Intersection detection and separators for simple polygons
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
OBBTree: a hierarchical structure for rapid interference detection
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
On the quantification of penetration between general objects
International Journal of Robotics Research
Rotational polygon overlap minimization and compaction
Computational Geometry: Theory and Applications - special issue on applied computational geometry
On finding narrow passages with probabilistic roadmap planners
WAFR '98 Proceedings of the third workshop on the algorithmic foundations of robotics on Robotics : the algorithmic perspective: the algorithmic perspective
Controlled perturbation for arrangements of polyhedral surfaces with application to swept volumes
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Rotational polygon containment and minimum enclosure using only robust 2D constructions
Computational Geometry: Theory and Applications - Special issue on applications and challenges
Timewarp rigid body simulation
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Robot Motion Planning
Penetration depth of two convex polytopes in 3D
Nordic Journal of Computing
Six-degree-of-freedom haptic rendering using incremental and localized computations
Presence: Teleoperators and Virtual Environments
Planning Algorithms
C-DIST: efficient distance computation for rigid and articulated models in configuration space
Proceedings of the 2007 ACM symposium on Solid and physical modeling
IEEE Transactions on Robotics
Efficient distance computation in configuration space
Computer Aided Geometric Design
Interactive Hausdorff distance computation for general polygonal models
ACM SIGGRAPH 2009 papers
A unified approach for physically-based simulations and haptic rendering
Proceedings of the 2009 ACM SIGGRAPH Symposium on Video Games
Global vector field computation for feedback motion planning
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
Automated digital dental articulation
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part III
PolyDepth: Real-time penetration depth computation using iterative contact-space projection
ACM Transactions on Graphics (TOG)
Haptic display of rigid body contact using generalized penetration depth
ICIRA'11 Proceedings of the 4th international conference on Intelligent Robotics and Applications - Volume Part I
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
ACM Transactions on Graphics (TOG)
Computer-Aided Design
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Penetration depth (PD) is a distance measure that is used to describe the extent of overlap between two intersecting objects. Most of the prior work in PD computation has been restricted to translationalPD, which is defined as the minimal translational motion that one of the overlapping objects must undergo in order to make the two objects disjoint. In this paper, we extend the notion of PD to take into account both translational and rotational motion to separate the intersecting objects, namely generalizedPD. When an object undergoes a rigid transformation, some point on the object traces the longest trajectory. The generalized PD between two overlapping objects is defined as the minimum of the longest trajectories of one object, under all possible rigid transformations to separate the overlapping objects. We present three new results to compute generalized PD between polyhedral models. First, we show that for two overlapping convex polytopes, the generalized PD is the same as the translational PD. Second, when the complement of one of the objects is convex, we pose the generalized PD computation as a variant of the convex containment problem and compute an upper bound using optimization techniques. Finally, when both of the objects are non-convex, we treat them as a combination of the above two cases and present an algorithm that computes a lower and an upper bound on the generalized PD. We highlight the performance of our algorithms on different models that undergo rigid motion in the 6-dimensional configuration space. Moreover, we utilize our algorithm for complete motion planning of rigid robots undergoing translational and rotational motion in a plane or in 3D space. In particular, we use generalized PD computation for performing C-obstacle query and checking path non-existence.