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from math import *
from kandinsky import *
from ion import *
from time import sleep


anglePerspective=pi/6
ko=2**(-.5)

def clear():
  fill_rect(0,0,320,240,color(255,255,255))

def drawl(A,B):
  x1=round(A[0])
  x2=round(B[0])
  y1=round(A[1])
  y2=round(B[1])
  if x1>x2:
    x1,y1,x2,y2=x2,y2,x1,y1
  if x1==x2:
    for i in range(min(y1,y2),max(y1,y2)+1):
      set_pixel(x1,i,color(0,0,0))
    return
  a=(y2-y1)/(x2-x1)
  if a<=1 and a>=-1:
    for i in range(x1,x2+1):
      set_pixel(i,y1+round((i-x1)*a),color(0,0,0))
    return
  if y1>y2:
    x1,y1,x2,y2=x2,y2,x1,y1
  for i in range(y1,y2+1):
    set_pixel(round(i/a+x1-y1/a),i,color(0,0,0))

def c3d22d(x,y,z,rot1,rot2,rot3):
  x,y,z=rotate(x,y,z,rot1,rot2,rot3)
  x2=x+ko*y*cos(anglePerspective)
  y2=-z-ko*y*sin(anglePerspective)
  return(x2*70+150,y2*70+100)

def rotate(x,y,z,rot1,rot2,rot3):
  #Rotation autour de l'axe Ox
  nx=x
  ny=cos(rot1)*y-sin(rot1)*z
  nz=sin(rot1)*y+cos(rot1)*z
  x,y,z=nx,ny,nz
  
  #Rotation autour de l'axe Oy
  nx=cos(rot2)*x+sin(rot2)*z
  ny=y
  nz=-sin(rot2)*x+cos(rot2)*z
  x,y,z=nx,ny,nz
  
  #Rotation autour de l'axe Oz
  nx=cos(rot3)*x-sin(rot3)*y
  ny=sin(rot3)*x+cos(rot3)*y
  nz=z
  x,y,z=nx,ny,nz
  
  return x,y,z

def drawcube(rot1,rot2,rot3):
  
  draw_string("x",round(c3d22d(1,0,0,rot1,rot2,rot3)[0]),round(c3d22d(1,0,0,rot1,rot2,rot3)[1]))
  draw_string("y",round(c3d22d(0,1,0,rot1,rot2,rot3)[0]),round(c3d22d(0,1,0,rot1,rot2,rot3)[1]))
  draw_string("z",round(c3d22d(0,0,1,rot1,rot2,rot3)[0]),round(c3d22d(0,0,1,rot1,rot2,rot3)[1]))


  drawl(c3d22d(-1,-1,-1,rot1,rot2,rot3),c3d22d(-1,-1,1,rot1,rot2,rot3))
  drawl(c3d22d(-1,-1,-1,rot1,rot2,rot3),c3d22d(-1,1,-1,rot1,rot2,rot3))
  drawl(c3d22d(-1,-1,-1,rot1,rot2,rot3),c3d22d(1,-1,-1,rot1,rot2,rot3))
  
  drawl(c3d22d(-1,-1,1,rot1,rot2,rot3),c3d22d(-1,1,1,rot1,rot2,rot3))
  drawl(c3d22d(-1,-1,1,rot1,rot2,rot3),c3d22d(1,-1,1,rot1,rot2,rot3))

  drawl(c3d22d(-1,1,1,rot1,rot2,rot3),c3d22d(-1,1,-1,rot1,rot2,rot3))
  drawl(c3d22d(-1,1,1,rot1,rot2,rot3),c3d22d(1,1,1,rot1,rot2,rot3))

  drawl(c3d22d(1,1,1,rot1,rot2,rot3),c3d22d(1,1,-1,rot1,rot2,rot3))
  drawl(c3d22d(1,1,1,rot1,rot2,rot3),c3d22d(1,-1,1,rot1,rot2,rot3))
  
  drawl(c3d22d(1,1,-1,rot1,rot2,rot3),c3d22d(1,-1,-1,rot1,rot2,rot3))
  drawl(c3d22d(1,1,-1,rot1,rot2,rot3),c3d22d(-1,1,-1,rot1,rot2,rot3))
  drawl(c3d22d(1,-1,-1,rot1,rot2,rot3),c3d22d(1,-1,1,rot1,rot2,rot3))

  
  drawl(c3d22d(0,0,-1,rot1,rot2,rot3),c3d22d(0,0,1,rot1,rot2,rot3))
  drawl(c3d22d(0,-1,0,rot1,rot2,rot3),c3d22d(0,1,0,rot1,rot2,rot3))
  drawl(c3d22d(-1,0,0,rot1,rot2,rot3),c3d22d(1,0,0,rot1,rot2,rot3))


def x(t,u):
  return cos(t)*cos(u)
def y(t,u):
  return cos(t)*sin(u)
def z(t,u):
  return sin(t)

