The Rigidity of Spherical Frameworks: Swapping Blocks and Holes (2009)
Finbow, Wendy, Ross, Elissa, Whiteley, Walter
A significant range of geometric structures whose rigidity is explored for both practical and theoretical purposes are formed by modifying generically isostatic triangulated spheres. In the block and...
David Orden, Günter Rote, Francisco Santos, Brigitte Servatius, Herman Servatius, Walter Whiteley
Abstract. We study non-crossing frameworks in the plane for which the classical reciprocal on the dual graph is also non-crossing. We give a complete description of the self-stresses on non-crossing...
Constraint Theory applied to Proteins (2008)
Mykyta Chubynsky, On Hespenheide, Donald J. Jacobs, Leslie A. Kuhn, Ming Lei, A. J. Rader, ...
In this article we review how constraint theory can be applied to proteins to give useful information about the rigid and flexible regions. This approach includes all the constraints in a biomolecule...
When is a symmetric pin-jointed framework isostatic? (2008)
Connelly, Robert, Fowler, Patrick, Guest, Simon, Schulze, Bernd, Whiteley, Walter
Maxwell's rule from 1864 gives a necessary condition for a framework to be isostatic in 2D or in 3D. Given a framework with point group symmetry, group representation theory is exploited to provide...
Geometric Properties of Assur Graphs (2008)
Servatius, Brigitte, Shai, Offer, Whiteley, Walter
In our previous paper, we presented the combinatorial theory for minimal isostatic pinned frameworks - Assur graphs - which arise in the analysis of mechanical linkages. In this paper we further...
Combinatorial Characterization of the Assur Graphs from Engineering (2008)
Servatius, Brigitte, Shai, Offer, Whiteley, Walter
We introduce the idea of Assur graphs, a concept originally developed and exclusively employed in the literature of the kinematics community. The paper translates the terminology, questions, methods...
Some notes on the equivalence of first-order rigidity in various geometries (2007)
Saliola, Franco V., Whiteley, Walter
These pages serve two purposes. First, they are notes to accompany the talk "Hyperbolic and projective geometry in constraint programming for CAD" by Walter Whiteley at the "Janos Bolyai Conference...
Using Angle of Arrival (Bearing) Information in Network Localization (2006)
Eren, Tolga, Whiteley, Walter, Belhumeur, Peter N.
In this paper, we consider using angle of arrival information (bearing) for network localization and control in two different fields of multi-agent systems: (i) wireless sensor networks; (ii) robot...
Rigid Formations with Leader-Follower Architecture (2006)
Eren, Tolga, Whiteley, Walter, Belhumeur, Peter N.
This paper is concerned with information structures used in rigid formations of autonomous agents that have leader-follower architecture. The focus of the paper is on sensor/network topologies to...
A theory of network localization (2006)
James Aspnes, Tolga Eren, David K. Goldenberg, Student Member, A. Stephen Morse, Walter Whiteley, ...
Abstract—In this paper, we provide a theoretical foundation for the problem of network localization in which some nodes know their locations and other nodes determine their locations by measuring...
Merging Globally Rigid Formations of Mobile Autonomous Agents (2005)
Eren, Tolga, Anderson, Brian, Whiteley, Walter, Morse, A. Stephen, Belhumeur, Peter N.
This paper is concerned with merging globally rigid formations of mobile autonomous agents. A key element in all future multi-agent systems will be the role of sensor and communication networks as an...
Rigid Formations with Leader-Follower Architecture (2005)
Eren, Tolga, Whiteley, Walter, Belhumeur, Peter N.
This paper is concerned with information structures used in rigid formations of autonomous agents that have leader-follower architecture. The focus of this paper is on sensor/network topologies to...
Information structures to secure control of rigid formations with leader-follower structure (2005)
Tolga Eren, Walter Whiteley, A. Stephen Morse, Peter N. Belhumeur
Abstract — This paper is concerned with rigid formations of mobile autonomous agents using a leader-follower structure. A formation is a group of agents moving in real 2- or 3dimensional space. A...
Information structures to secure control of rigid formations with leader-follower structure (2005)
Tolga Eren, Walter Whiteley, A. Stephen Morse, Peter N. Belhumeur
Abstract — This paper is concerned with rigid formations of mobile autonomous agents that have leader-follower architecture. In a previous paper, Baillieul and Suri gave a proposition as a...
