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Planning short paths with clearance using explicit corridors
 IN: IEEE INTERNATIONAL CONFERENCE ON ROBOTICS AND AUTOMATION
, 2010
"... A central problem of applications dealing with virtual environments is planning a collisionfree path for a character. Since environments and their characters are growing more realistic, a character’s path needs to be visually convincing, meaning that the path is smooth, short, has some clearance to ..."
Abstract

Cited by 27 (3 self)
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A central problem of applications dealing with virtual environments is planning a collisionfree path for a character. Since environments and their characters are growing more realistic, a character’s path needs to be visually convincing, meaning that the path is smooth, short, has some clearance to the obstacles in the environment, and avoids other characters. Up to now, it has proved difficult to meet these criteria simultaneously and in realtime. We introduce a new data structure, i.e. the Explicit Corridor Map, which allows creating the shortest path, the path that has the largest amount of clearance, or any path in between. Besides being efficient, the corresponding algorithms are surprisingly simple. By integrating the data structure and algorithms into the Indicative Route Method, we show that visually convincing short paths can be obtained in realtime.
Geometric Integrators for ODEs
 J. Phys. A
, 2006
"... Abstract. Geometric integration is the numerical integration of a differential equation, while preserving one or more of its “geometric ” properties exactly, i.e. to within roundoff error. Many of these geometric properties are of crucial importance in physical applications: preservation of energy, ..."
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Cited by 17 (5 self)
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Abstract. Geometric integration is the numerical integration of a differential equation, while preserving one or more of its “geometric ” properties exactly, i.e. to within roundoff error. Many of these geometric properties are of crucial importance in physical applications: preservation of energy, momentum, angular momentum, phase space volume, symmetries, timereversal symmetry, symplectic structure and dissipation are examples. In this paper we present a survey of geometric numerical integration methods for ordinary differential equations. Our aim has been to make the review of use for both the novice and the more experienced practitioner interested in the new developments and directions of the past decade. To this end, the reader who is interested in reading up on detailed technicalities will be provided with numerous signposts to the relevant literature. Geometric Integrators for ODEs 2 1.
Statistical learning by imitation of competing constraints in joint space and . . .
, 2009
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Enhancing corridor maps for realtime path planning in virtual environments
 COMPUTER ANIMATION AND SOCIAL AGENTS (CASA)
, 2008
"... A central problem in interactive virtual environments is planning highquality paths for characters avoiding obstacles in the environment. Current applications require a path planner that is fast (to ensure realtime interaction with the environment) and flexible (to avoid local hazards). In additio ..."
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Cited by 13 (4 self)
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A central problem in interactive virtual environments is planning highquality paths for characters avoiding obstacles in the environment. Current applications require a path planner that is fast (to ensure realtime interaction with the environment) and flexible (to avoid local hazards). In addition, paths need to be natural, i.e. smooth and short. To satisfy these requirements, we need an adequate representation of the free space stored in a convenient data structure, a fast mechanism for querying this data structure, and an algorithm that constructs natural paths for the characters. We improve an existing data structure, the Corridor Map, which represents the free space by a graph whose edges correspond to collisionfree corridors. We show that this structure, together with a kdtree, can be used for fast querying, resulting in a corridor that guides the global path of the character. Its local motions are controlled by force functions, providing the desired flexibility. Experiments show that the improvements lead to a method which can steer a crowd of ±10,000 characters in realtime.
Axisymmetric Numerical Relativity
, 2005
"... Chapters 2, 3 and 6 contain work done in collaboration with my supervisor and published in a joint paper [119]. The dynamical shift conditions in chapter 6 are a later addition by myself. The remaining chapters are my own work. All computer programmes were written by myself unless otherwise stated. ..."
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Cited by 12 (6 self)
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Chapters 2, 3 and 6 contain work done in collaboration with my supervisor and published in a joint paper [119]. The dynamical shift conditions in chapter 6 are a later addition by myself. The remaining chapters are my own work. All computer programmes were written by myself unless otherwise stated. c○Oliver Rinne, 2005 This thesis is concerned with formulations of the Einstein equations in axisymmetric spacetimes which are suitable for numerical evolutions. The common basis for our formulations is provided by the (2+1)+1 formalism. General matter sources and rotational degrees of freedom are included. A first evolution system adopts elliptic gauge conditions arising from maximal slicing and conformal flatness. The numerical implementation is based on the finitedifference approach, using a Multigrid algorithm for the elliptic equations and the method of lines for the hyperbolic evolution equations.
DISCRETE HAMILTONIAN VARIATIONAL INTEGRATORS
"... Abstract. We derive a variational characterization of the exact discrete Hamiltonian, which is a Type II generating function for the exact flow of a Hamiltonian system, by considering a Legendre transformation of Jacobi’s solution of the Hamilton–Jacobi equation. This provides an exact correspondenc ..."
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Cited by 12 (10 self)
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Abstract. We derive a variational characterization of the exact discrete Hamiltonian, which is a Type II generating function for the exact flow of a Hamiltonian system, by considering a Legendre transformation of Jacobi’s solution of the Hamilton–Jacobi equation. This provides an exact correspondence between continuous and discrete Hamiltonian mechanics, which arise from the continuous and discretetime Hamilton’s variational principle on phase space, respectively. The variational characterization of the exact discrete Hamiltonian naturally leads to a class of generalized Galerkin Hamiltonian variational integrators, which include the symplectic partitioned Runge–Kutta methods. This extends the framework of variational integrators to Hamiltonian systems with degenerate Hamiltonians, for which the standard theory of Lagrangian variational integrators cannot be applied. We also characterize the group invariance properties of discrete Hamiltonians which lead to a discrete Noether’s theorem. 1.
Bseries and order conditions for exponential integrators
"... Abstract. We introduce a general format of numerical ODEsolvers which include many of the recently proposed exponential integrators. We derive a general order theory for these schemes in terms of Bseries and bicolored rooted trees. To ease the construction of specific schemes we generalize an idea ..."
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Cited by 9 (4 self)
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Abstract. We introduce a general format of numerical ODEsolvers which include many of the recently proposed exponential integrators. We derive a general order theory for these schemes in terms of Bseries and bicolored rooted trees. To ease the construction of specific schemes we generalize an idea of Zennaro [Math. Comp., 46 (1986), pp. 119–133] and define natural continuous extensions in the context of exponential integrators. This leads to a relatively easy derivation of some of the most popular recently proposed schemes. The general format of schemes considered here makes use of coefficient functions which will usually be selected from some finite dimensional function spaces. We will derive lower bounds for the dimension of these spaces in terms of the order of the resulting schemes. Finally, we illustrate the presented ideas by giving examples of new exponential integrators of orders 4 and 5.
Ramification of rough paths
, 2006
"... The stack of iterated integrals of a path is embedded in a larger algebraic structure where iterated integrals are indexed by decorated rooted trees and where an extended Chen’s multiplicative property involves the DürrConnesKreimer coproduct on rooted trees. This turns out to be the natural setti ..."
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Cited by 8 (4 self)
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The stack of iterated integrals of a path is embedded in a larger algebraic structure where iterated integrals are indexed by decorated rooted trees and where an extended Chen’s multiplicative property involves the DürrConnesKreimer coproduct on rooted trees. This turns out to be the natural setting for a nongeometric theory of rough paths. MSC: 60H99; 65L99 Keywords: rough paths, rooted trees, Hopf algebras, Bseries.