Gershon Elber - Personal Site - Publications Page

Selected Publications

Manufacturing, Accessibility, and Visibility

"Accessibility for Line-Cutting in Freeform Surfaces", by Boris van Sosin, Michael Barton, Gershon Elber, 2019
"Using Curvature Bounds Towards Collision Free 5-Axis Tool-Paths", by Ben Ezair and Gershon Elber, 2019
"Orientation Analysis of 3D Objects Toward Minimal Support Volume in 3D-printing", by Fady Massarwi, Ben Ezair, Gershon Elber, 2015
"Precise Gouging-free Tool Orientations for 5-Axis CNC Machining", by Yong-Joon Kim, Gershon Elber, Michael Barton, and Helmut Pottmann, 2014
"Multi-DimensionalDynamic Programming in Ruled Surface Fitting", by Charlie C. L. Wang and Gershon Elber, 2014
"Line Accessibility of Free Form Surfaces", by Aviv Segall, Jonathan Mizrahi, Yong-Joon Kim, and Gershon Elber, 2014
"Geometric Multi-Covering", by Reuven Strauss, Florin Isvoranu and Gershon Elber, 2014
"Geometric Covering", by Nadav Shragai and Gershon Elber, 2013
"Papercraft Models using Generalized Cylinders", by Fady Massarwi, Craig Gotsman, and Gershon Elber, 2008
"Piecewise Developable Surface Approximation of General NURBS Surfaces, with Global Error Bounds", by Jacob Subag and Gershon Elber, 2006
"C^1 Continuous Toolpath Generation toward 5-axis High Speed Machining", by Gershon Elber, Elaine Cohen and Sam Drake, 2006
"Two-Dimensional Visibility Charts for Continuous Curves.", by Gershon Elber, Robert Sayegh, Gill Barequet and Ralph R. Martin, 2005
"MATHSM: Medial Axis Transform toward High Speed Machining of Pockets", by Gershon Elber, Elaine Cohen and Sam Drake, 2005
"Precise Global Collision Detection in Multi-Axis NC-Machining", by Oleg Ilushin, Gershon Elber, Dan Halperin and Ron Wein, 2005
"A Unified Approach to Accessibility in 5-axis Freeform Milling Environments", by Gershon Elber and Elaine Cohen, 1999
"Cone Visibility Decomposition of Freeform Surfaces", by Gershon Elber and Eyal Zussman, 1998
"5-Axis Freeform Surface Milling Using Piecewise Ruled Surface Approximation", by Gershon Elber and Russ Fish, 1997
"Model Fabrication Using Surface Layout Projects", by Gershon Elber, 1995
"Freeform Surface Region Optimization for Three- and Five-Axis Milling", by Gershon Elber, 1995
"Arbitrarily Precise Computation of Gauss Maps and Visibility Sets for Freeform Surfaces", by Gershon Elber and Elaine Cohen, 1995
"Tool Path Generation for Freeform Surface Models", by Gershon Elber and Elaine Cohen, 1994
"Accessibility in 5-Axis Milling Environment", by Gershon Elber, 1994

