def __init__(self):
"""F(x,y)=x^2 + y^2 - z = 0"""
Page.__init__(self, u"Paraboloide Elíptico<br><br>F(x,y)=(x, y, x<sup>2</sup>/a<sup>2</sup> + y<sup>2</sup>/b<sup>2</sup>)")
z = 0.5
par = RevolutionPlot3D(lambda r, t: r ** 2 + z, (0, 1.42), (0, 2 * pi))
x, y, z2, u, v, cose, sen, t = createVars(['x', 'y', 'z', 'u', 'v', 'cos', 'sen', 't'])
mesh1 = Plot3D(lambda x, y, h: h * (x ** 2 + y ** 2 + z - .01), (-1, 1), (-1, 1))
#mesh1.addEqn(x**2+y**2 - z2**2 == 1)
mesh1.addFunction(lambda x, y, h: h * (x ** 2 + y ** 2 + z + .01))
mesh1.setLinesVisible(True)
mesh1.setMeshVisible(False)
mesh1.setBoundingBox(zrange=(-1, 3.0))
par.setAmbientColor(_1(145, 61, 74))
par.setDiffuseColor(_1(145, 61, 74))
par.setSpecularColor(_1(145, 61, 74))
baseplane = BasePlane()
baseplane.setHeight(0)
baseplane.setRange((-2, 2, 7))
self.addChild(par)
self.addChild(mesh1)
self.addChild(baseplane)
def __init__(self):
u"""^2 + y^2 = z^2"""
Page.__init__(self, u"Esfera, parametrización por proyecciones estereográficas")
r = .998
esf = ParametricPlot3D(lambda t, f: (r * sin(t) * cos(f), r * sin(t) * sin(f), r * cos(t)), (0, pi, 70), (0, 2 * pi, 70))
# esf.setAmbientColor(_1(99,136,63))
esf.setDiffuseColor(_1(99, 136, 63))
esf.setSpecularColor(_1(99, 136, 63))
def proyZm1(u, v, t1):
"""proy desde el polo norte al plano z=-1"""
den = u ** 2 + v ** 2 + 4
x = u - t1 * (u - 4 * u / den)
y = v - t1 * (v - 4 * v / den)
z = -1 - t1 * (-2 + 8 / den)
return (x, y, z)
def proyZ1(u, v, t2):
"""proy desde el polo sur al plano z=1"""
den = u ** 2 + v ** 2 + 4
x = u - t2 * (u - 4 * u / den)
y = v - t2 * (v - 4 * v / den)
z = 1 - t2 * (2 - 8 / den)
return (x, y, z)
stereo = ParametricPlot3D(proyZm1, (-3, 3, 70), (-3, 3, 70))
stereo.setLinesVisible(True)
stereo.setMeshVisible(False)
stereo.setMeshDiffuseColor(_1(117, 55, 79))
stereo2 = ParametricPlot3D(proyZ1, (-3, 3, 70), (-3, 3, 70))
stereo2.setLinesVisible(True)
stereo2.setMeshVisible(False)
stereo2.setMeshDiffuseColor(_1(80, 87, 193))
stereo2.setTransparency(0.5)
stereo2.setTransparencyType(8)
baseplane = BasePlane()
baseplane.setHeight(-1.005)
baseplane.setRange((-4, 4, 7))
self.addChild(esf)
self.addChild(stereo2)
self.addChild(stereo)
self.addChild(baseplane)
params = [stereo,stereo2]
## no queremos los controles
for i,p in enumerate(params):
p.parameters['t%d' % (i+1)].hide()
anims = [p.parameters['t%d' % (i+1)].asAnimation() for i,p in enumerate(params)]
self.setupAnimations(anims)
def setupPlanes(self, r0=(-1, 1, 5)):
self.coordPlanes = {
'xy': BasePlane(plane="xy").setDiffuseColor((1, 1, 0)),
'xz': BasePlane(plane="xz").setDiffuseColor((1, 0, 1)),
'yz': BasePlane(plane="yz").setDiffuseColor((0, 1, 1))
}
for p in self.coordPlanes.values():
p.setRange(r0)
p.setHeight(r0[0])
self.addChild(p)
def __init__(self, color, origin, p1, p2):
