# A comparison of two fast algorithms for computing the distance between convex polyhedra

@article{Cameron1997ACO, title={A comparison of two fast algorithms for computing the distance between convex polyhedra}, author={Stephen Cameron}, journal={IEEE Trans. Robotics Autom.}, year={1997}, volume={13}, pages={915-920} }

The problem of tracking the distance between two convex polyhedra is finding applications in many areas of robotics. The algorithm of Lin and Canny (1991) is a well-known fast solution to this problem, but by recasting the algorithms into configuration space, we show that a minor modification to the earlier algorithm of Gilbert, Johnson, and Keerthi (1988) also gives this algorithm the same expected cost.

## 110 Citations

### Enhancing GJK: computing minimum and penetration distances between convex polyhedra

- Computer ScienceProceedings of International Conference on Robotics and Automation
- 1997

New results are presented that confirm an almost-constant time complexity for an enhanced version of Gilbert, Johnson and Keerthi's (GJK) algorithm, and also describe modifications to the algorithm to compute measures of penetration distance.

### An Algorithm on Collision Detection by Computing the Minimum Distance between Two Convex Polyhedra

- Computer Science2006 6th World Congress on Intelligent Control and Automation
- 2006

An algorithm for computing the minimum distance between two convex polyhedra is presented, which applies to polyhedral objects that can be represented as convex hulls of its vertex value in three-dimensional space.

### Minimum Distance Between the Faces of Two Convex Polyhedra: A Sufficient Condition

- Computer Science, MathematicsJ. Glob. Optim.
- 2003

An algorithm (QLDPA) for the fast computation of the distance between convex and bounded polyhedra is proposed as an application of it and computer experiments show its fast performance, especially when the total number of vertices is large.

### An Algorithm for Computing the Minimum Distance between Two Convex Polyhedra in Three-Dimensional Space

- Computer Science2008 International Symposium on Knowledge Acquisition and Modeling
- 2008

The algorithm transform the collision detection problem into non-linear programming problem of computing the minimum distance between two objects, and then detect collision by the value of minimum distance, and the simulation results demonstrate the performance of the new method.

### Collision Detection of Convex Polyhedra Based on Duality Transformation

- Computer Science
- 2005

A new method, called CD-Dual, for detecting collision between two convex polyhedron is proposed, based on a local search among the faces on the Minkowski difference of the polyhedra.

### Advanced computational geometry for proximity queries of convex polyhedras

- Computer Science2007 International Conference on Intelligent and Advanced Systems
- 2007

This paper summarizes the prominent algorithms for computing the minimum distance between convex polyhedras and their variations and a critical analysis of these algorithms is also presented.

### A local search algorithm for ray-convex polyhedron intersection

- Computer ScienceComput. Optim. Appl.
- 2012

A new algorithm (LSABV) for determining the intersection between a ray and a convex polyhedron (RCPI) in a fast way based on local search and the concept of visibility is presented.

### Distance Computation in a Curved World

- Computer Science
- 2007

This work explains why the problem is important, and focuses on computing the distance between convex objects defined by NURBS curves or patches, which can be solved using the algorithm of Gilbert and Foo from repeated evaluation of the support mapping.

### Computing distances between NURBS-defined convex objects

- Computer ScienceProceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146)
- 1998

This work focuses on computing the distance between convex objects defined by NURBS curves or patches, for which the critical step is the evaluation of the support mapping.

### A new algorithm for computing minimum distance

- Computer ScienceProceedings. 2000 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2000) (Cat. No.00CH37113)
- 2000

A mix between LC's idea and the GJK's algorithm can be used to solve the minimum distance between convex polyhedras, using local methods to calculate the distance between features and new "updating" conditions to add stability.

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New results are presented that confirm an almost-constant time complexity for an enhanced version of Gilbert, Johnson and Keerthi's (GJK) algorithm, and also describe modifications to the algorithm to compute measures of penetration distance.

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A simple and efficient algorithm for finding the closest points between two convex polynomials is described and can be used for collision detection, computation of the distance between two polyhedra in three-dimensional space, and other robotics problems.

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An algorithm for computing the Euclidean distance between a pair of convex sets in R/sup m/ has special features which makes its application in a variety of robotics problems attractive.

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It is shown that the computation of MTD can be recast as a configuration space problem, and an algorithm for computing MTD for convex polyhedra is described.

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- Computer ScienceIEEE Trans. Robotics Autom.
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A methodology for computing the distance between objects in three-dimensional space is presented. The convex polytope is replaced by a general convex set, avoiding the errors caused by the usual…

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The algorithm is implemented in C++, and embedded in a series of C++ class libraries for a graphic simulation system-which the authors have named ContactScope.

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The authors claim that many path planning problems can be solved by a mixture of global and local planning, and describe a variation on the algorithm of Gilbert, Johnson and Keerthi (1988), that they have packaged together with a hierarchical decomposition of objects for added efficiency.

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An exact and interactive collision detection system for large-scale environments, I-COLLIDE, based on pruning multiple-object pairs using bounding boxes and performing exact collision detection between selected pairs of polyhedral models.