1,992 research outputs found
Morphing Contact Representations of Graphs
We consider the problem of morphing between contact representations of a plane graph. In a contact representation of a plane graph, vertices are realized by internally disjoint elements from a family of connected geometric objects. Two such elements touch if and only if their corresponding vertices are adjacent. These touchings also induce the same embedding as in the graph. In a morph between two contact representations we insist that at each time step (continuously throughout the morph) we have a contact representation of the same type.
We focus on the case when the geometric objects are triangles that are the lower-right half of axis-parallel rectangles. Such RT-representations exist for every plane graph and right triangles are one of the simplest families of shapes supporting this property. Thus, they provide a natural case to study regarding morphs of contact representations of plane graphs.
We study piecewise linear morphs, where each step is a linear morph moving the endpoints of each triangle at constant speed along straight-line trajectories. We provide a polynomial-time algorithm that decides whether there is a piecewise linear morph between two RT-representations of a plane triangulation, and, if so, computes a morph with a quadratic number of linear morphs. As a direct consequence, we obtain that for 4-connected plane triangulations there is a morph between every pair of RT-representations where the "top-most" triangle in both representations corresponds to the same vertex. This shows that the realization space of such RT-representations of any 4-connected plane triangulation forms a connected set
A Note on Plus-Contacts, Rectangular Duals, and Box-Orthogonal Drawings
A plus-contact representation of a planar graph is called -balanced if
for every plus shape , the number of other plus shapes incident to each
arm of is at most , where is the maximum degree
of . Although small values of have been achieved for a few subclasses of
planar graphs (e.g., - and -trees), it is unknown whether -balanced
representations with exist for arbitrary planar graphs.
In this paper we compute -balanced plus-contact representations for
all planar graphs that admit a rectangular dual. Our result implies that any
graph with a rectangular dual has a 1-bend box-orthogonal drawings such that
for each vertex , the box representing is a square of side length
.Comment: A poster related to this research appeared at the 25th International
Symposium on Graph Drawing & Network Visualization (GD 2017
Computational Methods for Cognitive and Cooperative Robotics
In the last decades design methods in control engineering made substantial progress in
the areas of robotics and computer animation. Nowadays these methods incorporate the
newest developments in machine learning and artificial intelligence. But the problems
of flexible and online-adaptive combinations of motor behaviors remain challenging for
human-like animations and for humanoid robotics. In this context, biologically-motivated
methods for the analysis and re-synthesis of human motor programs provide new insights
in and models for the anticipatory motion synthesis.
This thesis presents the authorâs achievements in the areas of cognitive and developmental robotics, cooperative and humanoid robotics and intelligent and machine learning methods in computer graphics. The first part of the thesis in the chapter âGoal-directed Imitation for Robotsâ considers imitation learning in cognitive and developmental robotics.
The work presented here details the authorâs progress in the development of hierarchical
motion recognition and planning inspired by recent discoveries of the functions of mirror-neuron cortical circuits in primates. The overall architecture is capable of âlearning for
imitationâ and âlearning by imitationâ. The complete system includes a low-level real-time
capable path planning subsystem for obstacle avoidance during arm reaching. The learning-based path planning subsystem is universal for all types of anthropomorphic robot arms, and is capable of knowledge transfer at the level of individual motor acts.
Next, the problems of learning and synthesis of motor synergies, the spatial and spatio-temporal combinations of motor features in sequential multi-action behavior, and the
problems of task-related action transitions are considered in the second part of the thesis
âKinematic Motion Synthesis for Computer Graphics and Roboticsâ. In this part, a new
approach of modeling complex full-body human actions by mixtures of time-shift invariant
motor primitives in presented. The online-capable full-body motion generation architecture
based on dynamic movement primitives driving the time-shift invariant motor synergies
was implemented as an online-reactive adaptive motion synthesis for computer graphics
and robotics applications.
The last chapter of the thesis entitled âContraction Theory and Self-organized Scenarios
in Computer Graphics and Roboticsâ is dedicated to optimal control strategies in multi-agent scenarios of large crowds of agents expressing highly nonlinear behaviors. This last
part presents new mathematical tools for stability analysis and synthesis of multi-agent
cooperative scenarios.In den letzten Jahrzehnten hat die Forschung in den Bereichen der Steuerung und Regelung
komplexer Systeme erhebliche Fortschritte gemacht, insbesondere in den Bereichen
Robotik und Computeranimation. Die Entwicklung solcher Systeme verwendet heutzutage
neueste Methoden und Entwicklungen im Bereich des maschinellen Lernens und der
kĂŒnstlichen Intelligenz. Die flexible und echtzeitfĂ€hige Kombination von motorischen Verhaltensweisen
ist eine wesentliche Herausforderung fĂŒr die Generierung menschenĂ€hnlicher
Animationen und in der humanoiden Robotik. In diesem Zusammenhang liefern biologisch
motivierte Methoden zur Analyse und Resynthese menschlicher motorischer Programme
neue Erkenntnisse und Modelle fĂŒr die antizipatorische Bewegungssynthese.
