Parametric Geometric Objects

Creating parametric objects

# sphinx_gallery_thumbnail_number = 12
import pyvista as pv
from math import pi

This example demonstrates how to plot parametric objects using pyvista

Supertoroid

supertoroid = pv.ParametricSuperToroid(n1=0.5)
supertoroid.plot(color="tan", smooth_shading=True)

Out:

[(4.861252979770378, 4.8614418072850265, 4.861252979770378),
 (0.0, 0.0001888275146484375, 0.0),
 (0.0, 0.0, 1.0)]

Parametric Ellipsoid

# Ellipsoid with a long x axis
ellipsoid = pv.ParametricEllipsoid(10, 5, 5)
ellipsoid.plot(color="tan")

Out:

[(27.314664072661017, 27.315922684340094, 27.315922684340094),
 (-0.0012586116790771484, 0.0, 0.0),
 (0.0, 0.0, 1.0)]

Partial Parametric Ellipsoid

# cool plotting direction
cpos = [
    (21.9930, 21.1810, -30.3780),
    (-1.1640, -1.3098, -0.1061),
    (0.8498, -0.2515, 0.4631),
]


# half ellipsoid
part_ellipsoid = pv.ParametricEllipsoid(10, 5, 5, max_v=pi / 2)
part_ellipsoid.plot(color="tan", smooth_shading=True, cpos=cpos)

Out:

[(21.993, 21.181, -30.378),
 (-1.164, -1.3098, -0.1061),
 (0.8498535849578507, -0.2515158585748405, 0.4631292012167341)]

Pseudosphere

pseudosphere = pv.ParametricPseudosphere()
pseudosphere.plot(color="tan", smooth_shading=True)

Out:

[(9.462755175257607, 9.462755175257607, 9.462503792668267),
 (0.0, 0.0, -0.00025138258934020996),
 (0.0, 0.0, 1.0)]

Bohemian Dome

bohemiandome = pv.ParametricBohemianDome()
bohemiandome.plot(color="tan")

Out:

[(5.110157436636874, 5.109779841212222, 5.11003156652827),
 (0.0, -0.0003775954246520996, -0.00012587010860443115),
 (0.0, 0.0, 1.0)]

Bour

bour = pv.ParametricBour()
bour.plot(color="tan")

Out:

[(4.841760795218481, 4.844779532057776, 4.470163982016577),
 (-0.0030187368392944336, 0.0, -0.37461555004119873),
 (0.0, 0.0, 1.0)]

Boy’s Surface

boy = pv.ParametricBoy()
boy.plot(color="tan")

Out:

[(2.864744569020921, 3.3467303764397442, 3.496735627608949),
 (-0.4821150302886963, -0.00012922286987304688, 0.14987602829933167),
 (0.0, 0.0, 1.0)]

Catalan Minimal

catalanminimal = pv.ParametricCatalanMinimal()
catalanminimal.plot(color="tan")

Out:

[(31.542660237102616, 32.54206812456142, 31.542660237102616),
 (0.0, 0.9994078874588013, 0.0),
 (0.0, 0.0, 1.0)]

Conic Spiral

conicspiral = pv.ParametricConicSpiral()
conicspiral.plot(color="tan")

Out:

[(1.4978023605683783, 1.947848475191925, 1.9472122701147536),
 (-0.4000125899910927, 0.05003352463245392, 0.04939731955528259),
 (0.0, 0.0, 1.0)]

Cross Cap

crosscap = pv.ParametricCrossCap()
crosscap.plot(color="tan")

Out:

[(3.8626410496722956, 3.8628927898895045, 3.8628927898895045),
 (-0.0002517402172088623, 0.0, 0.0),
 (0.0, 0.0, 1.0)]

Dini

dini = pv.ParametricDini()
dini.plot(color="tan")

Out:

[(12.702617897617449, 10.672241344081987, 10.672493054496874),
 (2.0303765535354614, 0.0, 0.0002517104148864746),
 (0.0, 0.0, 1.0)]

Enneper

enneper = pv.ParametricEnneper()
enneper.plot(cpos="yz")