P.: Further results on sensor network localization using rigidity (2005)
Tolga Eren, Walter Whiteley, Peter N. Belhumeur
Abstract — Two further results, which extend the previous work on the use of rigidity in sensor network localization, are given. The previous work provided the conditions for the localization of an...
P.: Further results on sensor network localization using rigidity (2005)
Tolga Eren, Walter Whiteley, Peter N. Belhumeur
Abstract-Two further results, which extend the previous work on the use of rigidity in sensor network localization, are given, The previous work provided the conditions for the localization of an...
Rigid formations with leader-follower architecture (2005)
Tolga Eren, Walter Whiteley, Peter N. Belhumeur
Abstract — This paper is concerned with information structures used in rigid formations of autonomous agents that have leaderfollower architecture. The focus of this paper is on sensor/network...
Information Structures to Secure Control of Rigid Formations with Leader-Follower Structure (2004)
Eren, Tolga, Whiteley, Walter, Anderson, Brian D.O., Morse, A. Stephen, Belhumeur, Peter N.
This paper is concerned with rigid formations of mobile autonomous agents using a leader-follower structure. A formation is a group of agents moving in real 2- or 3- dimensional space. A formation is...
A Theoretical Analysis of the Conditions for Unambiguous Node Localization in Sensor Networks (2004)
Eren, Tolga, Whiteley, Walter, Belhumeur, Peter N.
In this paper we provide a theoretical foundation for the problem of network localization in which some nodes know their locations and other nodes determine their locations by measuring distances or...
A theoretical analysis of the conditions for unambiguous node localization in sensor networks (2004)
Tolga Eren, Walter Whiteley, Peter N. Belhumeur
Abstract — In this paper we provide a theoretical foundation for the problem of network localization in which some nodes know their locations and other nodes determine their locations by measuring...
Non-crossing frameworks with non-crossing reciprocals (2004)
David Orden, G Ünter Rote, Francisco Santos, Brigitte Servatius, Herman Servatius, Walter Whiteley
Abstract. We study non-crossing frameworks in the plane for which the classical reciprocal on the dual graph is also non-crossing. We give a complete description of the self-stresses on non-crossing...
Information structures to secure control of globally rigid formations (2004)
Tolga Eren, Walter Whiteley, A. Stephen, Morse Brian, D. O. Anderson, Peter N. Belhumeur
Abstract — Sensor and network topologies of rigid formations with distance information between mobile autonomous agents are considered. An approach based on rigidity for creating such topologies...
Operations on rigid formations of autonomous agents (2004)
Tolga Eren, A. Stephen Morse, Walter Whiteley, N. Belhumeur, ...
Abstract. This paper is concerned with the maintenance of rigid formations of mobile autonomous agents. A key element in all future multi-agent systems will be the role of sensor and communication...
Merging globally rigid formations of mobile autonomous agents (2004)
This paper is concerned with merging globally rigid formations of mobile autonomous agents. A key element in all future multi-agent systems will be the role of sensor and communication networks as an...
Single-vertex origami and spherical expansive motions (2004)
Ileana Streinu, Walter Whiteley
Abstract. We prove that all single-vertex origami shapes are reachable from the open flat state via simple, non-crossing motions. We also consider conical paper, where the total sum of the cone...
Planar Minimally Rigid Graphs and Pseudo-Triangulations (2004)
Ruth Haas, David Orden, Günter Rote, Francisco Santos, Brigitte Servatius, Herman Servatius, ...
Pointed pseudo-triangulations are planar minimally rigid graphs embedded in the plane with pointed vertices (adjacent to an angle larger than π). In this paper we prove that the opposite...
Merging globally rigid formations of mobile autonomous agents (2004)
Tolga Eren, Walter Whiteley, A. Stephen Morse, Peter N. Belhumeur
This paper focuses on developing techniques and strategies for the analysis and design of sensor and network topologies required to merge globally rigid formations for cooperative tasks. Central to...
Non-crossing frameworks with non-crossing reciprocals (2003)
Orden, David, Rote, Guenter, Santos, Francisco, Servatios, Brigitte, Servatius, Herman, Whiteley, Walter
We study non-crossing frameworks in the plane for which the classical reciprocal on the dual graph is also non-crossing. We give a complete description of the self-stresses on non-crossing frameworks...
