, the input sequence is mutated in place.
        """
        if self is not identity and self != identity:
            sa, sb, sc, sd, se, sf, _, _, _ = self
            for i, (x, y) in enumerate(seq):
                seq[i] = (x * sa + y * sd + sc, x * sb + y * se + sf)

    def __invert__(self):
        """Return the inverse transform.

        :raises: :except:`TransformNotInvertible` if the transform
            is degenerate.
        """
        if self.is_degenerate:
            raise TransformNotInvertibleError(
                "Cannot invert degenerate transform")
        idet = 1.0 / self.determinant
        sa, sb, sc, sd, se, sf, _, _, _ = self
        ra = se * idet
        rb = -sb * idet
        rd = -sd * idet
        re = sa * idet
        return tuple.__new__(Affine,
            (ra, rb, -sc * ra - sf * rb,
             rd, re, -sc * rd - sf * re,
             0.0, 0.0, 1.0))

    __hash__ = tuple.__hash__  # hash is not inherited in Py 3


identity = Affine(1, 0, 0, 0, 1, 0)
"""The identity transform"""

# Miscellaneous utilities


def loadsw(s):
    """Returns Affine from the contents of a world file string.

    This method also translates the coefficients from from center- to
    corner-based coordinates.

    :param s: str with 6 floats ordered in a world file.
    :rtype: Affine
    """
    if not hasattr(s, 'split'):
        raise TypeError("Cannot split input string")
    coeffs = s.split()
    if len(coeffs) != 6:
        raise ValueError("Expected 6 coefficients, found %d" % len(coeffs))
    a, d, b, e, c, f = [float(x) for x in coeffs]
    center = tuple.__new__(Affine, [a, b, c, d, e, f, 0.0, 0.0, 1.0])
    return center * Affine.translation(-0.5, -0.5)


def dumpsw(obj):
    """Return string for a world file.

    This method also translates the coefficients from from corner- to
    center-based coordinates.

    :rtype: str
    """
    center = obj * Affine.translation(0.5, 0.5)
    return '\n'.join(repr(getattr(center, x)) for x in list('adbecf')) + '\n'


# vim: ai ts=4 sts=4 et sw=4 tw=78