#!/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
import string
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 centre_sym(vals):
    fin = 0
    while not fin:
        (fin, cpt) = (1, 0)
        (o1, o2) = (random.randrange(-6, 7) * .5, random.randrange(-6, 7) *
                    .5)
        while fin and cpt < len(vals):
            fin = fin and -3 <= 2 * o1 - vals[cpt][0] <= 3 and -3 <= 2 * \
                o2 - vals[cpt][1] <= 3
            cpt = cpt + 1
    return (o1, o2)


def place_pts(vals, O):
    txt = ["  \\pstGeonode[PointSymbol=none,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=x, linecolor=Black, dotsize=6pt](%s,%s){O}" % O)
    txt.append("\n  \\pspolygon[linewidth=1pt]")
    for i in range(len(vals)):
        txt.append("(%s)" % chr(i + 97))
    return ("").join(txt)


def place_pts_sym(vals):
    txt = ["  \\pstSymO[PointSymbol=x,PointName=none]{O}{"]
    for i in range(len(vals)):
        if i > 0:
            txt.append(",")
        txt.append("%s" % chr(i + 97))
    txt.append("}[")
    for i in range(len(vals)):
        if i > 0:
            txt.append(",")
        txt.append("%s1" % chr(i + 97))
    txt.append("]\n\pspolygon[linecolor=Black,linestyle=dashed, linewidth=1pt]")
    for i in range(len(vals)):
        txt.append("(%s1)" % chr(i + 97))
    return ("").join(txt)


def exo_quadrillage(f0, f1):
    pass

def symetrie_c_quiz(O, vals, nbpts):
    langles = [0, 90, 45, 135]
    angle2 = langles.pop(random.randrange(len(langles)))
    angle3 = langles.pop(random.randrange(len(langles)))
    if O == (0, 0):
        vals_ok = vals
    else:
        vals_ok = [(i[0]-2*O[0], i[1]-2*O[1]) for i in vals]
    vals_cor = [[vals_ok,-1], [vals_ok,angle2], [vals_ok,angle3]]   # -1 indica simetria centro O
    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,%s){\\bullet}(%s,%s){\\fs3O}" %(O[0]*20+68, O[1]*20+68, O[0]*20+75, O[1]*20+65)) # Centro O
    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,type_m=1) 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:
        #quiz_txt += ("(%s,%s){\\bullet}(%s,%s){\\fs3O}" % # Otros Centros O
        #               (O[0]*20+208+count_vals*140, O[1]*20+68, O[0]*20+215+count_vals*140, O[1]*20+65))
        if v[1] == -1:   # -1 indica simetria centro O
            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
        elif 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
        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
        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
        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
        count_vals += 1
    quiz_txt += "}$$<br/>\n"
    quiz_sol = ""
    for x in range(3):
        if vals_cor[x][1] == -1:   # -1 indica simetria centro O
            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 == -1:   # -1 indica simetria centro O
        pt1_m = (-pt1[0], -pt1[1])
        pt2_m = (-pt2[0], -pt2[1])
    elif 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 main():
    exo = ["\\exercice",
           _(u"Construire la symétrique de chacune des figures par rapport au point O en"),
           _(u"utilisant le quadrillage :\\par "), "\\psset{unit=.9cm}"]
    cor = ["\\exercice*",
           _(u"Construire la symétrique de chacune des figures par rapport au point O en"),
           _(u"utilisant le quadrillage :\\par "), "\\psset{unit=.9cm}"]
    quiz = ["cloze"]
    nbpts = 5
    for i in range(3):
        vals = valeurs_quad(nbpts)
        O = centre_sym(vals)
        txt = place_pts(vals, O)
        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)
        cor.append(place_pts_sym(vals))
        exo.append("\end{pspicture*}")
        cor.append("\end{pspicture*}")
        if i < 2:
            exo.append("\\hfill")
            cor.append("\\hfill")
        quiz_nom = (_(u"Symétrie centrale %s") % str(i+1))
        quiz_exo_cor = _(u"Indique quel c'est le symétrique en ce qui concerne le centre $$O$$ de la forme encadrée de la gauche:<br/>\n")
        quiz_txt, quiz_sol = symetrie_c_quiz(O, vals, nbpts)
        quiz_exo_cor += quiz_txt
        quiz_exo_cor += (_(u"Réponse: La symétrique en ce qui concerne le centre $$O$$ est le {1:MULTICHOICE:%s}") %
                           quiz_sol)
        quiz.append([quiz_nom, quiz_exo_cor, ""])
    return (exo, cor, quiz)