Abstract: One of the main goals of these notes is to explain how rotations in R n are induced by the action of a certain group, Spin(n), on R n, in a way that generalizes the action of the unit...
Notes on Spherical Harmonics and Linear Representations of Lie Groups (2009)
1.2 Spherical Harmonics on the 2-Sphere...................... 8
CONSTRAINED QUADRILATERAL MESHES OF BOUNDED SIZE (2008)
Suneeta Ramaswami, Marcelo Siqueira, Tessa Sundaram, Jean Gallier, James Gee
We introduce a new algorithm to convert triangular meshes of polygonal regions, with or without holes, into strictly convex quadrilateral meshes of small bounded size. Our algorithm includes all...
5 6 Topological Repairing of 3D Digital Images (2008)
Marcelo Siqueira, Longin Jan Latecki, Nicholas Tustison, Jean Gallier, James Gee
Abstract We present here a new randomized algorithm for repairing the topology of objects represented by 3D binary digital images. By “repairing the topology”, we mean a sys-and optimized for...
Marcelo Siqueira, Jean Gallier, Longin Jan Latecki
A 3D binary digital image is said to be well-composed if and only if the set of points in the faces shared by the voxels of foreground and background points of the image is a surface in R 3....
Marcelo Siqueira, Jean Gallier, Longin Jan Latecki
A 3D binary digital image is said to be well-composed if and only if the set of points in the faces shared by the voxels of foreground and background points of the image is a surface in R 3....
Topological Evolution of Surfaces (appeared in Graphics Interface ’96, pp. 194-203) (2008)
This paper presents a framework for generating smooth-looking transformations between pairs of surfaces that may differ in topology. The user controls the transformation by specifying a sparse...
Jean Gallier, David Plaisted, Wayne Snyder
Abstract. In this paper, it is shown that there is an algorithm that, given any finite set E of ground equations, produces a reduced canonical rewriting system R equivalent to E in polynomial time....
(appeared in Graphics Interface ’96, pp. 194-203) Topological Evolution of Surfaces (2008)
This paper presents a framework for generating smoothlooking transformations between pairs of surfaces that may differ in topology. The user controls the transformation by specifying a sparse control...
Logarithms and Square Roots of Real Matrices (2008)
Abstract. In these notes, we consider the problem of finding the logarithm or the square root of a real matrix. It is known that for every real n × n matrix, A, ifnorealeigenvalue of A is negative...
Logarithms and Square Roots of Real Matrices (2008)
Abstract. In these notes, we consider the problem of finding the logarithm or the square root of a real matrix. It is known that for every real n × n matrix, A, ifnorealeigenvalue of A is negative...
Construction of c ∞ surfaces from triangular meshes using parametric pseudo-manifolds (2008)
Marcelo Siqueira, Dianna Xu, Jean Gallier
Sophia-Antipolis, France, during the summer of 2007. We are grateful to Nicholas Ayache and the members of the ASCLEPIOS group for their hospitality. Some people have read incomplete versions of the...
Fast and Simple Methods For Computing Control Points (2007)
Doug Decarlo, Jean Gallier, Weiqing Gu, Shenjun Jiang
. The purpose of this paper is to present simple and fast methods for computing control points for polynomial curves and polynomial surfaces given explicitly in terms of polynomials (written as sums...
Digital Equipment Corporation 1991 (2007)
The purpose of this paper is to give an exposition of material dealing with constructive logics, typed -calculi, and linear logic. The first part of this paper gives an exposition of background...
Drawing Closed Rational Surfaces (2007)
. In this short paper, we consider the practical problem of drawing a closed rational surface specified by a net of control points. The main result is that for any rational surface F , the entire...
Some basic mathematical tools such as convew sets, polytopes and combinatorial topology, are used quite heavily in applied fields such as geometric modeling, meshing, computer vision, medical imaging...
Some basic mathematical tools such as convew sets, polytopes and combinatorial topology, are used quite heavily in applied fields such as geometric modeling, meshing, computer vision, medical imaging...
Fast and Simple Methods For Computing Control Points (2006)
Abstract. The purpose of this paper is to present simple and fast methods for computing control points for polynomial curves and polynomial surfaces given explicitly in terms of polynomials (written...
