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Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
Abstract

Cited by 1108 (51 self)
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This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning under uncertainty, sensorbased planning, visibility, decisiontheoretic planning, game theory, information spaces, reinforcement learning, nonlinear systems, trajectory planning, nonholonomic planning, and kinodynamic planning.
Dual polyhedra and mirror symmetry for Calabi–Yau hypersurfaces in toric varieties
 J. Alg. Geom
, 1994
"... We consider families F(∆) consisting of complex (n − 1)dimensional projective algebraic compactifications of ∆regular affine hypersurfaces Zf defined by Laurent polynomials f with a fixed ndimensional Newton polyhedron ∆ in ndimensional algebraic torus T = (C ∗ ) n. If the family F(∆) defined by ..."
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Cited by 467 (20 self)
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We consider families F(∆) consisting of complex (n − 1)dimensional projective algebraic compactifications of ∆regular affine hypersurfaces Zf defined by Laurent polynomials f with a fixed ndimensional Newton polyhedron ∆ in ndimensional algebraic torus T = (C ∗ ) n. If the family F(∆) defined by a Newton polyhedron ∆ consists of (n − 1)dimensional CalabiYau varieties then the dual, or polar, polyhedron ∆ ∗ in the dual space defines another family F( ∆ ∗ ) of CalabiYau varieties, so that we obtain the remarkable duality between two different families of CalabiYau varieties. It is shown that the properties of this duality coincide with the properties of Mirror Symmetry discovered by physicists for CalabiYau 3folds. Our method allows to construct many new examples of CalabiYau 3folds and new candidates for their mirrors which were previously unknown for physicists. We conjecture that there exists an isomorphism between two conformal field theories corresponding to CalabiYau varieties from two families F(∆) and F( ∆ ∗). 1
VertexUnfoldings of Simplicial Manifolds
"... We present an algorithm to unfold any triangulated 2manifold (in particular, any simplicial polyhedron) into a nonoverlapping, connected planar layout in linear time. The manifold is cut only along its edges. The resulting layout is connected, but it may have a disconnected interior; the triangles ..."
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Cited by 15 (3 self)
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We present an algorithm to unfold any triangulated 2manifold (in particular, any simplicial polyhedron) into a nonoverlapping, connected planar layout in linear time. The manifold is cut only along its edges. The resulting layout is connected, but it may have a disconnected interior
Vertexunfoldings of simplicial polyhedra
, 2008
"... We present two algorithms for unfolding the surface of any polyhedron, all of whose faces are triangles, to a nonoverlapping, connected planar layout. The surface is cut only along polyhedron edges. The layout is connected, but it may have a disconnected interior: the triangles are connected at vert ..."
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Cited by 1 (1 self)
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We present two algorithms for unfolding the surface of any polyhedron, all of whose faces are triangles, to a nonoverlapping, connected planar layout. The surface is cut only along polyhedron edges. The layout is connected, but it may have a disconnected interior: the triangles are connected at vertices, but not necessarily joined along edges.
VERTEX COLORINGS OF SIMPLICIAL COMPLEXES
"... 1.1. Notation and the basic definition 2 2. Davis–Januszkiewicz spaces 3 3. The Stanley–Reisner face algebra 4 ..."
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1.1. Notation and the basic definition 2 2. Davis–Januszkiewicz spaces 3 3. The Stanley–Reisner face algebra 4
Progressive Simplicial Complexes
, 1997
"... In this paper, we introduce the progressive simplicial complex (PSC) representation, a new format for storing and transmitting triangulated geometric models. Like the earlier progressive mesh (PM) representation, it captures a given model as a coarse base model together with a sequence of refinement ..."
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Cited by 172 (2 self)
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In this paper, we introduce the progressive simplicial complex (PSC) representation, a new format for storing and transmitting triangulated geometric models. Like the earlier progressive mesh (PM) representation, it captures a given model as a coarse base model together with a sequence
Mesh Optimization
, 1993
"... We present a method for solving the following problem: Given a set of data points scattered in three dimensions and an initial triangular mesh wH, produce a mesh w, of the same topological type as wH, that fits the data well and has a small number of vertices. Our approach is to minimize an energy f ..."
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Cited by 397 (8 self)
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We present a method for solving the following problem: Given a set of data points scattered in three dimensions and an initial triangular mesh wH, produce a mesh w, of the same topological type as wH, that fits the data well and has a small number of vertices. Our approach is to minimize an energy function that explicitly models the competing desires of conciseness of representation and fidelity to the data. We show that mesh optimization can be effectively used in at least two applications: surface reconstruction from unorganized points, and mesh simplification (the reduction of the number of vertices in an initially dense mesh of triangles).
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