Planar Minimally Rigid Graphs and Pseudo-Triangulations (2003)
Haas, Ruth, Orden, David, Rote, Guenter, Santos, Francisco, Servatius, Brigitte, Servatius, Herman, ...
Pointed pseudo-triangulations are planar minimally rigid graphs embedded in the plane with pointed vertices (adjacent to an angle larger than 180 degrees. In this paper we prove that the opposite...
Operations on Rigid Formations of Autonomous Agents (2003)
Anderson, Brian D. O., Belhumeur, Peter N., Eren, Tolga, Morse, A. Stephen, Whiteley, Walter
This paper is concerned with the maintenance of rigid formations of mobile autonomous agents. A key element in all future multi-agent systems will be the role of sensor and communication networks as...
Sensor and network topologies of formations of autonomous agents are considered. The aim of the paper is to suggest an approach for such topologies for formations with direction, bearing and angle...
Planar Minimally Rigid Graphs and Pseudo-Triangulations (2003)
Ruth Haas, David Orden, Günter Rote, Francisco Santos, Brigitte Servatius, Hermann Servatius, ...
Pointed pseudo-triangulations are planar minimally rigid graphs embedded in the plane with pointed vertices (incident to an angle larger than #). In this paper we prove that the opposite statement is...
The decline and rise of geometry in 20th century North America (1999)
While I will begin with my own evidence for the decline of geometry in this century and my own description on how such a decline has proceeded, my basic theme is hopeful. Geometry has not died...
Constraining plane configurations in cad: combinatorics of lengths and directions (1999)
Brigitte Servatius, Walter Whiteley
Abstract. Configurations of points in the plane constrained by only directions or by lengths alone lead to equivalent theories known as parallel drawings and infinitesimal rigidity of plane...
Second-order rigidity and prestress stability for tensegrity frameworks (1996)
Robert Connelly, Walter Whiteley
Abstract. This paper defines two concepts of rigidity for tensegrity frameworks (frameworks with cables, bars, and struts): prestress stability and second-order rigidity. We demonstrate a hierarchy...
Plane Self Stresses and projected Polyhedra I: The Basic Pattem (1993)
Crapo, Henry, Whiteley, Walter
Voilà plus d’un siècle, le géomètre (et physicien) Clerk Maxwell décrivait une relation surprenante entre les autocontraintes statiques des charpentes de graphes planaires, et les projections...
Plane Self Stresses and projected Polyhedra I: The Basic Pattem (1993)
Crapo, Henry, Whiteley, Walter
Voilà plus d’un siècle, le géomètre (et physicien) Clerk Maxwell décrivait une relation surprenante entre les autocontraintes statiques des charpentes de graphes planaires, et les projections...
Plane Self Stresses and projected Polyhedra I: The Basic Pattem (1993)
Crapo, Henry, Whiteley, Walter
Voilà plus d’un siècle, le géomètre (et physicien) Clerk Maxwell décrivait une relation surprenante entre les autocontraintes statiques des charpentes de graphes planaires, et les projections...
Vertex Splitting in Isostatic Frameworks (1990)
On démontre que des divisions de sommet le long de 0, 1 ou 2 arêtes d'une charpente de barres et de joints dans I'espace tridimensionnel respectent I'indépendance pour p resque toutes les...
Vertex Splitting in Isostatic Frameworks (1990)
On démontre que des divisions de sommet le long de 0, 1 ou 2 arêtes d'une charpente de barres et de joints dans I'espace tridimensionnel respectent I'indépendance pour p resque toutes les...
Vertex Splitting in Isostatic Frameworks (1990)
On démontre que des divisions de sommet le long de 0, 1 ou 2 arêtes d'une charpente de barres et de joints dans I'espace tridimensionnel respectent I'indépendance pour p resque toutes les...
Generating Isostatic Frameworks (1985)
Tay, Tiong-Seng, Whiteley, Walter
La littérature d’ingénierie renferme bon nombre de techniques pour construire de grandes charpentes statiquement rigides à partir de plus petites. Malheureusement, certains de ces principes sont...
Generating Isostatic Frameworks (1985)
Tay, Tiong-Seng, Whiteley, Walter
La littérature d’ingénierie renferme bon nombre de techniques pour construire de grandes charpentes statiquement rigides à partir de plus petites. Malheureusement, certains de ces principes sont...