BaseObject.__init__(self)
self.range = (-1, 1, 10)
self.base_plane = BasePlane()
self.base_plane.setDiffuseColor(color)
self.base_plane.setEmissiveColor(color)
self.separator.addChild(self.base_plane.root)
# local axis
self.localXAxis = Line([], color=(1, 0, 0))
self.localYAxis = Line([], color=(1, 0, 0))
self.separator.addChild(self.localXAxis.root)
self.separator.addChild(self.localYAxis.root)
# calculate the points
self.setPoints(origin, p1, p2)
def __init__(self):
"x^2 + y^2 = z^2"
Page.__init__(self, u"Semicono de revolución<br><br>F(θ,ρ)=(θ,ρ,π/4)")
cono = RevolutionPlot3D(lambda r, t: r + 1, (0, 1), (0, 2 * pi))
cono1 = RevolutionPlot3D(lambda r, t, h: h * (r + 1), (0.05, 1), (0, 2 * pi)) #@UndefinedVariable
cono1.setLinesVisible(True)
cono1.setMeshVisible(False)
cono.setDiffuseColor(_1(149, 24, 82))
cono.setSpecularColor(_1(149, 24, 82))
baseplane = BasePlane()
baseplane.setHeight(0)
baseplane.setRange((-2, 2, 7))
self.addChild(cono)
self.addChild(cono1)
self.addChild(baseplane)
def __init__(self):
"x^2 - y^2 - z = 0"
Page.__init__(self, u"Paraboloide Hiperbólico<br><br>F(x,y)=(x, y, x<sup>2</sup>-y<sup>2</sup>)")
z = 1.5
parab = Plot3D(lambda x, y: x ** 2 - y ** 2 + z, (-1, 1), (-1, 1))
parab1 = Plot3D(lambda x, y, h: h * (x ** 2 - y ** 2 + z), (-1, 1), (-1, 1)) #@UndefinedVariable
parab1.setLinesVisible(True)
parab1.setMeshVisible(False)
parab.setAmbientColor(_1(145, 61 , 74))
parab.setDiffuseColor(_1(127, 119, 20))
parab.setSpecularColor(_1(145, 61 , 74))
baseplane = BasePlane()
baseplane.setHeight(0)
baseplane.setRange((-2, 2, 7))
self.addChild(parab)
self.addChild(parab1)
self.addChild(baseplane)
def __init__(self):
"""F(x,y)=x^2 + y^2 - z = 0"""
Page.__init__(
self,
u"Paraboloide Elíptico<br><br>F(x,y)=(x, y, x<sup>2</sup>/a<sup>2</sup> + y<sup>2</sup>/b<sup>2</sup>)"
)
z = 0.5
par = RevolutionPlot3D(lambda r, t: r**2 + z, (0, 1), (0, 2 * pi))
x, y, z2, u, v, cose, sen, t = createVars(
['x', 'y', 'z', 'u', 'v', 'cos', 'sen', 't'])
mesh1 = Plot3D(lambda x, y, h: h * (x**2 + y**2 + z - .01), (-1, 1),
(-1, 1))
mesh1.addEqn(x**2 + y**2 - z2**2 == 1)
mesh1.addFunction(lambda x, y, h: h * (x**2 + y**2 + z + .01))
mesh1.setLinesVisible(True)
mesh1.setMeshVisible(False)
mesh1.setBoundingBox(zrange=(-1, 1.5))
par.setAmbientColor(_1(145, 61, 74))
par.setDiffuseColor(_1(145, 61, 74))
par.setSpecularColor(_1(145, 61, 74))
baseplane = BasePlane()
baseplane.setHeight(0)
baseplane.setRange((-2, 2, 7))
self.addChild(par)
self.addChild(mesh1)
self.addChild(baseplane)
class Plane(BaseObject):
"""A plane that contains the points: origin, p1, p2 """
def __init__(self, color, origin, p1, p2):
BaseObject.__init__(self)
self.range = (-1, 1, 10)
self.base_plane = BasePlane()
self.base_plane.setDiffuseColor(color)
self.base_plane.setEmissiveColor(color)