Symbolic Computation on Freeforms

"Precise Hausdorff Distance Computation for Freeform Surfaces Based on Computations with Osculating Toroidal Patches", by Sang-Hyun Son, Myung-Soo Kim and Gershon Elber, 2021
"Self-Intersection Computation for Freeform Surfaces Based on a Regional Representation Scheme for Miter Points", by Youngjin Park, Q Youn Hong, Myung-Soo Kim, and Gershon Elber, 2021
"Solving Piecewise Polynomial Constraint Systems with Decomposition and a Subdivision-Based Solver", by Boris van Sosin and Gershon Elber, 2017
"Dense Packing of Congruent Circles in Free-form Non-convex Containers", by Jinesh Machchhar and Gershon Elber, 2017
"Revisiting the Problem of Zeros of Univariate Scalar Beziers", by Jinesh Machchhar and Gershon Elber, 2016
"Topologically Guaranteed Bivariate Solutions of Under-constrained Multivariate Piecewise Polynomial Systems", by Jonathan Mizrahi and Gershon Elber, 2015
"Precise Contact Motion Planning for Deformable Planar Curved Shapes", by Yong-Joon Kim, Gershon Elber, and Myung-Soo Kim, 2015
"High-Precision Continuous Contact Motion for Planar Freeform Geometric Curves", by Yong-Joon Kim, Gershon Elber, and Myung-Soo Kim, 2014
"Modeling by Composition", by Gershon Elber and Myung Soo Kim, 2014
"Global Solutions of Well-constrained Transcendental Systems using Expression Trees and a Single Solution Test", by Maxim Aizenshtein, Michael Barton and Gershon Elber, 2012
"Precise Hausdorff Distance Computation between Polygonal Meshes", by Michael Barton, Iddo Hanniel, Gershon Elber and Myung Soo Kim, 2010
"Efficient Solution to Systems of Multivariate Polynomials using Expression Trees", by Gershon Elber and Tom Grandine, 2009
"Kinematic Simulation of Planar and Spatial Mechanisms Using a Polynomial constraints Solver", by Michael Barton, Nadav Shragai, and Gershon Elber, 2009
"Computing the Voronoi Cells of Planes, Spheres and Cylinders in R^3.", by Iddo Hanniel and Gershon Elber, 2009
"Hausdorff and Minimal Distances between Parametric Freeforms in R^2 and R^3", by Gershon Elber and Tim Grandine, 2008
"Precise Voronoi Cell Extraction of Free-form Planar Piecewise C1-Continuous Closed Rational Curves.", by Iddo Hanniel, Ramanathan Muthuganapathy, Gershon Elber and Myung-Soo Kim, 2007
"Subdivision Termination Criteria in Subdivision Multivariate Solvers", by Iddo Hanniel and Gershon Elber, 2007
"Trimming Local and Global Self-Intersections in Offset Curves/Surfaces using Distance Maps", by Joon-Kyung Seong, Gershon Elber and Myung Soo Kim, 2006
"Trimming Local and Global Self-Intersections in Offset Curves using Distance Maps", by Gershon Elber, 2006
"Global Curvature Analysis and Segmentation of Volumetric Data Sets using Trivariate B-spline Functions", by Octavian Soldea, Gershon Elber and Ehud Rivlin, 2006
"Computing the Minimum Enclosing Circle of a Set of Planar Curves.", by Gill Barequet, Gershon Elber and Myung-Soo Kim, 2005
"Optimal Bounding Cones of Vectors in Three-Dimensions", by Gill Barequet and Gershon Elber, 2005
"Are Two Curves the Same?", by Diana Pekerman, Joon-Kyung Seong, Gershon Elber and Myung-Soo Kim, 2005
"Exact and Efficient Computation of Moments of Free-Form Surface and Trivariate Based Geometry", by Octavian Soldea, Gershon Elber and Ehud Rivlin, 2002
"Solving Geometric Constraints Using Multivariate Rational Spline Functions", by Gershon Elber and Myung-Soo Kim, 2001
"Curve Evaluation and Interrogation on Surfaces", by Gershon Elber, 2001
"The Convex Hull of Freeform Surfaces", by J. K. Seong, G. Elber, J. K. Johnston and M. S. Kim, 2001.
"Convex Hull of Rational Plane Curves", by Gershon Elber, Myung-Soo Kim and Hee-Seok Heo, 2001
"Bisectors and Alpha-Sectors of Rational Varieties", by Gershon Elber, Gil Barequet and Myung-Soo Kim, 2001
"A Computation Model for Nonrational Bisector Surfaces: Curve-Surface and Surface-Surface Bisectors", by Gershon Elber and Myung-Soo Kim, 2000
"Alpha-Sectors of Rational Varieties", by Gil Barequest and Gershon Elber, 2000
"Rational Bisectors of CSG Primitives", by Gershon Elber, 1999
"Computing Rational Bisectors of Point/Surface and Sphere/Surface Pairs", by Gershon Elber and Myung-Soo Kim, 1999
"Polynomial/Rational Approximation of Minkowski Sum Boundary Curves", by In Kwon Lee, Myung-Soo Kim and Gershon Elber, 1998
"Bisector Surface of Rational Space Curves", by Gershon Elber and Myung-Soo Kim, 1998
"Bisector Curves of Planar Rational Curves", by Gershon Elber and Myung-Soo Kim, 1998
"Qualitative and Quantitative Comparison of Offset Curves Approximation Methods", by Gershon Elber, In-Kwon Lee and Myung Soo Kim, 1997
"A Symbolic Approach to Freeform Parametric Surface Blends", by Kwansik Kim and Gershon Elber, 1997
"Filleting and Rounding Using Trimmed Tensor Product Surfaces", by Gershon Elber and Elaine Cohen, 1997
"Geometric Shape Recognition of Freeform Curves and Surfaces", by Gershon Elber and Myung-Soo Kim, 1997
"Symbolic and Numeric Computation in Curve Interrogation", by Gershon Elber, 1995
"Second Order Surface Analysis Using Hybrid Symbolic and Numeric Operators", by Gershon Elber and Elaine Cohen, 1993
"Hybrid Symbolic and Numeric Operators as Tools for Analysis of Freeform Surfaces", by Gershon Elber and Elaine Cohen, 1993
"Offset Approximation Improvement by Control Points Perturbation", by Gershon Elber and Elaine Cohen, 1992
"Error Bounded Variable Distance Offset Operator for Free Form Curves and Surfaces", by Gershon Elber and Elaine Cohen, 1991

