This page is a sub-page of our page on Surfaces.
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Related KMR-pages:
• Canal Surfaces
• Developable Surfaces
• Focal Surfaces
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Other related sources of information:
• Images of Dupin cyclides
• Dupin Cyclide (without focal curves) at Wikipedia
• Clifford torus at Wikipedia
• Torus at Wikipedia
• Dupin Cyclide (with focal curves) at MathCurve.com
• Charles Dupin at Wikipedia
• Cyclides (as inversions of tori, cones and cylinders) by Alain Esculier
• Cyclide at Wolfram MathWorld
• Paraboloid at Wikipedia
• Paraboloidal coordinates at Wikipedia
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The interactive simulations on this page can be navigated with the Free Viewer of the Graphing Calculator.
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Dupin Cyclides – The closest relatives to the Sphere:
Interactive simulation of a Dupin Cyclide with its Principal Net.
Change the parameters a, b, c in order to change the shape of the surface, and change the parameters k, m in order to move the principal curves. For a Dupin Cyclide, both families of principal curves are circles. The formulas are reached by pulling down at the top of the frame.
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Dupin Cyclide – PN1:
The interactive simulation that created this movie.
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Dupin Cyclide – PN2:
The interactive simulation that created this movie.
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Dupin Cyclide – PN1 lines:
The interactive simulation that created this movie.
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Dupin Cyclide – PN2 lines:
The interactive simulation that created this movie.
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Dupin Cyclide – WaveFronts:
The interactive simulation that created this movie.
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Dupin Cyclide Wave-front 2:
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Inversion of a Dupin cyclide (pn1 lines):
The interactive simulation that created this movie
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Inversion of parallel Dupin cyclides
The interactive simulation that created this movie
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Dupin Cyclides as Inversions of Right Circular Cones:
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Inversion of a right circular cone with a moving tangent plane:
The interactive simulation that created this movie.
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Inversion of a right circular cone 1:
The interactive simulation that created this movie.
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Inversion of a right circular cone 2:
The interactive simulation that created this movie.
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Inversion of a right circular cone 3:
The interactive simulation that created this movie.
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Inversion of a rotating right circular cone:
The interactive simulation that created this movie.
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A circular cylinder can be regarded as a right circular cone with its vertex at infinity.
Inversion of a circular cylinder with a moving tangent plane:
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Inversion of a rotating circular cylinder 2:
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Inversion of a rotating circular cylinder 3:
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Inversion of a rotating circular cylinder 4:
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Confocal Paraboloids acting as mirrors to a planar wavefront
Confocal Paraboloids – reflected Dupin cyclide.gcf
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Reflection of a planar wavefront in a saddle surface
turns the wavefront into a Dupin cyclide:
Confocal-paraboloids-planar-wavefront-into-cyclide-reflection.gcf
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A set of (horizontally positioned) confocal paraboloids give the same (Dupine cyclide) reflection of a planar wave front that is incident along the vertical axis:
The interactive simulation that created this movie.
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The same variation of the confocal paraboloid mirrors is shown here without the reflected wavefront (which is the same for all the paraboloids among the confocal family:
Confocal Paraboloids – reflect vertical rays into Dupin cyclide.gcf
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