self.separator.addChild(self.base_plane.root)
# local axis
self.localXAxis = Line([], color=(1, 0, 0))
self.localYAxis = Line([], color=(1, 0, 0))
self.separator.addChild(self.localXAxis.root)
self.separator.addChild(self.localYAxis.root)
# calculate the points
self.setPoints(origin, p1, p2)
def setPoints(self, origin, vector1, vector2):
v1 = (vector1 - origin)
v2 = (vector2 - origin)
## the plane generated by {v1, v2}
def plane(h, t):
return Vec3(origin) + h * v1 + t * v2
self.base_plane.setRange(self.range, plane=plane)
## lines along the generators
t_min, t_max, n = self.range
self.localXAxis.setPoints(
[plane(*pt) for pt in [(t_min, 0), (t_max, 0)]])
self.localYAxis.setPoints(
[plane(*pt) for pt in [(0, t_min), (0, t_max)]])
class Plane(BaseObject):
"""A plane that contains the points: origin, p1, p2 """
def __init__(self, color, origin, p1, p2):
BaseObject.__init__(self)
self.range = (-1, 1, 10)
self.base_plane = BasePlane()
self.base_plane.setDiffuseColor(color)
self.base_plane.setEmissiveColor(color)
self.separator.addChild(self.base_plane.root)
# local axis
self.localXAxis = Line([], color=(1, 0, 0))
self.localYAxis = Line([], color=(1, 0, 0))
self.separator.addChild(self.localXAxis.root)
self.separator.addChild(self.localYAxis.root)
# calculate the points
self.setPoints(origin, p1, p2)
def setPoints(self, origin, vector1, vector2):
v1 = (vector1 - origin)
v2 = (vector2 - origin)
## the plane generated by {v1, v2}
def plane(h, t):
return Vec3(origin) + h * v1 + t * v2
self.base_plane.setRange(self.range, plane=plane)
## lines along the generators
t_min, t_max, n = self.range
self.localXAxis.setPoints([plane(*pt) for pt in [(t_min, 0), (t_max, 0)]])
self.localYAxis.setPoints([plane(*pt) for pt in [(0, t_min), (0, t_max)]])
def __init__(self):
"x^4 + 2x^2y^2 + y^4 -z = 0"
Page.__init__(
self,
u"Superficie cuártica<br><br>F(x,y)=(x,y,x<sup>4</sup>+2x<sup>2</sup>y<sup>2</sup>+y<sup>4</sup>)"
)
# cuart = Plot3D(lambda x,y: x**4 + 2*x**2*y**2 + y**4 + 1, (-1,1),(-1,1))
cuart = RevolutionPlot3D(lambda r, t: r**4 + 1, (0, 1), (0, 2 * pi))
# cuart.setScaleFactor((1,1,.6))
mesh1 = Plot3D(lambda x, y, h: h * (x**4 + 2 * x**2 * y**2 + y**4 + 1),
(-1, 1), (-1, 1))
mesh1.setLinesVisible(True)
mesh1.setMeshVisible(False)
mesh1.setBoundingBox(zrange=(-1, 2))
# cuart.setAmbientColor(_1(168,211,8))
cuart.setDiffuseColor(_1(168, 211, 8))
cuart.setSpecularColor(_1(168, 211, 8))
baseplane = BasePlane()
baseplane.setHeight(0)
baseplane.setRange((-2, 2, 7))
self.addChild(cuart)
self.addChild(mesh1)
self.addChild(baseplane)
def __init__(self):
"x^3 - 3xy^2 - z = 0"
Page.__init__(self, u"Silla del mono<br><br>F(x,y)=(x, y, x<sup>3</sup> - 3xy<sup>2</sup>)")
silla = Plot3D(lambda x, y: x ** 3 - 3 * x * y ** 2 + 2.5, (-1, 1), (-1, 1))
silla.setAmbientColor(_1(151, 139, 125))