(NP) Rendering and Texturing of Freeforms

"Real-time Haptic Incision Simulation using FEM-based Discontinuous Free Form Deformation", by Guy Sela, Jacob Subag, Alex Lindblad, Dan Albocher, Sagi Schein and Gershon Elber, 2007
"Probabilistic Silhouette Based Importance Toward Line-Art Non-Photorealistic Rendering", by Gershon Elber and Elaine Cohen, 2006
"Real Time Geometric Detailing using Programmable Hardware", by Sagi Schein, Eran Karpen and Gershon Elber, 2005
"Geometric Deformation-Displacement Maps", by Gershon Elber, 2002
"Discontinuous Free Form Deformations", by Sagi Schein and Gershon Elber, 2004
"Artistic Surface Rendering Using Layout of Text", by Tatiana Surazhsky and Gershon Elber, 2002
"Rendering with Parallel Stripes", by Gershon Elber, 2001
"Interactive Direct Render of Trivariate B-spline Scalar Functions", by Alon Raviv and Gershon Elber, 2001
"Arbitrary Precise Orientation Specification for Layout of Text", by Tatiana Surazhsky and Gershon Elber, 2000
"Interactive Line Art Rendering of Freeform Surfaces", by Gershon Elber, 1999
"Visibility as an Intrinsic Property of Geometric Models", by Adi Bar-Lev and Gershon Elber, 1998
"Line Art Illustrations of Parametric and Implicit Forms", by Gershon Elber, 1998
"Adaptive Isocurves Based Rendering for Freeform Surface", by Gershon Elber and Elaine Cohen, 1996
"Line Illustration in Computer Graphics", by Gershon Elber, 1995
"Line Art Rendering via a Coverage of Isoparametric Curves", by Gershon Elber, 1995
"Adaptive Isocurves Based Rendering: The Hardware Way", by Gershon Elber, 1994

Modeling with Freeforms

"Kernel-based Construction Operators for Boolean Sum and Ruled Geometry", by Haitham Fadila, Q Youn Hong, Gershon Elber, 2023
"Synthesis of 3D Jigsaw Puzzles over Freeform 2-Manifolds", by Gershon Elber and Myung-Soo Kim, 2021
"Euclidean Offset and Bisector Approximations of Curves over Freeform Surfaces", by Gershon Elber and Myung Soo Kim, 2020
"Untrimming: Precise conversion of trimmed-surfaces to tensor-product surfaces", by Fady Massarwi, Boris van Sosin, and Gershon Elber, 2018
"Precise Algebraic-based Swept Volumes for Arbitrary Free-form Shaped Tools towards Multi-axis CNC Machining Verification", by Jinesh Machchhar, Denys Plakhotnik, and Gershon Elber, 2017
"Modeling (Seemingly) Impossible Models", by Gershon Elber, 2011
"Spiral Fat Arcs - Bounding Regions with Cubic Convergence", by Michael Barton and Gershon Elber, 2011
"Topologically guaranteed solution of surface-surface intersections via no-loop and single-component tests", by Michael Barton, Gershon Elber and Iddo Hanniel, 2011
"Sketch Based Design of 2D and 3D Freeform Geometry", by Masha Nikolski and Gershon Elber, 2009
"Real-time Freeform Deformation using Programmable Hardware", by Sagi Schein and Gershon Elber, 2006
"Contouring 1- and 2-Manifolds in Arbitrary Dimensions.", by Joon-Kyung Seong, Gershon Elber and Myung-Soo Kim, 2005
"Generalized Functional and Decorative Filleting and Blending Operations", by Gershon Elber, 2005
"Placement of Deformable Objects", by Sagi Schein and Gershon Elber, 2004
"Constrained Multiresolution Geometric Modeling", by Stefanie Hahmann and Gershon Elber, 2003
"Multiresolution Curve Editing with Linear Constraints", by Gershon Elber, 2001
"Three Dimensional Freeform Sculpting Via Zero Sets of Scalar Trivariate Functions", by Alon Raviv and Gershon Elber, 2000
"The Intersection of Two Ringed Surfaces and Some Related Problems", by Hee-Seok Heo, Sung Je Hong, Joon-Kyung Seong, Myung-Soo Kim and Gershon Elber, 2000
"Surface Design Using Global Constraints on Total Curvature", by Michael Plavnik and Gershon Elber, 1998
"Orthogonal Decomposition of Non-Uniform Bspline Spaces Using Wavelets", by Roman Kazinnik and Gershon Elber, 1997
"Global Error Bounds and Amelioration of Sweep Surfaces", by Gershon Elber, 1997