Abstract. This note contains two remarks. The first remark concerns the extension of the well-known Cayley representation of rotation matrices by skew symmetric matrices to rotation matrices...
Abstract. This note contains two remarks. The first remark concerns the extension of the well-known Cayley representation of rotation matrices by skew symmetric matrices to rotation matrices...
The Completeness of Propositional Resolution A Simple and Constructive Proof (2006)
Abstract. It is well known that the resolution method (for propositional logic) is complete. However, completeness proofs found in the literature use an argument by contradiction showing that if a...
The Completeness of Propositional Resolution A Simple and Constructive Proof (2006)
Abstract. It is well known that the resolution method (for propositional logic) is complete. However, completeness proofs found in the literature use an argument by contradiction showing that if a...
Computing Exponentials of Real Matrices Diagonalizable Over C (2006)
Abstract. In this note, we consider the problem of computing the exponential of a real matrix. It is shown that if A is a real n × n matrix and A can be diagonalized over C, then there is a formula...
Graduate Group Chairperson (2006)
Marcelo Siqueira, Jean Gallier, Rajeev Alur, Marcelo Siqueira
To my wife Poliana, my daughter Sofia, and my parents Roberto and Dilma. iii Acknowledgments First and foremost, I would like to thank my thesis advisor, Jean Gallier, for his guidance and advice...
Making 3D Binary Digital Images Well-Composed (2004)
Siqueira, Marcelo, Latecki, Longin Jan, Gallier, Jean
A 3D binary digital image is said to be well-composed if and only if the set of points in the faces shared by the voxels of foreground and background points of the image is a surface in R3....
Mo Deling, Jean Gallier, Jean Gallier, A Pano, Mo Deling, Ma Rch
curved shap es, using curves and surfaces
Constructive Logics. Part I: A Tutorial on Proof Systems and Typed λ-Calculi (2003)
The purpose of this paper is to give an exposition of material dealing with constructive logic, typed -calculi, and linear logic. The emergence in the past ten years of a coherent eld of research...
Computing Exponentials of Real Matrices Diagonalizable Over C (2000)
. In this note, we consider the problem of computing the exponential of a real matrix. It is shown that if A is a real n \Theta n matrix and A can be diagonalized over C , then there is a formula for...
Computing Exponentials of Skew Symmetric Matrices And Logarithms of Orthogonal Matrices (2000)
. We show that there is a generalization of Rodrigues's formula for computing the exponential map exp: so(n) ! SO(n) from skew symmetric matrices to orthogonal matrices when n 4, and we give a...
A Kinematic Model of the Human Arm Using Triangular B'ezier Spline Surfaces (2000)
Deepak Tolani Norman, Norman Badler, Jean Gallier
. This paper presents a kinematic model of the human arm in which the workspace of the elbow is modeled as a triangular B'ezier spline surface. It is also explained how this model is used for...
Chaining Layered Integrity Checks (1999)
Jean Gallier, William A. Arbaugh, William A. Arbaugh, William A. Arbaugh, Jonathan M. Smith
No work the size of this dissertation is done in isolation, and I would like to thank the people who worked with and supported me over the last four years. Harold F. Bower has worked with me on...
Simple Methods For Drawing Rational Surfaces as Four or Six Bézier Patches (1999)
. In this paper, we give several simple methods for drawing a whole rational surface (without base points) as several B'ezier patches. The first two methods apply to surfaces specified by...
A Simple Method For Drawing a Rational Curve as Two Bézier Segments (1999)
. In this paper, we give a simple method for drawing a closed rational curve specified in terms of control points as two B'ezier segments. The main result is the following: For every affine...
On the Efficiency of Strategies for Subdividing Polynomial Triangular Surface Patches (1999)
. In this paper, we investigate the efficiency of various strategies for subdividing polynomial triangular surface patches. We give a simple algorithm performing a regular subdivision in four calls...
Dimitris Metaxas, Jean Gallier, Douglas M. Decarlo, Douglas M. Decarlo
Looking back, it’s quite difficult for me to say why this work proceeded in the manner in which it did. But I must say that I feel quite strongly about some of the ideas presented here—this must...
