Confocal Quadrics

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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