Chandrajit L. Bajaj

Progressive Compression and Transmission of Arbitrary Triangular Meshes (2003)

We use a combination of both symbolic and numerical techniques to construct several degree bounded G continuous, piecewise spline approximations of real implicit algebraic surfaces for both computer...

Chandrajit L Bajaj, Valerio Pascucci, Guozhong Zhuang

The recent growth in the size and availability of large triangular surface models has generated research in compact multi-resolution progressive representation and data transmission. An ongoing...

The Contour Spectrum (2003)

Chandrajit L. Bajaj, Valerio Pascucci, Daniel R. Schikore

Weintroduce the contour spectrum, a user interface component that improves qualitativeuserinteraction and provides real-time exact quantification in the visualization of isocontours. The contour...

Splitting a Complex of Convex Polytopes In Any Dimension (2003)

Chandrajit L. Bajaj, Valerio Pascucci

Introduction We present a locality-based algorithm to solve the problem of splitting a complex of convex polytopes with a hyperplane or a convex subset of it. The solution to this problem has several...

Dynamic Maintenance and Visualization of Molecular Surfaces (2003)

Chandrajit L. Bajaj, Valerio Pascucci, Ariel Shamir, Robert J. Holt, Arun N. Netravali

Molecular surface computations are often necessary in order to perform synthetic drug design. A critical step in this process is the computation and update of an exact boundary representation for the...

The Combinatorics of Real Algebraic Splines over a Simplicial Complex (2003)

Piecewise Rational Approximations of Real Algebraic Curves (2003)

We bound the dimension of fixed degree real algebraic interpolatory spline spaces. For a given planar triangulation T real algebraic splines interpolate specified z i values at the vertices v i = (x...

Dynamic Maintenance and Visualization of Molecular Surfaces (2002)

We use a combination of both algebraic and numerical techniques to construct a C¹-continuous, piecewise (m, n) rational epsilon-approximation of a real algebraic plane curve of degree d. At...

Chandrajit L. Bajaj, Valerio Pascucci, Ariel Shamir, Robert J. Holt, Arun N. Netravali

Molecular surface computations are often necessary in order to perform synthetic drug design. A critical step in this process is the computation and update of an exact boundary representation for the...

Case Study: Interactive Rendering of Adaptive Mesh Refinement Data (2002)

Sanghun Park, Chandrajit L. Bajaj, Vinay Siddavanahalli

Adaptive mesh refinement (AMR) is a popular computational simulation technique used in various scientific and engineering fields. Although AMR data is organized in a hierarchical multi-resolution...

NURBS Approximation of A-Splines and A-Patches (2002)

Chandrajit L. Bajaj, Guoliang Xu, Robert J. Holt, Arun N. Netravali

Given A-spline curves and A-patch surfaces that are implicitly defined on triangles and tetrahedra, we determine their NURBS representations. We provide a trimmed NURBS form for A-spline curves and a...

Modeling with Hybrid Multiple-sided A-patches (2002)

Guoliang Xu, Chandrajit L. Bajaj, Susan Evans

We propose a new scheme for modeling a smooth interpolatory surface, from a surface discretization consisting of triangles, quadrilaterals and pentagons, by algebraic surface patches which are...

Hierarchical Multiresolution Reconstruction of Shell Surfaces (2002)

Chandrajit L. Bajaj, Guoliang Xu, Robert J. Holt, Arun N. Netravali

We present an adaptive, hierarchical Hh-multiresolution reconstruction algorithm to model shell surface objects from a matched pair of triangulated surfaces. Shell surfaces are an interval of...

Regular algebraic curve segments (III) - Applications in interactive design and data fitting (2001)

Modeling with Hybrid Multiple-sided A-patches (2001)

In this paper (part three of the trilogy) we use low degree G¹ and G² continuous regular algebraic spline curves defined within parallelograms, to interpolate an ordered set of data...

