This page is a sub-page of our page on Surfaces.
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Related KMR-pages:
• Optical properties of Quadrics
• Dupin Cyclides
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Other relevant sources of information:
• Quadrics at Wikipedia
• Confocal Conics at Wikipedia
• Elliptic coordinate system at Wikipedia
• Parabolic coordinates at Wolfram MathWorld
• Elliptic cylindrical coordinates at Wikipedia
• Ellipsoidal coordinates at Wikipedia
• Paraboloidal coordinates at Wikipedia
• Confocal Ellipsoidal coordinates at Wolfram MathWorld
• Confocal Paraboloidal coordinates at Wolfram MathWorld
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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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The Confocal Quadrics of a given quadric is the pencil of quadrics that touch the given quadric and the absolute quadric.
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Confocal Quadrics 1:
The interactive simulation that created this movie.
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Confocal Quadrics – Intersect XY plane:
The interactive simulation that created this movie.
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Confocal Quadrics – Intersect XZ plane:
The interactive simulation that created this movie.
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Confocal Quadrics 2 – Elliptic Coordinates:
The interactive simulation that created this movie.
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Confocal Quadrics 2 – – Elliptic Coordinates – Intersect XY-plane:
The interactive simulation that created this movie.
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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 paraboloids mirrors is shown here without the reflected wavefront (which is the same for all the paraboloids of the confocal family:
Confocal Paraboloids – reflect vertical rays into Dupin cyclide.gcf
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