Out:

[(42.946638627281644, 0.0, 0.0),
 (0.0, 0.0, 0.0),
 (0.0, 0.0, 1.0)]

Figure-8 Klein

figure8klein = pv.ParametricFigure8Klein()
figure8klein.plot()

Out:

[(6.241280195618312, 6.241271850968044, 6.471927580738704),
 (0.0, -8.344650268554688e-06, 0.23064738512039185),
 (0.0, 0.0, 1.0)]

Henneberg

henneberg = pv.ParametricHenneberg()
henneberg.plot(color="tan")

Out:

[(30.00610627059714, 30.004212273404757, 30.004212273404757),
 (0.0018939971923828125, 0.0, 0.0),
 (0.0, 0.0, 1.0)]

Klein

klein = pv.ParametricKlein()
klein.plot(color="tan")

Out:

[(6.208944243443206, 8.311908167851165, 6.361395341408446),
 (0.0, 2.102963924407959, 0.15245109796524048),
 (0.0, 0.0, 1.0)]

Kuen

kuen = pv.ParametricKuen()
kuen.plot(color="tan")

Out:

[(24.185856659732003, 40.19100280555262, 39.70432718547358),
 (-15.518470525741577, 0.4866756200790405, 0.0),
 (0.0, 0.0, 1.0)]

Mobius

mobius = pv.ParametricMobius()
mobius.plot(color="tan")

Out:

[(5.656253052433871, 5.208850753983401, 5.656253052433871),
 (0.0, -0.44740229845046997, 0.0),
 (0.0, 0.0, 1.0)]

Plucker Conoid

pluckerconoid = pv.ParametricPluckerConoid()
pluckerconoid.plot(color="tan")

Out:

[(9.721636447629232, 9.722391638478536, 9.721636447629232),
 (0.0, 0.0007551908493041992, 0.0),
 (0.0, 0.0, 1.0)]

Random Hills

randomhills = pv.ParametricRandomHills()
randomhills.plot(color="tan")

Out:

[(28.78004574694181, 42.59238058247112, 32.59238058247114),
 (-3.8123348355293274, 9.99999999999999, 0.0),
 (0.0, 0.0, 1.0)]

Roman

roman = pv.ParametricRoman()
roman.plot(color="tan")

Out:

[(1.9315274394739659, 1.9315274394739659, 1.9315274394739659),
 (0.0, 0.0, 0.0),
 (0.0, 0.0, 1.0)]

Super Ellipsoid

superellipsoid = pv.ParametricSuperEllipsoid(n1=0.1, n2=2)
superellipsoid.plot(color="tan")

Out:

[(3.862698576895865, 3.862195245473059, 3.862698576895865),
 (0.0, -0.0005033314228057861, 0.0),
 (0.0, 0.0, 1.0)]

Torus

torus = pv.ParametricTorus()
torus.plot(color="tan")

Out:

[(4.860818223814616, 4.861195819239268, 4.860818223814616),
 (0.0, 0.0003775954246520996, 0.0),
 (0.0, 0.0, 1.0)]

Circular Arc

pointa = [-1, 0, 0]
pointb = [0, 1, 0]
center = [0, 0, 0]
resolution = 100

arc = pv.CircularArc(pointa, pointb, center, resolution)

pl = pv.Plotter()
pl.add_mesh(arc, color='k', line_width=4)
pl.show_bounds()
pl.view_xy()
pl.show()

Out:

[(-0.5000000000499987, 0.5, 2.7320508074322785),
 (-0.5000000000499987, 0.5, 0.0),
 (0.0, 1.0, 0.0)]

Extruded Half Arc

pointa = [-1, 0, 0]
pointb = [1, 0, 0]
center = [0, 0, 0]
resolution = 100

arc = pv.CircularArc(pointa, pointb, center, resolution)
poly = arc.extrude([0, 0, 1])
poly.plot(color="tan", cpos='iso', show_edges=True)

Out:

[(2.7320508075688776, 2.2320508075688776, 3.2320508075688776),
 (0.0, -0.5, 0.5),
 (0.0, 0.0, 1.0)]