#!/usr/bin/python
# -*- coding: utf-8 -*-
#
# Pyromaths
# Un programme en Python qui permet de créer des fiches d'exercices types de
# mathématiques niveau collège ainsi que leur corrigé en LaTeX.
# Copyright (C) 2006 -- Jérôme Ortais (jerome.ortais@pyromaths.org)
#
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program; if not, write to the Free Software
# Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
#

import random
from math import atan, cos, pi, sin, floor, ceil

#===============================================================================
# Symétrique d'une figure par rapport à une droite avec quadrillage
#===============================================================================


def valeurs_quad2(nb_pts):
    vals = []
    for i in range(nb_pts):
        angle = random.randrange((i * 360) / nb_pts, ((i + 1) * 360) /
                                 nb_pts)
        vals.append(((random.randrange(1, 7) * .5) * cos((angle * pi) /
                    180), (random.randrange(1, 7) * .5) * sin((angle *
                    pi) / 180)))
    return vals


def valeurs_quad(nb_pts):
    vals = []
    for i in range(nb_pts):
        (alpha, beta) = ((i * 360) / nb_pts, ((i + 1) * 360) / nb_pts)
        (x, y) = (0, 0)
        while x == 0 or angle < alpha or angle > beta:
            (x, y) = (random.randrange(-6, 7) * .5, random.randrange(-6,
                      7) * .5)
            if x > 0:
                angle = int((atan((y * 1.0) / x) * 180) / pi + 360) % \
                    360
            if x < 0:
                angle = int((atan((y * 1.0) / x) * 180) / pi + 180)
        vals.append((x, y))
    return vals


def place_pts(vals, angle):
    txt = ["  \\pstGeonode[PointSymbol=x,PointName=none]"]
    for i in range(len(vals)):
        txt.append("(%s,%s)" % vals[i])
        txt.append("{%s}" % chr(i + 97))
    txt.append("\n\\pstGeonode[PointSymbol=none,PointName=none](-4.5;%s){A}(4.5;%s){B}" % (angle, angle))
    txt.append("\n\\psline[linecolor=Black, linewidth=1pt, nodesep=-4.5](A)(B)")
    txt.append("\n\\pspolygon[linecolor=Maroon, linewidth=1pt]")
    for i in range(len(vals)):
        txt.append("(%s)" % chr(i + 97))
    return ("").join(txt)


def Symetrie_quiz(angle, vals, nbpts):
    langles = [0, 90, 45, 135]
    langles.remove(angle)
    angle2 = langles.pop(random.randrange(len(langles)))
    angle3 = langles.pop(random.randrange(len(langles)))
    vals_cor = [[vals,angle], [vals,angle2], [vals,angle3]]
    random.shuffle(vals_cor)
    quiz_txt = "$$\\fs1\\picture(570,140){"
    quiz_txt += "(10,10){\\line(120,0)}(10,9){\\line(120,0)}(10,10){\\line(0,120)}(9,10){\\line(0,120)}"  # Recuadro
    quiz_txt += "(130,130){\\line(-120,0)}(130,129){\\line(-120,0)}(130,130){\\line(0,-120)}(129,130){\\line(0,-120)}"
    quiz_txt += ("%s{\\bullet}%s{\\bullet}%s{\\bullet}%s{\\bullet}%s{\\bullet}" %
                   tuple(["("+str(i[0]*20+68)+","+str(i[1]*20+68)+")" for i in vals])) # puntos 1ºFigura
    quiz_txt += ("%s%s%s%s%s" % tuple([union_m(vals[i-1],vals[i],70) for i in range(nbpts)])) #  rectas 1ºFigura
    quiz_txt += "(260,100){\\fs3\\fbox{1^o}}(400,100){\\fs3\\fbox{2^o}}(540,100){\\fs3\\fbox{3^o}}" #  Numeración
    count_vals = 0
    for v in vals_cor:
        if v[1] == 0:
            quiz_txt += ("%s{\\bullet}%s{\\bullet}%s{\\bullet}%s{\\bullet}%s{\\bullet}" %
                           tuple(["("+str(i[0]*20+208+count_vals*140)+","+str(i[1]*-20+68)+")" for i in v[0]])) # puntos demás Figura
            quiz_txt += ("%s%s%s%s%s" %
                           tuple([union_m(v[0][i-1],v[0][i],210+count_vals*140,v[1]) for i in range(nbpts)])) #  rectas demás Figura
            if v[1] == angle:
                quiz_txt += "(10,70){\\line(120,0)}"
        elif v[1] == 90:
            quiz_txt += ("%s{\\bullet}%s{\\bullet}%s{\\bullet}%s{\\bullet}%s{\\bullet}" %
                           tuple(["("+str(i[0]*-20+208+count_vals*140)+","+str(i[1]*20+68)+")" for i in v[0]])) # puntos demás Figura
            quiz_txt += ("%s%s%s%s%s" %
                           tuple([union_m(v[0][i-1],v[0][i],210+count_vals*140,v[1]) for i in range(nbpts)])) #  rectas demás Figura
            if v[1] == angle:
                quiz_txt += "(70,10){\\line(0,120)}"
        elif v[1] == 45:
            quiz_txt += ("%s{\\bullet}%s{\\bullet}%s{\\bullet}%s{\\bullet}%s{\\bullet}" %
                           tuple(["("+str(i[1]*20+208+count_vals*140)+","+str(i[0]*20+68)+")" for i in v[0]])) # puntos demás Figura
            quiz_txt += ("%s%s%s%s%s" %
                           tuple([union_m(v[0][i-1],v[0][i],210+count_vals*140,v[1]) for i in range(nbpts)])) #  rectas demás Figura
            if v[1] == angle:
                quiz_txt += "(10,10){\\line(120,120)}"
        elif v[1] == 135:
            quiz_txt += ("%s{\\bullet}%s{\\bullet}%s{\\bullet}%s{\\bullet}%s{\\bullet}" %
                           tuple(["("+str(i[1]*-20+208+count_vals*140)+","+str(i[0]*-20+68)+")" for i in v[0]])) # puntos demás Figura
            quiz_txt += ("%s%s%s%s%s" %
                           tuple([union_m(v[0][i-1],v[0][i],210+count_vals*140,v[1]) for i in range(nbpts)])) #  rectas demás Figura
            if v[1] == angle:
                quiz_txt += "(10,130){\\line(120,-120)}"
        count_vals += 1
    quiz_txt += "}$$<br/>\n"
    quiz_sol = ""
    for x in range(3):
        if vals_cor[x][1] == angle:
            quiz_sol += (u"~=%sº" % str(x+1))
        else:
            quiz_sol += (u"~%sº" % str(x+1))
    return quiz_txt, quiz_sol