Diese Dissertation prÀsentiert die Ergebnisse der Arbeiten des Autors im Gebiet der
kognitiven und Entwicklungsrobotik, kooperativer und humanoider Robotersysteme sowie
intelligenter und maschineller Lernmethoden in der Computergrafik. Der erste Teil der
Dissertation im Kapitel âZielgerichtete Nachahmung fĂŒr Roboterâ behandelt das Imitationslernen
in der kognitiven und Entwicklungsrobotik. Die vorgestellten Arbeiten beschreiben
neue Methoden fĂŒr die hierarchische Bewegungserkennung und -planung, die durch
Erkenntnisse zur Funktion der kortikalen Spiegelneuronen-Schaltkreise bei Primaten inspiriert
wurden. Die entwickelte Architektur ist in der Lage, âdurch Imitation zu lernenâ
und âzu lernen zu imitierenâ. Das komplette entwickelte System enthĂ€lt ein echtzeitfĂ€higes
Pfadplanungssubsystem zur Hindernisvermeidung wĂ€hrend der DurchfĂŒhrung von Armbewegungen.
Das lernbasierte Pfadplanungssubsystem ist universell und fĂŒr alle Arten von
anthropomorphen Roboterarmen in der Lage, Wissen auf der Ebene einzelner motorischer
Handlungen zu ĂŒbertragen.
Im zweiten Teil der Arbeit âKinematische Bewegungssynthese fĂŒr Computergrafik und
Robotikâ werden die Probleme des Lernens und der Synthese motorischer Synergien, d.h.
von rÀumlichen und rÀumlich-zeitlichen Kombinationen motorischer Bewegungselemente
bei Bewegungssequenzen und bei aufgabenbezogenen Handlungs ĂŒbergĂ€ngen behandelt.
Es wird ein neuer Ansatz zur Modellierung komplexer menschlicher Ganzkörperaktionen
durch Mischungen von zeitverschiebungsinvarianten Motorprimitiven vorgestellt. Zudem
wurde ein online-fĂ€higer Synthesealgorithmus fĂŒr Ganzköperbewegungen entwickelt, der
auf dynamischen Bewegungsprimitiven basiert, die wiederum auf der Basis der gelernten
verschiebungsinvarianten Primitive konstruiert werden. Dieser Algorithmus wurde fĂŒr
verschiedene Probleme der Bewegungssynthese fĂŒr die Computergrafik- und Roboteranwendungen
implementiert.
Das letzte Kapitel der Dissertation mit dem Titel âKontraktionstheorie und selbstorganisierte
Szenarien in der Computergrafik und Robotikâ widmet sich optimalen Kontrollstrategien
in Multi-Agenten-Szenarien, wobei die Agenten durch eine hochgradig nichtlineare
Kinematik gekennzeichnet sind. Dieser letzte Teil prÀsentiert neue mathematische Werkzeuge
fĂŒr die StabilitĂ€tsanalyse und Synthese von kooperativen Multi-Agenten-Szenarien
Visualizing the dynamics of London's bicycle hire scheme
Visualizing ïŹows between origins and destinations can be straightforward when dealing with small numbers of journeys or simple geographies. Representing ïŹows as lines embedded in geographic space has commonly been used to map transport ïŹows, especially when geographic patterns are important as they are when characterising cities or managing transportation. However, for larger numbers of ïŹows, this approach requires careful design to avoid problems of occlusion, salience bias and information overload. Driven by the requirements identiïŹed by users and managers of the London Bicycle Hire scheme we present three methods of representation of bicycle hire use and travel patterns. Flow maps with curved ïŹow symbols are used to show overviews in ïŹow structures. Gridded views of docking station location that preserve geographic relationships are used to explore docking station status over space and time in a graphically eïŹcient manner. Origin-Destination maps that visualise the OD matrix directly while maintaining geographic context are used to provide visual details on demand. We use these approaches to identify changes in travel behaviour over space and time, to aid station rebalancing and to provide a framework for incorporating travel modelling and simulation
The PSurface library
We describe PSurface, a C++ library that allows to store and access piecewise linear maps between simplicial surfaces in R^2 and R^3. Piecewise linear maps can be used, e.g., to construct boundary approximations for finite element grids, and grid intersections for domain decomposition methods. In computer graphics the maps allow to build level-of-detail representations as well as texture- and bump maps. The PSurface library can be used as the basis for the implementation of a wide range of algorithms that use piecewise linear maps between triangulated surfaces. A few simple examples are given in this work. We document the data structures and algorithms and show how PSurface is used in the numerical analysis framework Dune and the visualization software Amira
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