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Kinetic bounding volume hierarchies for deformable objects
 In ACM Int’l Conf. on Virtual Reality Continuum and Its Applications (VRCIA), Hong Kong
, 2006
"... We present novel algorithms for updating bounding volume hierarchies of objects undergoing arbitrary deformations. Therefore, we introduce two new data structures, the kinetic AABB tree and the kinetic BoxTree. The eventbased approach of the kinetic data structures framework enables us to show that ..."
Abstract

Cited by 5 (1 self)
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We present novel algorithms for updating bounding volume hierarchies of objects undergoing arbitrary deformations. Therefore, we introduce two new data structures, the kinetic AABB tree and the kinetic BoxTree. The eventbased approach of the kinetic data structures framework enables us to show that our algorithms are optimal in the number of updates. Moreover, we show a lower bound for the total number of BV updates, which is independent of the number of frames. We used our kinetic bounding volume hierarchies for collision detection and performed a comparison with the classical bottomup update method. The results show that our algorithms perform up to ten times faster in practically relevant scenarios.
A Kinetic Triangulation Scheme for Moving Points in The Plane ∗
"... We present a simple randomized scheme for triangulating a set P of n points in the plane, and construct a kinetic data structure which maintains the triangulation as the points of P move continuously along piecewise algebraic trajectories of constant description complexity. Our triangulation scheme ..."
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Cited by 2 (1 self)
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We present a simple randomized scheme for triangulating a set P of n points in the plane, and construct a kinetic data structure which maintains the triangulation as the points of P move continuously along piecewise algebraic trajectories of constant description complexity. Our triangulation scheme experiences an expected number of O(n 2 βs+2(n) log 2 n) discrete changes, and handles them in a manner that satisfies all the standard requirements from a kinetic data structure: compactness, efficiency, locality and responsiveness. Here s is the maximum number of times where any specific triple of points of P can become collinear, βs+2(q) = λs+2(q)/q, and λs+2(q) is the maximum length of DavenportSchinzel sequences of order s + 2 on n symbols. Thus, compared to the previous solution of Agarwal et al. [4], we achieve a (slightly) improved bound on the number of discrete changes in the triangulation. In addition, we believe that our scheme is simpler to implement and analyze. Categories and Subject Descriptors F.2.2 [Analysis of algorithms and problem complexity]: Nonnumerical algorithms and problems—Geometrical problems and computations; G.2.1 [Discrete mathematics]: Combinatorics—Combinatorial algorithms
Kinetic Bounding Volume Hierarchies for Collision Detection of Deformable Objects
, 2006
"... We present novel algorithms for updating bounding volume hierarchies of objects undergoing arbitrary deformations. Therefore, we introduce two new data structures, the kinetic AABB tree and the kinetic BoxTree. The eventbased approach of the kinetic data structures framework enables us to show that ..."
Abstract

Cited by 2 (2 self)
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We present novel algorithms for updating bounding volume hierarchies of objects undergoing arbitrary deformations. Therefore, we introduce two new data structures, the kinetic AABB tree and the kinetic BoxTree. The eventbased approach of the kinetic data structures framework enables us to show that our algorithms are optimal in the number of updates. Moreover, we show a lower bound for the total number of BV updates, which is independent of the number of frames. Furthermore, we present a kinetic data structures which uses the kinetic AABB tree for collision detection and show that this structure can be easily extended for continuous collision detection of deformable objects. We performed a comparison of our kinetic approaches with the classical bottomup update method. The results show that our algorithms perform up to ten times faster in practically relevant scenarios.
A Lagrangian Approach to Dynamic Interfaces through Kinetic Triangulation of the Ambient Space
 COMPUTER GRAPHICS FORUM
, 2007
"... In this paper, we propose a robust and efficient Lagrangian approach for modeling dynamic interfaces between different materials undergoing large deformations and topology changes, in two dimensions. Our work brings an interesting alternative to popular techniques such as the level set method and th ..."