silla.setDiffuseColor(_1(151, 139, 125))
silla.setSpecularColor(_1(151, 139, 125))
# silla.setShininess(1)
# plano.setScaleFactor((1,1,.6))
def cVec(pto):
"pto: Vec3"
return pto * 1.1
silla.addVectorField(cVec)
# def setXscale(t):
# scale.scaleFactor = (1,1,t)
# Slider(
# rangep=('z', .2, 1, 1, 20),
# func=setXscale,
# parent=self
# )
#
silla1 = Plot3D(lambda x, y, h: h * (x ** 3 - 3 * x * y ** 2 + 2.5), (-1, 1), (-1, 1)) #@UndefinedVariable
# silla1.setScaleFactor((1,1,.6))
silla1.setLinesVisible(True)
silla1.setMeshVisible(False)
baseplane = BasePlane()
baseplane.setHeight(0)
baseplane.setRange((-2, 2, 7))
self.addChild(silla)
self.addChild(silla1)
self.addChild(baseplane)
def __init__(self):
#u"""x^2 + y^2 + z^2 = 1"""
super(EsferaCasquetes,self).__init__(u"Otro atlas de la esfera")
r = .98
esf = ParametricPlot3D(lambda t, f: (r * sin(t) * cos(f), r * sin(t) * sin(f), r * cos(t)), (0, pi, 70), (0, 2 * pi, 70))
esf.setDiffuseColor(_1(99, 136, 63))
esf.setSpecularColor(_1(99, 136, 63))
pars = [
lambda u,v, t1: (u, v, 1.5-t1*(1.5-sqrt(1 - u**2 - v**2))),
lambda u,v, t2: (u, v, -1.5-t2*(-1.5+sqrt(1 - u**2 - v**2))),
lambda u,v, t3: (u, 1.5-t3*(1.5-sqrt(1 - u**2 - v**2)),v),
lambda u,v, t4: (u, -1.5-t4*(-1.5+sqrt(1 - u**2 - v**2)),v),
lambda u,v, t5: (1.5-t5*(1.5-sqrt(1 - u**2 - v**2)),u,v),
lambda u,v, t6, : (-1.5-t6*(-1.5+sqrt(1 - u**2 - v**2)),u,v)
]
d = 0.707106
colores = [(0,0,1),(0,0,1),(0,1,0),(0,1,0),(1,0,0),(1,0,0)]
planos = [ParametricPlot3D(par, (-d, d, 40), (-d, d, 40)).setLinesVisible(True).setMeshVisible(False).setMeshDiffuseColor(colores[i]) for i,par in enumerate(pars)]
baseplane = BasePlane()
baseplane.setHeight(-1.005)
baseplane.setRange((-2,2, 7))
self.addChild(esf)
for p in planos:
self.addChild(p)
self.addChild(baseplane)
## no queremos los controles
for i,plano in enumerate(planos):
plano.parameters['t%d' % (i+1)].hide()
anims = [plano.parameters['t%d' % (i+1)].asAnimation() for i,plano in enumerate(planos)]
self.setupAnimations(anims)
def __init__(self):
"x^4 + 2x^2y^2 + y^4 -z = 0"
Page.__init__(self, u"Superficie cuártica<br><br>F(x,y)=(x,y,x<sup>4</sup>+2x<sup>2</sup>y<sup>2</sup>+y<sup>4</sup>)")
# cuart = Plot3D(lambda x,y: x**4 + 2*x**2*y**2 + y**4 + 1, (-1,1),(-1,1))
cuart = RevolutionPlot3D(lambda r, t: r ** 4 + 1, (0, 1.4), (0, 2 * pi))
# cuart.setScaleFactor((1,1,.6))
mesh1 = Plot3D(lambda x, y, h: h * (x ** 4 + 2 * x ** 2 * y ** 2 + y ** 4 + 0.9), (-1, 1), (-1, 1))
mesh1.setLinesVisible(True)
mesh1.setMeshVisible(False)
mesh1.setBoundingBox(zrange=(-1, 6))
# cuart.setAmbientColor(_1(168,211,8))
cuart.setDiffuseColor(_1(168, 211, 8))
cuart.setSpecularColor(_1(168, 211, 8))
baseplane = BasePlane()
baseplane.setHeight(0)
baseplane.setRange((-2, 2, 7))
self.addChild(cuart)
self.addChild(mesh1)
self.addChild(baseplane)
