shortest distance between two circles in 3D

版本 1.0.2 (13.0 KB) 作者: Aaron T. Becker's Robot Swarm Lab
Returns the shortest distance between two circles in 3D, the pair(s) of closest points, and if the circles are equidistant.
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更新时间 2023/4/26

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  • 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 atbecker@uh.edu, 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

引用格式

Aaron T. Becker's Robot Swarm Lab (2024). shortest distance between two circles in 3D (https://www.mathworks.com/matlabcentral/fileexchange/128183-shortest-distance-between-two-circles-in-3d), MATLAB Central File Exchange. 检索来源 .

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版本 已发布 发行说明
1.0.2

added tags
1.0.1

If the min distance points on circle 0 and 1 both differ by less than PRECISION, the code now declares they are equivalent and only returns 1 pair. Also added extra debugging cases to testdistanceCircleCircle3D().
1.0.0