Generating Isostatic Frameworks (1985)
Tay, Tiong-Seng, Whiteley, Walter
La littérature d’ingénierie renferme bon nombre de techniques pour construire de grandes charpentes statiquement rigides à partir de plus petites. Malheureusement, certains de ces principes sont...
Recent Advances in the Generic Ridigity of Structures (1984)
Tay, Tiong-Seng, Whiteley, Walter
Nous présentons ici un aperçu des théorèmes et des conjectures qui decrivent les graphes qui produisent des structures génériquement rigides dans un espace à n dimensions. Les structures...
Recent Advances in the Generic Ridigity of Structures (1984)
Tay, Tiong-Seng, Whiteley, Walter
Nous présentons ici un aperçu des théorèmes et des conjectures qui decrivent les graphes qui produisent des structures génériquement rigides dans un espace à n dimensions. Les structures...
Recent Advances in the Generic Ridigity of Structures (1984)
Tay, Tiong-Seng, Whiteley, Walter
Nous présentons ici un aperçu des théorèmes et des conjectures qui decrivent les graphes qui produisent des structures génériquement rigides dans un espace à n dimensions. Les structures...
Cones, infinity and one-story buildings (1983)
Considérons un édifice à un seul étage construit à partir d’une série de colonnes verticales (barres et joints possiblement de longueurs différentes), une charpente de toit reliant le haut...
Cones, infinity and one-story buildings (1983)
Considérons un édifice à un seul étage construit à partir d’une série de colonnes verticales (barres et joints possiblement de longueurs différentes), une charpente de toit reliant le haut...
Cones, infinity and one-story buildings (1983)
Considérons un édifice à un seul étage construit à partir d’une série de colonnes verticales (barres et joints possiblement de longueurs différentes), une charpente de toit reliant le haut...
Statics of Frameworks and Motions of Panel Structures: A projective Geometric Introduction (1982)
Crapo, Henry, Whiteley, Walter
Deux domaines traditionnellement &pares, la statique de charpentes faites debarres et de joints et la cinématique instantanée de structures à panneaux articuIés sont ici réunis dans une approche...
Motions and stresses of projected polyhedra (1982)
L’utilisation de mouvements infinitésimaux de structures à panneaux permet d’apporter une nouvelle preuve au théorème de Clerk Maxwell affirmant que la projection d’un polyèdre de...
Motions of Trusses and Bipartite Frameworks (1982)
Ce projet de recherche a été subventionné par le CRSNG du Canada (A3568).
Statics of Frameworks and Motions of Panel Structures: A projective Geometric Introduction (1982)
Crapo, Henry, Whiteley, Walter
Deux domaines traditionnellement &pares, la statique de charpentes faites debarres et de joints et la cinématique instantanée de structures à panneaux articuIés sont ici réunis dans une approche...
Motions and stresses of projected polyhedra (1982)
L’utilisation de mouvements infinitésimaux de structures à panneaux permet d’apporter une nouvelle preuve au théorème de Clerk Maxwell affirmant que la projection d’un polyèdre de...
Motions of Trusses and Bipartite Frameworks (1982)
Ce projet de recherche a été subventionné par le CRSNG du Canada (A3568).
Statics of Frameworks and Motions of Panel Structures: A projective Geometric Introduction (1982)
Crapo, Henry, Whiteley, Walter
Deux domaines traditionnellement &pares, la statique de charpentes faites debarres et de joints et la cinématique instantanée de structures à panneaux articuIés sont ici réunis dans une approche...
Motions and stresses of projected polyhedra (1982)
L’utilisation de mouvements infinitésimaux de structures à panneaux permet d’apporter une nouvelle preuve au théorème de Clerk Maxwell affirmant que la projection d’un polyèdre de...
Motions of Trusses and Bipartite Frameworks (1982)
Ce projet de recherche a été subventionné par le CRSNG du Canada (A3568).
Realizability of Polyhedra (1979)
We address ourselves to three types of combinatorial and projective problems, all of which concern the patterns of faces, edges and vertices of polyhedra. These patterns, as combinatorial structures,...
Realizability of Polyhedra (1979)
We address ourselves to three types of combinatorial and projective problems, all of which concern the patterns of faces, edges and vertices of polyhedra. These patterns, as combinatorial structures,...
Realizability of Polyhedra (1979)
We address ourselves to three types of combinatorial and projective problems, all of which concern the patterns of faces, edges and vertices of polyhedra. These patterns, as combinatorial structures,...