Analytic formulas for distance between geometric shapes.

Paul Heckbert ph+ at cs.cmu.edu
Wed Jul 31 01:11:59 PDT 2002

```Reference regarding distance from a point to an ellipsoid (requires roots of
6th degree polynomial):

@INCOLLECTION{Hart94,
AUTHOR={John C. Hart},
TITLE={Distance to an Ellipsoid},
BOOKTITLE={Graphics Gems IV},
EDITOR={Paul Heckbert},
PAGES={113-119},
YEAR={1994},
KEYWORDS={ray tracing, ellipse},
SUMMARY={
Gives the formulas necessary to find the distance from a point to an
ellipsoid, or from a point to an ellipse.  These formulas can be useful
for geometric modeling or for ray tracing.
},
}

----- Original Message -----
From: "Dickinson, John" <John.Dickinson at nrc.ca>
To: "compgeom-discuss at research. bell-labs. com (E-mail)"
<compgeom-discuss at research.bell-labs.com>
Sent: Wednesday, July 24, 2002 11:29 AM
Subject: Analytic formulas for distance between geometric shapes.

> I am looking for analytic formulas for distance between basic geometric
> shapes arbitrarily located and orientated in space.  Any references
(papers,
> books) would be greatly appreciated.
>
> The Sphere is the easy example as the distance between two spheres in the
> distance between their centers minus the sum of their radii.  On the other
> hand orientated boxes can't be done analytically but must be done face by
> face.
>
> How about other shapes formed by implicit quadratic equations (eggs,
> ovaloids, ...) that form not purely symmetric shapes which can be
orientated
> inspace. Do any of these shapes have analytic formulae for distance?
>
> John
>
> --
> -((Insert standard disclaimer here))-|---  Ray's Rule for Precision ----
> John Kenneth Dickinson, Ph.D.        |   "Measure with micrometer;
> Research Council Officer  IMTI-NRC   |    Mark with chalk;
> email: john.dickinson at nrc.ca         |    Cut with axe."
>
>
>
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```