Image-Based Ventricular Blood Flow Analysis (1998)
Dimitris Metaxas, Jean Gallier, Timothy N. Jones, Timothy N. Jones
We describe a novel and non-invasive method for the quantitative analysis of blood flow in the left ventricle of specific human patients using information derived from medical images. There are three...
A Note On Logical PERs and Reducibility Logical Relations strike again! (1998)
. We prove a general theorem for establishing properties expressed by binary relations on typed (first-order) -terms, using a variant of the reducibility method and logical PERs. As an application,...
ALIEN: A Generalized Computing Model Of Active Networks (1998)
Jonathan M. Smith, Jean Gallier, David Scott Alexander, David Scott Alexander
alien: A Generalized Computing Model of Active Networks David Scott Alexander Jonathan M. Smith Active Networks are networks whose actions may be changed during operation either by introducing new...
Typing Untyped Lambda-Terms, or Reducibility Strikes Again! (1997)
. It was observed by Curry that when (untyped) -terms can be assigned types, for example, simple types, these terms have nice properties (for example, they are strongly normalizing) . Coppo, Dezani,...
On the Correspondence between Proofs and λ-Terms (1997)
. The correspondence between natural deduction proofs and -terms is presented and discussed. A variant of the reducibility method is presented, and a general theorem for establishing properties of...
Constructive Logics. Part II: Linear Logic and Proof Nets (1997)
. The purpose of this paper is to give an exposition of material dealing with constructive logics, typed -calculi, and linear logic. The first part of this paper gives an exposition of background...
On the efficiency of strategies for subdividing polynomial triangular surface patches (1997)
Abstract. In this paper, we investigate the efficiency of various strategies for subdividing polynomial triangular surface patches. We give a simple algorithm performing a regular subdivision in four...
Topological Evolution of Surfaces (1996)
This paper presents a framework for generating smooth-looking transformations between pairs of surfaces that may differ in topology. The user controls the transformation by specifying a sparse...
Topological Evolution of Surfaces (1996)
This paper presents a framework for generating smooth-looking transformations between pairs of surfaces that may differ in topology. The user controls the transformation by specifying a sparse...
Typing Untyped Lambda-Terms, or Reducibility Strikes Again! (1995)
. It was observed by Curry that when (untyped) -terms can be assigned types, for example, simple types, these terms have nice properties (for example, they are strongly normalizing) . Coppo, Dezani,...
Proving Properties of Typed Lambda Terms Using Realizability, Covers, and Sheaves (1995)
. The main purpose of this paper is to take apart the reducibility method in order to understand how its pieces fit together, and in particular, to recast the conditions on candidates of reducibility...
Kripke Models and the (in)equational Logic of the Second-Order Lambda-Calculus (1995)
. We define a new class of Kripke structures for the second-order -calculus, and investigate the soundness and completeness of some proof systems for proving inequalities (rewrite rules) as well as...
Proving Properties of Typed lambda-Terms Using Realizability, Covers, and Sheaves (1994)
The main purpose of this paper is to take apart the reducibility method in order to understand how its pieces fit together, and in particular, to recast the conditions on candidates of reducibility...
Constructive Logics. Part I: A Tutorial on Proof Systems and Typed λ-Calculi (1991)
The purpose of this paper is to give an exposition of material dealing with constructive logics, typed -calculi, and linear logic. The emergence in the past ten years of a coherent field of research...
9 Constructive Logics. Part II: Linear Logic and Proof Nets (1991)
This work was done while the author was on sabbatical leave from the University of
Thierry Coquand, Jean Gallier, Le Chesnay Cedex
. We give a proof that all terms that type-check in the theory of constructions are strongly normalizing (under fi-reduction). The main novelty of this proof is that it uses a "Kripke-like"...
A Study of Semantics, Types, and Languages for Databases and Object Oriented Programming (1989)
Peter Buneman, Val Breazu-tannen, Jean Gallier, Atsushi Ohori, Atsushi Ohori
The purpose of this thesis is to investigate a type system for databases and object-oriented programming and to design a statically typed programming language for these applications. Such a language...
Simple methods for drawing rational surfaces as four or six Bézier patches (1910)
Abstract. In this paper, we give several simple methods for drawing a whole rational surface (without base points) as several Bézier patches. The first two methods apply to surfaces specified by...