def __init__(self):
super(Toro,self).__init__(u"Curvas tóricas")
tmin, tmax, npuntos = (0, 2 * pi, 3000)
a = 1
b = 0.5
c = .505
def toroParam1(u, v):
return ((a + b * cos(v)) * cos(u), (a + b * cos(v)) * sin(u), b * sin(v))
def toroParam2(u, v):
return ((a + c * cos(v)) * cos(u), (a + c * cos(v)) * sin(u), c * sin(v))
def curvaPlana(t):
return (t, t)
def curvaToro(t):
return toroParam2(*curvaPlana(t))
toro = ParametricPlot3D(toroParam1, (0, 2 * pi, 150), (0, 2 * pi, 100))
toro.setTransparencyType(SoTransparencyType.SORTED_OBJECT_SORTED_TRIANGLE_BLEND)
toro.setTransparency(.4)
curva = Curve3D(curvaToro, (tmin, tmax, npuntos), color=_1(146, 33, 86), width=3, nvertices=1)
curves = []
curves.append( curva )
# Super hack muy malo!!!
ncurves = 17
for i in range(1,ncurves):
curves.append( Curve3D(curvaToro, (tmin, tmax, npuntos),
color=_1((146-i*84)%240, (32+i*128)%250, (86+i*62)%220), width=3, nvertices=1) )
curves[i].hide()
def recalculaCurva(**kargs):
"""a: vueltas horizontales, b: vueltas verticales"""
keys = kargs.keys()
if "a" in keys:
recalculaCurva.a = kargs["a"]
if "b" in keys:
recalculaCurva.b = kargs["b"]
def curvaPlana(t):
return (recalculaCurva.a * t + recalculaCurva.atrans,
recalculaCurva.b * t + recalculaCurva.btrans )
def curvaToro(t):
return toroParam2(*curvaPlana(t))
recalculaCurva.atrans = 0
recalculaCurva.btrans = 0
curva.updatePoints(curvaToro)
for i in range(1,ncurves):
curves[i].hide()
n = gcd( recalculaCurva.a, recalculaCurva.b )
if n > 1 and recalculaCurva.a != 0 and recalculaCurva.b != 0:
self.chbox.setText( u"Ocultar curvas adicionales."
+ u"\nNúmero total de curvas disjuntas: " + str(n) )
self.chbox.setEnabled(True)
#print n
for i in range(1,n):
#if recalculaCurva.a >= recalculaCurva.b:
recalculaCurva.atrans = i*2*pi/recalculaCurva.b
#else:
#recalculaCurva.btrans = i*2*pi/recalculaCurva.b
curves[i].updatePoints(curvaToro)
if not self.chbox.isChecked():
curves[i].show()
else:
self.chbox.setText("Ocultar curvas adicionales")
self.chbox.setEnabled(False)
recalculaCurva.a = 1
recalculaCurva.b = 1
sp1 = SpinBox("a", (0, 20, 1), lambda x: recalculaCurva(a=x), parent=self)
sp2 = SpinBox("b", (0, 20, 1), lambda x: recalculaCurva(b=x), parent=self)
def showExtraCurves():
#recalculaCurva(recalculaCurva.a,recalculaCurva.b)
n = gcd( recalculaCurva.a, recalculaCurva.b )
if n > 1 and recalculaCurva.a != 0 and recalculaCurva.b != 0:
for i in range(1,n):
curves[i].show()
def hideExtraCurves():
for i in range(1,ncurves):
curves[i].hide()
self.chbox = CheckBox( hideExtraCurves, showExtraCurves,
"Ocultar curvas adicionales", state=False )
self.chbox.setEnabled(False)
self.addWidget( self.chbox )
self.addChild(toro)
#self.addChild(curva)
self.addChildren( curves )
curva.animation.setDuration(5000)
#self.setupAnimations([curva])
self.setupAnimations( curves )
#recalculaCurva(1,1)
curva.updatePoints(curvaToro)
def __init__(self, text, ob, state=True, parent=None):
CheckBox.__init__(self, ob.show, ob.hide, text, state)
if parent:
parent.addWidget(self)
class Toro(Page):
u"""
<p>
En un <b>toro</b> hueco hay curvas que rodean tanto al hoyo central
<b>(a)</b> como al hueco <b>(b)</b>. Las mostradas en la interacción
se cierran sin cortarse aunque den varias vueltas en torno al hueco,
al hoyo central o ambos.
