# -*- coding: utf-8 -*-

"""
transforms
"""

# imports ####################################################################
from math import radians, cos, sin, hypot, degrees, atan2, tan

from ._common import _Base


# transforms #################################################################

class _Transform(_Base):
    """represents an affine transformation matrix
    
    The affine transform that transforms coordinates (x_1, y_1) expressed in space 1 to corrdinates (x2, y2) expressed in space 2, is expressed with 6 floating point values (a, b, c, d, e, f) such that :
    x_2 = a * x_1 + c * y_1 + e
    y_2 = b * x_1 + d * y_1 + f
    
    """
    _state_attributes = ["tag"]
    attributes = []

    @property
    def tag(self):
        """the svg tag that represents this transform
        """
        raise NotImplementedError  # this tag is suppsed to be defined in derived classes
    
    def project(self, x=0, y=0):
        """transforms a point using this transform
        
        :returns: the transformed point
        """
        a, b, c, d, e, f = self.abcdef
        return a * x + c * y + e, b * x + d * y + f
    
    @property
    def abcdef(self):
        """
            return the 6 elements a,b,c,d,e,f defining this transformation
        """
        return
    
    def __mul__(self, other):
        sa, sb, sc, sd, se, sf = self.abcdef
        oa, ob, oc, od, oe, of = other.abcdef
        a, c, e = sa * oa + sc * ob, sa * oc + sc * od, sa * oe + sc * of + se
        b, d, f = sb * oa + sd * ob, sb * oc + sd * od, sb * oe + sd * of + sf
        return Matrix(a, b, c, d, e, f)
    
    def params(self, error=1e-6):
        """separate translation, rotation, shear and scale"""
        a, b, c, d, e, f = self.abcdef
        tx, ty = e, f
        
        if abs(b * c) < error:
            cosa, sina = 1., 0.
            sx, hy = a, b
            hx, sy = c, d
        else:
            sign = 1. if a * d >= b * c else -1.
            cosa, sina = a + sign * d, b - sign * c
            h = hypot(cosa, sina)
            cosa, sina = cosa / h, sina / h
            sx, hy = a * cosa + b * sina, b * cosa - a * sina
            hx, sy = c * cosa + d * sina, d * cosa - c * sina
            sx -= hx * hy / sy
        return (tx, ty), (cosa, sina), (hx, hy), (sx, sy)

    def uniform(self):
        """returns this matrix in the form of a 3x3 matrix for homogen coordinates
        """
        a, b, c, d, e, f = self.abcdef
        return [(a, b, 0., c, d, 0., e, f, 1.)]

    def __str__(self):
        return "%s(" % self.tag + \
               ",".join(str(getattr(self, a)) for a in self.attributes) + \
               ")"


class Translate(_Transform):
    tag = "translate"
    attributes = ["tx", "ty"]
    _state_attributes = _Transform._state_attributes + attributes
    
    def __init__(self, tx=0, ty=0):
        self.tx, self.ty = tx, ty

    def inverse(self):
        return Translate(-self.tx, -self.ty)
    
    @property
    def abcdef(self):
        return 1., 0., 0., 1., self.tx, self.ty


class Scale(_Transform):
    tag = "scale"
    attributes = ["sx", "sy"]
    _state_attributes = _Transform._state_attributes + attributes
    
    def __init__(self, sx=1., sy=None):
        self.sx = sx
        self.sy = sy or sx
    
    def inverse(self):
        return Scale(1. / self.sx, 1. / self.sy)
    
    @property
    def abcdef(self):
        return self.sx, 0., 0., self.sy, 0., 0.

    
class Rotate(_Transform):
    tag = "rotate"
    attributes = ["a", "cx", "cy"]
    _state_attributes = _Transform._state_attributes + attributes
    
    def __init__(self, a=0, cx=0, cy=0):
        self.a = a
        self.cx, self.cy = cx, cy

    def inverse(self):
        return Rotate(-self.a, self.cx, self.cy)
    
    @property
    def abcdef(self):
        a, cx, cy = radians(self.a), self.cx, self.cy
        c, s = cos(a), sin(a)
        return c, s, -s, c, cx * (1. - c) + cy * s, cy * (1. - c) - cx * s


class SkewX(_Transform):
    tag = "skewX"
    attributes = ["ax"]
    _state_attributes = _Transform._state_attributes + attributes
    
    def __init__(self, ax=0.):
        self.ax = ax

    def inverse(self):
        return SkewX(-self.ax)
    
    @property
    def abcdef(self):
        t = tan(radians(self.ax))
        return 1., 0., t, 1., 0., 0.


class SkewY(_Transform):
    tag = "skewY"
    attributes = ["ay"]
    _state_attributes = _Transform._state_attributes + attributes
    
    def __init__(self, ay=0.):
        self.ay = ay

    def inverse(self):
        return SkewY(-self.ay)
    
    @property
    def abcdef(self):
        t = tan(radians(self.ay))
        return 1., t, 0., 1., 0., 0.


class Matrix(_Transform):
    tag = "matrix"
    attributes = ["a", "b", "c", "d", "e", "f"]
    _state_attributes = _Transform._state_attributes + attributes
    
    def __init__(self, a=1., b=0., c=0., d=1., e=0., f=0.):
        self.a, self.c, self.e = a, c, e
        self.b, self.d, self.f = b, d, f
    
    def get_abcdef(self):
        return self.a, self.b, self.c, self.d, self.e, self.f
    
    def set_abcdef(self, abcdef):
        self.a, self.b, self.c, self.d, self.e, self.f = abcdef
    abcdef = property(get_abcdef, set_abcdef)
    
    def inverse(self):
        a, b, c, d, e, f = self.abcdef
        det = a * d - b * c
        return Matrix(*(u / det for u in (d, -b, -c, a, c * f - e * d, b * e - a * f)))


def ortho(left, right, bottom, top):
    width, height = right - left, top - bottom
    a, c, e = 2. / width, 0.,          -(left + right) / width
    b, d, f = 0.,         2. / height, -(bottom + top) / height
    return Matrix(a, b, c, d, e, f)


def stretch(x, y, width, height):
    a, c, e = width, 0.,     x
    b, d, f = 0.,    height, y
    return Matrix(a, b, c, d, e, f)


def shrink(x, y, width, height):
    a, c, e = 1. / width, 0.,        -x / width
    b, d, f = 0.,       1. / height, -y / height
    return Matrix(a, b, c, d, e, f)


# helpers ####################################################################

def product(p=Matrix(), *qs):
    for q in qs:
        p = p * q
    return p


def _list_from_params(t, r, sk, s, error=1e-6):
    (tx, ty), (cosa, sina), (hx, hy), (sx, sy) = t, r, sk, s
    transforms = []
    if (tx, ty) != (0., 0.):
        transforms.append(Translate(tx, ty))
    if abs(sina) > abs(cosa) * error:
        transforms.append(Rotate(degrees(atan2(sina, cosa))))
    if abs(hx) > abs(sy) * error:
        transforms.append(SkewX(degrees(atan2(hx, sy))))
    if abs(hy) > abs(sx) * error:
        transforms.append(SkewY(degrees(atan2(hy, sx))))
    if any(abs(1. - s) > error for s in (sx, sy)):
        transforms.append(Scale(sx, sy))
    return transforms


def normalized(transform):
    return _list_from_params(*product(*transform).params())