shortest distance between two circles in 3D

Returns the shortest distance between two circles in 3D, the pair(s) of closest points, and if the circles are equidistant.

• distanceCircleCircle3D.m Computes the shortest distances in 3D between two circles by solving an 8th order polynomial (after checking for special cases).
• fminconDistanceCircleCircle3D.m performs the same task numerically, but is slower, only returns one solution, doesn't always find the optimum, and requires the Optimization toolbox.
• testdistanceCircleCircle3D.m draws the circles and their minimum non-intersection tori. It also draws the special cases in 2D and many interesting cases in 3D.
• compareAccuracyCircleCircle3D.m generates nSamples random circles and compares the accuracy and performance of distanceCircleCircle3D and fminConDistanceCircleCircle3D

distanceCircleCircle3D(N0, r0, C0, N1, r1, C1)

Inputs: two circles circle 0, and circle 1, each described by 3 parameters.

1. N0: circle 0 normal vector (3x1)
2. r0: circle 0 radius
3. C0: circle 0 center position (3x1)
4. N1: circle 1 normal vector (3x1)
5. r1: circle 1 radius
6. C1: circle 1 center position (3x1)

If no inputs are given, two random circles in 3D are generated.

Outputs:

result, a struct that includes the elements:

1. distance: shortest distance (scalar)
2. sqrDistance: squared shortest distance (scalar)
3. numClosestPairs: how many closest pairs on the circles exist ,
4. circle0Closest: coordinates of closest point on circle 0, 3xnumClosestPairs
5. circle1Closest: coordinates of closest point on circle 1, 3xnumClosestPairs
6. equidistant: if infinite solutions exist

Transcribed from C++ to Matlab by Aaron Becker [e-mail], and Victor Montano, based on the 3D circle-circle distance algorithm described in https://www.geometrictools.com/Documentation/DistanceToCircle3.pdf and available at https://www.geometrictools.com/GTE/Mathematics/DistCircle3Circle3.h

The notation used in the code matches that of the document.

David Eberly, Geometric Tools, Redmond WA 98052

Copyright (c) 1998-2023

Distributed under the Boost Software License, Version 1.0.

https://www.boost.org/LICENSE_1_0.txt

https://www.geometrictools.com/License/Boost/LICENSE_1_0.txt

Version: 6.0.2022.01.06