<p>
Hay otras curvas que se enredan infinitamente en el toro sin cortarse y
constituyen un <b>conjunto denso</b> en el toro.”
<p>
Con la parametrización del toro<br>
<b>((r cos u + R) cos v, (r cos u + R) sen v, r sen v)</b>,<br>
los puntos de las curvas tóricas mostradas en la interacción satisfacen
<b>v = mu</b>, donde <b>m = b/a</b> es un número racional.
"""
def __init__(self):
super(Toro,self).__init__(u"Curvas tóricas")
tmin, tmax, npuntos = (0, 2 * pi, 3000)
a = 1
b = 0.5
c = .505
def toroParam1(u, v):
return ((a + b * cos(v)) * cos(u), (a + b * cos(v)) * sin(u), b * sin(v))
def toroParam2(u, v):
return ((a + c * cos(v)) * cos(u), (a + c * cos(v)) * sin(u), c * sin(v))
def curvaPlana(t):
return (t, t)
def curvaToro(t):
return toroParam2(*curvaPlana(t))
toro = ParametricPlot3D(toroParam1, (0, 2 * pi, 150), (0, 2 * pi, 100))
toro.setTransparencyType(SoTransparencyType.SORTED_OBJECT_SORTED_TRIANGLE_BLEND)
toro.setTransparency(.4)
curva = Curve3D(curvaToro, (tmin, tmax, npuntos), color=_1(146, 33, 86), width=3, nvertices=1)
curves = []
curves.append( curva )
# Super hack muy malo!!!
ncurves = 17
for i in range(1,ncurves):
curves.append( Curve3D(curvaToro, (tmin, tmax, npuntos),
color=_1((146-i*84)%240, (32+i*128)%250, (86+i*62)%220), width=3, nvertices=1) )
curves[i].hide()
def recalculaCurva(**kargs):
"""a: vueltas horizontales, b: vueltas verticales"""
keys = kargs.keys()
if "a" in keys:
recalculaCurva.a = kargs["a"]
if "b" in keys:
recalculaCurva.b = kargs["b"]
def curvaPlana(t):
return (recalculaCurva.a * t + recalculaCurva.atrans,
recalculaCurva.b * t + recalculaCurva.btrans )
def curvaToro(t):
return toroParam2(*curvaPlana(t))
recalculaCurva.atrans = 0
recalculaCurva.btrans = 0
curva.updatePoints(curvaToro)
for i in range(1,ncurves):
curves[i].hide()
n = gcd( recalculaCurva.a, recalculaCurva.b )
if n > 1 and recalculaCurva.a != 0 and recalculaCurva.b != 0:
self.chbox.setText( u"Ocultar curvas adicionales."
+ u"\nNúmero total de curvas disjuntas: " + str(n) )
self.chbox.setEnabled(True)
#print n
for i in range(1,n):
#if recalculaCurva.a >= recalculaCurva.b:
recalculaCurva.atrans = i*2*pi/recalculaCurva.b
#else:
#recalculaCurva.btrans = i*2*pi/recalculaCurva.b
curves[i].updatePoints(curvaToro)
if not self.chbox.isChecked():
curves[i].show()
else:
self.chbox.setText("Ocultar curvas adicionales")
self.chbox.setEnabled(False)
recalculaCurva.a = 1
recalculaCurva.b = 1
sp1 = SpinBox("a", (0, 20, 1), lambda x: recalculaCurva(a=x), parent=self)
sp2 = SpinBox("b", (0, 20, 1), lambda x: recalculaCurva(b=x), parent=self)
def showExtraCurves():
#recalculaCurva(recalculaCurva.a,recalculaCurva.b)
n = gcd( recalculaCurva.a, recalculaCurva.b )
if n > 1 and recalculaCurva.a != 0 and recalculaCurva.b != 0:
for i in range(1,n):
curves[i].show()
def hideExtraCurves():
for i in range(1,ncurves):
curves[i].hide()
self.chbox = CheckBox( hideExtraCurves, showExtraCurves,
"Ocultar curvas adicionales", state=False )
self.chbox.setEnabled(False)
self.addWidget( self.chbox )
self.addChild(toro)
#self.addChild(curva)
self.addChildren( curves )
curva.animation.setDuration(5000)
#self.setupAnimations([curva])
self.setupAnimations( curves )
#recalculaCurva(1,1)
curva.updatePoints(curvaToro)
def __init__(self, text,ob, state=True, parent = None):
CheckBox.__init__(self,ob.show,ob.hide,text,state)
if parent:
parent.addWidget(self)