def __init__(self, color, origin, p1, p2):
BaseObject.__init__(self)
self.range = (-1, 1, 10)
self.base_plane = BasePlane()
self.base_plane.setDiffuseColor(color)
self.base_plane.setEmissiveColor(color)
self.separator.addChild(self.base_plane.root)
# local axis
self.localXAxis = Line([], color=(1, 0, 0))
self.localYAxis = Line([], color=(1, 0, 0))
self.separator.addChild(self.localXAxis.root)
self.separator.addChild(self.localYAxis.root)
# calculate the points
self.setPoints(origin, p1, p2)
def __init__(self):
#u"""x^2 + y^2 + z^2 = 1"""
super(EsferaCasquetes, self).__init__(u"Otro atlas de la esfera")
r = .998
esf = ParametricPlot3D(
lambda t, f:
(r * sin(t) * cos(f), r * sin(t) * sin(f), r * cos(t)),
(0, pi, 70), (0, 2 * pi, 70))
esf.setDiffuseColor(_1(99, 136, 63))
esf.setSpecularColor(_1(99, 136, 63))
pars = [
lambda u, v, t1: (u, v, 1.5 - t1 * (1.5 - sqrt(1 - u**2 - v**2))),
lambda u, v, t2: (u, v, -1 - t2 * (-1 + sqrt(1 - u**2 - v**2))),
lambda u, v, t3: (u, 1.5 - t3 * (1.5 - sqrt(1 - u**2 - v**2)), v),
lambda u, v, t4: (u, -1.5 - t4 *
(-1.5 + sqrt(1 - u**2 - v**2)), v),
lambda u, v, t5: (1.5 - t5 * (1.5 - sqrt(1 - u**2 - v**2)), u, v),
lambda u, v, t6, : (-1.5 - t6 *
(-1.5 + sqrt(1 - u**2 - v**2)), u, v)
]
d = .7
colores = [(0, 0, 1), (0, 0, 1), (0, 1, 0), (0, 1, 0), (1, 0, 0),
(1, 0, 0)]
planos = [
ParametricPlot3D(par, (-d, d, 40), (-d, d, 40)).setLinesVisible(
True).setMeshVisible(False).setMeshDiffuseColor(colores[i])
for i, par in enumerate(pars)
]
baseplane = BasePlane()
baseplane.setHeight(-1.005)
baseplane.setRange((-2, 2, 7))
self.addChild(esf)
for p in planos:
self.addChild(p)
self.addChild(baseplane)
## no queremos los controles
for i, plano in enumerate(planos):
plano.parameters['t%d' % (i + 1)].hide()
anims = [
plano.parameters['t%d' % (i + 1)].asAnimation()
for i, plano in enumerate(planos)
]
self.setupAnimations(anims)
def __init__(self):
"x^3 - 3xy^2 - z = 0"
Page.__init__(
self,
u"Silla del mono<br><br>F(x,y)=(x, y, x<sup>3</sup> - 3xy<sup>2</sup>)"
)
silla = Plot3D(lambda x, y: x**3 - 3 * x * y**2 + 2.5, (-1, 1),
(-1, 1))
silla.setAmbientColor(_1(151, 139, 125))
silla.setDiffuseColor(_1(151, 139, 125))
silla.setSpecularColor(_1(151, 139, 125))
# silla.setShininess(1)
# plano.setScaleFactor((1,1,.6))
def cVec(pto):
"pto: Vec3"
return pto * 1.1
silla.addVectorField(cVec)
# def setXscale(t):
# scale.scaleFactor = (1,1,t)
# Slider(
# rangep=('z', .2, 1, 1, 20),
# func=setXscale,
# parent=self
# )
#
silla1 = Plot3D(lambda x, y, h: h * (x**3 - 3 * x * y**2 + 2.5),
(-1, 1), (-1, 1)) #@UndefinedVariable
# silla1.setScaleFactor((1,1,.6))
silla1.setLinesVisible(True)
silla1.setMeshVisible(False)
baseplane = BasePlane()
baseplane.setHeight(0)
baseplane.setRange((-2, 2, 7))
self.addChild(silla)
self.addChild(silla1)
self.addChild(baseplane)