def union_m(pt1, pt2, d_m, type_m=-1):
    if type_m == 0:
        pt1_m = (pt1[0], -pt1[1])
        pt2_m = (pt2[0], -pt2[1])
    elif type_m == 90:
        pt1_m = (-pt1[0], pt1[1])
        pt2_m = (-pt2[0], pt2[1])
    elif type_m == 45:
        pt1_m = (pt1[1], pt1[0])
        pt2_m = (pt2[1], pt2[0])
    elif type_m == 135:
        pt1_m = (-pt1[1], -pt1[0])
        pt2_m = (-pt2[1], -pt2[0])
    else:
        pt1_m = pt1
        pt2_m = pt2
    v_x = (pt2_m[0] - pt1_m[0])*20
    v_y = (pt2_m[1] - pt1_m[1])*20
    return ("(%s,%s){\\line(%s,%s)}" %(pt1_m[0]*20 + d_m, pt1_m[1]*20 + 70, v_x, v_y))


def SymetrieQuadrillage():
    exo = ["\\exercice", _(u"Construire la symétrique de chacune des figures par rapport à la droite en"), _(u"utilisant le quadrillage :\\par"), "\\psset{unit=.9cm}"]
    cor = ["\\exercice*", _(u"Construire la symétrique de chacune des figures par rapport à la droite en"), _(u"utilisant le quadrillage :\\par"), "\\psset{unit=.9cm}"]
    quiz = ["cloze"]

    nbpts = 5
    langles = [0, 90, 45, 135]
    for j in range(3):
        angle = langles.pop(random.randrange(len(langles)))
        vals = valeurs_quad(nbpts)
        txt = place_pts(vals, angle)
        exo.append("\\begin{pspicture*}(-3,-3)(3,3)")
        exo.append("\\psgrid[subgriddiv=2,gridlabels=0pt]")
        exo.append(txt)
        cor.append("\\begin{pspicture*}(-3,-3)(3,3)")
        cor.append("\\psgrid[subgriddiv=2,gridlabels=0pt]")
        cor.append(txt)
        txt_cor = "\\pstOrtSym[PointSymbol=x,PointName=none]{A}{B}{"
        for i in range(len(vals)):
            if i > 0:
                txt_cor += ","
            txt_cor += "%s" % chr(i + 97)
        txt_cor += "}["
        for i in range(len(vals)):
            if i > 0:
                txt_cor += ","
            txt_cor += "%s1" % chr(i + 97)
        txt_cor += "]\n  \pspolygon[linecolor=Black, linestyle=dashed, linewidth=1pt]"
        for i in range(len(vals)):
            txt_cor += "(%s1)" % chr(i + 97)
        cor.append(txt_cor)
        exo.append("\\end{pspicture*}")
        cor.append("\\end{pspicture*}")
        if j < 2:
            exo.append("\\hfill")
            cor.append("\\hfill")
        quiz_nom = (_(u"Symétrie axiale %s") % str(j+1))
        quiz_exo_cor = _(u"Indique quel c'est le symétrique au sujet de la droite de la figure encadrée de la gauche:<br/>\n")
        quiz_txt, quiz_sol = Symetrie_quiz(angle, vals, nbpts)
        quiz_exo_cor += quiz_txt
        quiz_exo_cor += (_(u"Réponse: La symétrique en ce qui concerne la droite est le {1:MULTICHOICE:%s}") %
                           quiz_sol)
        quiz.append([quiz_nom, quiz_exo_cor, ""])
    return (exo, cor, quiz)