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Cited by 1 (0 self)
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In this paper, we propose a robust and efficient Lagrangian approach for modeling dynamic interfaces between different materials undergoing large deformations and topology changes, in two dimensions. Our work brings an interesting alternative to popular techniques such as the level set method and the particle level set method, for twodimensional and axisymmetric simulations. The principle of our approach is to maintain a twodimensional triangulation which embeds the onedimensional polygonal description of the interfaces. Topology changes can then be detected as inversions of the faces of this triangulation. Each triangular face is labeled with the type of material it contains. The connectivity of the triangulation and the labels of the faces are updated consistently during deformation, within a neat framework developed in computational geometry: kinetic data structures. Thanks to the exact computation paradigm, the reliability of our algorithm, even in difficult situations such as shocks and topology changes, can be certified. We demonstrate the applicability and the efficiency of our approach with a series of numerical experiments in two dimensions. Finally, we discuss the feasibility of an extension to three dimensions.
unknown title
"... In the last lecture we started out by briefly discussing range trees (a topic we started two lectures ago). In particular, we showed how to support dynamic insertions and deletions in range trees efficiently. After this, we discussed the vertical line stabbing problem — given a collection of interva ..."
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In the last lecture we started out by briefly discussing range trees (a topic we started two lectures ago). In particular, we showed how to support dynamic insertions and deletions in range trees efficiently. After this, we discussed the vertical line stabbing problem — given a collection of intervals, support queries of the form “How many intervals intersect the line x = x0?”. We showed that both interval trees and segment trees could solve this problem efficiently. Segment trees are a bit more memoryefficient, but interval trees are more flexible for other applications. We used these data structures to solve the windowing problem — given a collection of line segments, report how many lie in a given axisaligned rectangle. In solving the windowing problem, we had to introduce an additional data structure called a priority search tree. In this lecture we study kinetic data structures. These are data structures that contain information about objects in motion. They support the following three types of queries: (i) modify the motion path of an object; (ii) move forward to a specified point in time; (iii) return information about the state of the objects in the current time. We will go over kinetic sorting and kinetic heaps, and then state several results about kinetic data structures without proof. After covering kinetic data structures, we will discuss the ray shooting problem — given a simple (possibly nonconvex) polygon, support queries asking for the first point of intersection of a ray with the polygon. We will show how to support O(log 2 (n)) queries and outline an approach for achieving a query time of O(log(n)).
IfI0602 ClausthalZellerfeld 2006Kinetic Bounding Volume Hierarchies for Collision Detection of Deformable Objects
"... We present novel algorithms for updating bounding volume hierarchies of objects undergoing arbitrary deformations. Therefore, we introduce two new data structures, the kinetic AABB tree and the kinetic BoxTree. The eventbased approach of the kinetic data structures framework enables us to show that ..."
Abstract
 Add to MetaCart
We present novel algorithms for updating bounding volume hierarchies of objects undergoing arbitrary deformations. Therefore, we introduce two new data structures, the kinetic AABB tree and the kinetic BoxTree. The eventbased approach of the kinetic data structures framework enables us to show that our algorithms are optimal in the number of updates. Moreover, we show a lower bound for the total number of BV updates, which is independent of the number of frames. Furthermore, we present a kinetic data structures which uses the kinetic AABB tree for collision detection and show that this structure can be easily extended for continuous collision detection of deformable objects. We performed a comparison of our kinetic approaches with the classical bottomup update method. The results show that our algorithms perform up to ten times faster in practically relevant scenarios. 1
COMPUTER GRAPHICS forum A Lagrangian Approach to Dynamic Interfaces through Kinetic Triangulation of the Ambient Space
, 2010
"... In this paper, we propose a robust and efficient Lagrangian approach for modeling dynamic interfaces between different materials undergoing large deformations and topology changes, in two dimensions. Our work brings an interesting alternative to popular techniques such as the level set method and th ..."
Abstract
 Add to MetaCart
In this paper, we propose a robust and efficient Lagrangian approach for modeling dynamic interfaces between different materials undergoing large deformations and topology changes, in two dimensions. Our work brings an interesting alternative to popular techniques such as the level set method and the particle level set method, for twodimensional and axisymmetric simulations. The principle of our approach is to maintain a twodimensional triangulation which embeds the onedimensional polygonal description of the interfaces. Topology changes can then be detected as inversions of the faces of this triangulation. Each triangular face is labeled with the type of material it contains. The connectivity of the triangulation and the labels of the faces are updated consistently during deformation, within a neat framework developed in computational geometry: kinetic data structures. Thanks to the exact computation paradigm, the reliability of our algorithm, even in difficult situations such as shocks and topology changes, can be certified. We demonstrate the applicability and the efficiency of our approach with a series of numerical experiments in two dimensions. Finally, we discuss the feasibility of an extension to three dimensions.