def __init__(self):
"x^2 + y^2 = z^2"
Page.__init__(
self,
u"Semicono de revolución<br><br>F(θ,ρ)=(θ,ρ,π/4)"
)
cono = RevolutionPlot3D(lambda r, t: r + 1, (0, 1), (0, 2 * pi))
cono1 = RevolutionPlot3D(lambda r, t, h: h * (r + 1), (0.05, 1),
(0, 2 * pi)) #@UndefinedVariable
cono1.setLinesVisible(True)
cono1.setMeshVisible(False)
cono.setDiffuseColor(_1(149, 24, 82))
cono.setSpecularColor(_1(149, 24, 82))
baseplane = BasePlane()
baseplane.setHeight(0)
baseplane.setRange((-2, 2, 7))
self.addChild(cono)
self.addChild(cono1)
self.addChild(baseplane)
def __init__(self):
"x^2 - y^2 - z = 0"
Page.__init__(
self,
u"Paraboloide Hiperbólico<br><br>F(x,y)=(x, y, x<sup>2</sup>-y<sup>2</sup>)"
)
z = 1.5
parab = Plot3D(lambda x, y: x**2 - y**2 + z, (-1, 1), (-1, 1))
parab1 = Plot3D(lambda x, y, h: h * (x**2 - y**2 + z), (-1, 1),
(-1, 1)) #@UndefinedVariable
parab1.setLinesVisible(True)
parab1.setMeshVisible(False)
parab.setAmbientColor(_1(145, 61, 74))
parab.setDiffuseColor(_1(127, 119, 20))
parab.setSpecularColor(_1(145, 61, 74))
baseplane = BasePlane()
baseplane.setHeight(0)
baseplane.setRange((-2, 2, 7))
self.addChild(parab)
self.addChild(parab1)
self.addChild(baseplane)
def __init__(self):
"""x^2 - y^2 - z = 0"""
Page.__init__(self, u"Paraboloide hiperbólico<br><br>x<sup>2</sup>/a<sup>2</sup> - y<sup>2</sup>/b<sup>2</sup> = z")
z = 1.5
def fn(x, y):
return x ** 2 - y ** 2 + z
def polar(function):
def polar_fn(r, t):
x = r * cos(t)
y = r * sin(t)
return x, y, function(x, y)
return polar_fn
paraboloid = ParametricPlot3D(polar(fn), (.001, 1, 20), (0, 2 * pi, 60))
paraboloid. \
setAmbientColor(_1(145, 61, 74)). \
setDiffuseColor(_1(127, 119, 20)). \
setSpecularColor(_1(145, 61, 74))
base_plane = BasePlane()
base_plane.setHeight(0)
base_plane.setRange((-2, 2, 7))
## the hiperbolic paraboloid in parametric form
def fn_par(x,y): return Vec3(x, y, x ** 2 - y ** 2 + z)
## its derivatives
def fn_x(x,y): return Vec3(1, 0, 2 * x)
def fn_y(x,y): return Vec3(0, 1, -2 * y)
tangent_plane = TangentPlane2(fn_par, fn_x, fn_y, (0, 0), _1(252, 250, 225))
tangent_plane.setRange((-1.2, 1.2, 7))
self.addChild(paraboloid)
self.addChild(base_plane)
self.addChild(tangent_plane)
def spiral(t):
c = t / (2 * pi)
t2 = t * 2
return c * cos(t2), c * sin(t2)
animate_points = 200
def animate_plane(n):
tangent_plane.setLocalOrigin(spiral(2 * pi * n / float(animate_points)))
def animate_plane_2(t):
tangent_plane.setLocalOrigin(spiral(t))
a1 = Animation(animate_plane, (10000, 0, animate_points))
Slider(('t', 0, 2 * pi, 0, animate_points), animate_plane_2, duration=10000, parent=self)
self.setupAnimations([a1])
def __init__(self):
u"""^2 + y^2 = z^2"""
Page.__init__(
self, u"Esfera, parametrización por proyecciones estereográficas")
r = .998
esf = ParametricPlot3D(
lambda t, f:
(r * sin(t) * cos(f), r * sin(t) * sin(f), r * cos(t)),
(0, pi, 70), (0, 2 * pi, 70))
# esf.setAmbientColor(_1(99,136,63))
esf.setDiffuseColor(_1(99, 136, 63))
esf.setSpecularColor(_1(99, 136, 63))
def proyZm1(u, v, t1):
"""proy desde el polo norte al plano z=-1"""
den = u**2 + v**2 + 4
x = u - t1 * (u - 4 * u / den)
y = v - t1 * (v - 4 * v / den)
z = -1 - t1 * (-2 + 8 / den)
return (x, y, z)
def proyZ1(u, v, t2):
"""proy desde el polo sur al plano z=1"""
den = u**2 + v**2 + 4
x = u - t2 * (u - 4 * u / den)
y = v - t2 * (v - 4 * v / den)
z = 1 - t2 * (2 - 8 / den)
return (x, y, z)
stereo = ParametricPlot3D(proyZm1, (-3, 3, 70), (-3, 3, 70))
stereo.setLinesVisible(True)
stereo.setMeshVisible(False)
stereo.setMeshDiffuseColor(_1(117, 55, 79))
stereo2 = ParametricPlot3D(proyZ1, (-3, 3, 70), (-3, 3, 70))
stereo2.setLinesVisible(True)
stereo2.setMeshVisible(False)
stereo2.setMeshDiffuseColor(_1(80, 87, 193))
stereo2.setTransparency(0.5)
stereo2.setTransparencyType(8)
baseplane = BasePlane()
baseplane.setHeight(-1.005)
baseplane.setRange((-4, 4, 7))
self.addChild(esf)
self.addChild(stereo2)
self.addChild(stereo)
self.addChild(baseplane)
params = [stereo, stereo2]
## no queremos los controles
for i, p in enumerate(params):
p.parameters['t%d' % (i + 1)].hide()
anims = [
p.parameters['t%d' % (i + 1)].asAnimation()
for i, p in enumerate(params)
]
self.setupAnimations(anims)
def __init__(self):
"""x^2 - y^2 - z = 0"""
Page.__init__(self, u"Paraboloide hiperbólico<br><br>x<sup>2</sup>/a<sup>2</sup> - y<sup>2</sup>/b<sup>2</sup> = z")
z = 1.5
def fn(x, y):
return x ** 2 - y ** 2 + z
def polar(function):
def polar_fn(r, t):
x = r * cos(t)
y = r * sin(t)
return x, y, function(x, y)
return polar_fn
paraboloid = ParametricPlot3D(polar(fn), (.001, 1, 20), (0, 2 * pi, 60))
paraboloid. \
setAmbientColor(_1(145, 61, 74)). \
setDiffuseColor(_1(127, 119, 20)). \
setSpecularColor(_1(145, 61, 74))
base_plane = BasePlane()
base_plane.setHeight(0)
base_plane.setRange((-2, 2, 7))
## the hiperbolic paraboloid in parametric form
def fn_par(x,y): return Vec3(x, y, x ** 2 - y ** 2 + z)
## its derivatives
def fn_x(x,y): return Vec3(1, 0, 2 * x)
def fn_y(x,y): return Vec3(0, 1, -2 * y)
tangent_plane = TangentPlane2(fn_par, fn_x, fn_y, (0, 0), _1(252, 250, 225))
tangent_plane.setRange((-1.2, 1.2, 7))
self.addChild(paraboloid)
self.addChild(base_plane)
self.addChild(tangent_plane)
def spiral(t):
c = t / (2 * pi)
t2 = t * 2
return c * cos(t2), c * sin(t2)
animate_points = 200
def animate_plane(n):
tangent_plane.setLocalOrigin(spiral(2 * pi * n / float(animate_points)))
def animate_plane_2(t):
tangent_plane.setLocalOrigin(spiral(t))
a1 = Animation(animate_plane, (10000, 0, animate_points))
Slider(('t', 0, 2 * pi, 0, animate_points), animate_plane_2, duration=10000, parent=self)
self.setupAnimations([a1])
