Introduction to algorithms
Efficiently Planning Compliant Motion in thePlane
SIAM Journal on Computing
Minimal tangent visibility graphs
Computational Geometry: Theory and Applications
A pedestrian approach to ray shooting: shoot a ray, take a walk
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Kinetic collision detection between two simple polygons
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Separation-sensitive collision detection for convex objects
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Separation Sensitive Kinetic Separation Structures for Convex Polygons
JCDCG '00 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
Minimum link paths in polygons and related problems
Minimum link paths in polygons and related problems
Algorithmic issues in modeling motion
ACM Computing Surveys (CSUR)
Spatial embedding of pseudo-triangulations
Proceedings of the nineteenth annual symposium on Computational geometry
Kinetic collision detection between two simple polygons
Computational Geometry: Theory and Applications
Convexity minimizes pseudo-triangulations
Computational Geometry: Theory and Applications - Special issue on the 14th Canadian conference on computational geometry — CCCG02
Collision detection for deforming necklaces
Computational Geometry: Theory and Applications - Special issue on the 18th annual symposium on computational geometry—SoCG2002
Kinetic collision detection with fast flight plan changes
Information Processing Letters
Pointed and colored binary encompassing trees
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Kinetic sorting and kinetic convex hulls
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Kinetic sorting and kinetic convex hulls
Computational Geometry: Theory and Applications
Kinetic collision detection for convex fat objects
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Minimum weight pseudo-triangulations
Computational Geometry: Theory and Applications
Shooting permanent rays among disjoint polygons in the plane
Proceedings of the twenty-fifth annual symposium on Computational geometry
Pointed binary encompassing trees: Simple and optimal
Computational Geometry: Theory and Applications
Kinetic collision detection with fast flight plan changes
Information Processing Letters
Decompositions, partitions, and coverings with convex polygons and pseudo-triangles
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Minimum weight pseudo-triangulations
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
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We describe how to construct and kinetically maintain a tessellation of the free space between a collection of k disjoint simple polygonal objects with a total of N vertices, R of which are reflex. Our linear size tessellation consists of pseudo-triangles and has the following properties: (i) it contains disjoint outer hierarchical representations of all objects where the size of the outer boundary of these representations is proportional to a minimum link separator for the objects, and (ii) any line segment in the free space intersects at most O((k + log R) log N) pseudo-triangles (each of constant size).We maintain our tessellation by using the Kinetic Data Structure (KDS) framework. Our structure is compact, maintaining an active set of certificates whose number is linear in the size of a minimum link subdivision for the objects. It is also responsive; on the failure of a certificate invariants can be restored in time logarithmic in the total number of vertices. While its efficiency is difficult to establish precisely, it is shown that at most O(k + κmaxlog R)log N events happen during straight line motion of one object A in the context of k (fixed) others, where κmax denotes the maximum size of the minimum link polygon separating object A from the rest, during the motion.Furthermore, ray shooting queries (that use point location) can be answered in O((k + log R) log N) time for rays with arbitrary direction.