Function Repository Resource:

Find a quadric surface that passes through nine given 3D points

Contributed by: Ed Pegg Jr
 ResourceFunction["NinePointQuadric"][pts,{x,y,z}] returns the implicit Cartesian equation in the variables x,y and z of the quadric surface that goes through the points pts. ResourceFunction["NinePointQuadric"][pts] uses the formal variables x, y and z.

## Examples

### Basic Examples (3)

Find the quadric surface going through nine points (based of the decimal digits of 927):

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Show the quadric surface (a hyperboloid of one sheet) with the points:

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Find the quadric surface going through nine points (based of the decimal digits of 928):

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Show the quadric surface (a hyperbolic paraboloid) with the points:

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Find the quadric surface going through nine points based of the decimal digits of 925:

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Show the quadric surface (an ellipsoid) with the points:

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Use the resource function QuadricSurfacePlot to show this same ellipsoid:

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### Scope (2)

Use formal variables:

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Nine random real points:

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Show the quadric surface (a hyperboloid of 2 sheets) with the points:

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### Possible Issues (3)

Pick nine points on a sphere:

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Find the surface of the sphere:

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The following set of nine points should give the same sphere equation, but the matrix method fails due to degeneracy:

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## Version History

• 1.0.0 – 25 July 2022