VReps, Heterogeneity and Microstructures/Lattices

"A Review of a B-spline based Volumetric Representation: Design, Analysis and Fabrication of Porous and/or Heterogeneous Geometries", by Gershon Elber
"Heterogeneous Conforming Compliant Microstructure Mechanisms", by Gershon Elber
"Implicit Functionally Graded Conforming Microstructures", by Q Youn Hong, Gershon Elber, Myung-Soo Kim
"Conformal Microstructure Synthesis in Trimmed Trivariate Based V-Reps", by Q Youn Hong and Gershon Elber
"Heterogeneous Parametric Trivariate Fillets", by Ramy Masalha, Emiliano Cirillo and Gershon Elber
"Volumetric Untrimming: Precise decomposition of trimmed trivariates into tensor products", by Fady Massarwi, Pablo Antolin, and Gershon Elber, 2019
"Optimizing micro-tiles in micro-structures as a design paradigm", by Pablo Antolin, Annalisa Buffa, Elaine Cohen, John F Dannenhoffer, Gershon Elber, Stefanie Elgeti, Robert Haimes, and Richard Riesenfeld, 2019
"Volumetric Covering Print-Paths for Additive Manufacturing of 3D Models", by Ben Ezair, Saul Fuhrmann and Gershon Elber, 2018
"Crossing Knot Lines in Composition of Freeform B-spline Geometry", by Boris van Sosin and Gershon Elber, 2018
"Hierarchical, random and bifurcation tiling with heterogeneity in micro-structures construction via functional composition", by Fady Massarwi, Jinesh Machchhar, Pablo Antolin, and Gershon Elber, 2018.
"A B-spline based Framework for Volumetric Object Modeling", by Fady Massarwi and Gershon Elber, 2016

Others

"3D-Dithered Ortho-Pictures: 3D Models from Independent 2D Images", by Gershon Elber, 2015
"Rendering Traditional Mosaics", by Gershon Elber and George Wolberg, 2003
"Metamorphosis of Planar Curves via Curvature Interpolation", by Tatiana Suarzhsky and Gershon Elber, 2002
"Matching Free Form Surfaces", by Tatiana Surazhsky and Gershon Elberm 2001
"Breaking the Shower Glass", by Gershon Elber, 1999
"Output Sensitive Extraction of Silhouettes from Polygonal Geometry", by F. Benichou and Gershon Elber, 1999
"Image Morphing with Feature Preserving Texture", by Ayellet Tal and Gershon Elber, 1999
"Self-Intersection Elimination in Metamorphosis of Two-Dimensional Curves", by Tatiana Samoilov and Gershon Elber, 1998
"Matching of Freeform Curves", by Shmuel Cohen, Gershon Elber and Reuven Bar-Yehuda, 1997
"Fast Iso-Surface Extraction Using Marching Gradients", by Olga Tebeleva and Gershon Elber, 1996
"Metamorphosis of Freeform Curves and Surfaces", by Gershon Elber, 1995
"PhD Thesis - Free Form Surface Analysis Using a Hybrid of Symbolic and Numeric Computation", by Gershon Elber, 1992