def dynamicPlot():
  print("Cette fonction va créer un\nobjet 3d autour duquel vous\npourrez pivoter. Renseignez\nles données, puis l'objet\napparaîtra.Vous pourrez\nutiliser les touches de la\nligne de la touche Shift pour\nle pivoter autour d'un axe.")
  broken=False
  modified=True
  rot1,rot2,rot3=0,0,0
  nbo=int(input("Combien d'objets? 1+"))
  cara_obj=[]
  for itobj in range(nbo):
    print("Définissons l'objet", itobj)
    cara_obj.append(askInfos())
  gr=float(input("zoom (1 conseillé) "))
  while not broken:
    if modified:
      clear()
      for obj in cara_obj:
        xa,ya,za,tmin,tmax,umin,umax,nbstep,maillage=obj
        plot(xa,ya,za,tmin,tmax,umin,umax,rot1,rot2,rot3,nbstep,maillage,gr)
      modified=False
    if keydown(KEY_SHIFT):
      rot1-=.1
      modified=True
    if keydown(KEY_ALPHA):
      rot1+=.1
      modified=True
    if keydown(KEY_XNT):
      rot2-=.1
      modified=True
    if keydown(KEY_VAR):
      rot2+=.1
      modified=True
    if keydown(KEY_TOOLBOX):
      rot3-=.1
      modified=True
    if keydown(KEY_BACKSPACE):
      rot3+=.1
      modified=True
    if keydown(KEY_OK) or keydown(KEY_EXE):
      broken=True
    sleep(.1)
  


def askInfos():
  xas="lambda t,u: "+input("x(t,u)=")
  xa=eval(xas)
  yas="lambda t,u: "+input("y(t,u)=")
  ya=eval(yas)
  zas="lambda t,u: "+input("z(t,u)=")
  za=eval(zas)
  tmin=float(input("tmin "))
  tmax=float(input("tmax "))
  umin=float(input("umin "))
  umax=float(input("umax "))
  nbstep=float(input("precision (20 conseillé) "))
  return xa,ya,za,tmin,tmax,umin,umax,nbstep,1;


def plot(x,y,z,tmin,tmax,umin,umax,rot1=0,rot2=0,rot3=0,nbstep=100,maillage=False,gr=1,cl=(0,0,0)):
  color(cl)
  drawcube(rot1,rot2,rot3)
  ts=(tmax-tmin)/nbstep
  us=(umax-umin)/nbstep
  t=tmin
  if not maillage:
    while t<=tmax:
      u=umin-us
      while u<umax:
        u+=us
        try:
          absc3d=x(t,u)/gr
          ordo3d=y(t,u)/gr
          cote3d=z(t,u)/gr
        except:
          continue
        if abs(absc3d)<=1 and abs(ordo3d)<=1 and abs(cote3d)<=1:
          absc2d,ordo2d=c3d22d(absc3d,ordo3d,cote3d,rot1,rot2,rot3)
          if type(absc2d)!=complex and type(ordo2d)!=complex:
            set_pixel(round(absc2d),round(ordo2d),color(0,0,0))
      t+=ts
  else:
    while t<=tmax:
      u=umin-us
      while u<umax:
        u+=us
        try:
          absc3dP=x(t,u)/gr
          ordo3dP=y(t,u)/gr
          cote3dP=z(t,u)/gr
        except:
          continue
        if abs(absc3dP)<=1 and abs(ordo3dP)<=1 and abs(cote3dP)<=1:
          try:
            absc3dT=x(t+ts,u)/gr
            ordo3dT=y(t+ts,u)/gr
            cote3dT=z(t+ts,u)/gr
            absc3dU=x(t,u+us)/gr
            ordo3dU=y(t,u+us)/gr
            cote3dU=z(t,u+us)/gr
          except:
            continue
          if abs(absc3dT)<=1 and abs(ordo3dT)<=1 and abs(cote3dT)<=1 and t+ts<=tmax:
            absc2d1,ordo2d1=c3d22d(absc3dP,ordo3dP,cote3dP,rot1,rot2,rot3)
            absc2d2,ordo2d2=c3d22d(absc3dT,ordo3dT,cote3dT,rot1,rot2,rot3)
            if type(absc2d1)!=complex and type(ordo2d1)!=complex and type(absc2d2)!=complex and type(ordo2d2)!=complex:
              drawl((absc2d1,ordo2d1),(absc2d2,ordo2d2))
          if abs(absc3dU)<=1 and abs(ordo3dU)<=1 and abs(cote3dU)<=1 and u+us<=umax:
            absc2d1,ordo2d1=c3d22d(absc3dP,ordo3dP,cote3dP,rot1,rot2,rot3)
            absc2d2,ordo2d2=c3d22d(absc3dU,ordo3dU,cote3dU,rot1,rot2,rot3)
            if type(absc2d1)!=complex and type(ordo2d1)!=complex and type(absc2d2)!=complex and type(ordo2d2)!=complex:
              drawl((absc2d1,ordo2d1),(absc2d2,ordo2d2))
      t+=ts