Guoliang Xu, Chandrajit L. Bajaj, Susan Evans

We propose a new scheme for modeling a smooth interpolatory surface, from a surface discretization consisting of triangles, quadrilaterals and pentagons, by algebraic surface patches which are...

Feasibility of a Skeletal Modeler for Conceptual Mechanical Design (2001)

David Charles Thompson, Richard H. Crawford, Kristin L. Wood, S. V. Sreenivasan, Ronald E. Barr, Chandrajit L. Bajaj

vii List of Symbols xi Chapter 1 The Need For A Conceptual Modeler 1 1.1 Current practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 The Process of Modeling . . . . . . . . . . ....

Automatic Reconstruction of Surfaces and Scalar Fields from 3D Scans (2001)

Chandrajit L. Bajaj, Fausto Bernardini, Guoliang Xu

We present an efficient and uniform approach for the automatic reconstruction of surfaces of CAD (computer aided design) models and scalar fields defined on them, from an unorganized collection of...

Regular Algebraic Curve Segments (II) --Interpolation and Approximation (2001)

Guoliang Xu, Chandrajit L. Bajaj, Chuan I Chu

In this paper (part two of the trilogy) we introduce three classes of reduced form D--regular algebraic curves and use them for interpolation and approximation of various algebraic curves. Explicit...

Modeling with Cubic A-Patches (2001)

Collaborative Multimedia in Scientific Design (2001)

We present a sufficient criterion for the Bernstein-Bezier (BB) form of a trivariate polynomial within a tetrahedron, such that the real zero contour of the polynomial defines a smooth, connected and...

Free-Form Modeling with Implicit Surface Patches (2001)

We discuss the application of multimedia in scientific design, and describe a multi-user distributed and collaborative scientific manipulation environment, Shastra, implemented on the multimedia...

Piecewise Approximations of Real Algebraic Surfaces (2001)

Introduction While it is possible to model a general closed surface of arbitrary genus as a single implicit surface patch, the geometry of such a global surface is difficult to specify, interactively...

Decimation of 2D Scalar Data with Error Control (2001)

We use a combination of both symbolic and numerical techniques to construct several degree bounded G 0 and G 1 continuous, piecewise approximations of real algebraic surfaces. These approximations...

Daniel R. Schikore, Chandrajit L. Bajaj

Scientific applications frequently use dense scalar data defined over a 2D mesh. Often these meshes are created at a high density in order to capture the high frequency components of sampled data or...

Triangulation and Display of Rational Parametric Surfaces (2001)

The SHILP solid modeling and display toolkit V 1.1 (2001)

We present a comprehensive algorithm to construct a topologically correct triangulation of the real affine part of a rational parametric surface with few restrictions on the defining rational...

Dynamic Maintenance and Visualization of Molecular Surfaces (2001)

This is a user manual for the SHILP solid modeling and display toolkit. SHILP is a collection of interactive tools for three dimensional geometric design and display of solids defined with algebraic...

Chandrajit L. Bajaj, Valerio Pascucci, Robert J. Holt, Arun N. Netravali

Molecular surface computations are basic molecular modeling operations that are necessary to deal with in order to perform synthetic drug design. Computing and updating exact boundary representations...

Tetrahedral Meshes From Planar Cross Sections (2001)

Chandrajit L. Bajaj, Edward J. Coyle, Kwun-nan Lin

In biomedicine, many three dimensional (3D) objects are sampled in terms of slices such as computed tomography (CT), magnetic resonance imaging (MRI), and ultrasound imaging. It is often necessary to...

Two and Three Dimensional Computer Graphic Evaluation of the Subacute Spinal Cord Injury (2001)

Loren J. Moriarty, Bradley S. Duerstock, Chandrajit L. Bajaj, Kwunnan Lin, Richard B. Borgens, Ph. D. Macrophage

imbedded within it. Out three dimensional surface reconstructions can be interrogated to determine volumes and surface areas of structures within the data set. Using these methods we have learned...

Interactive Shape Control and Rapid Display of A-patches (2001)

A Triangulation-Based Object Reconstruction Method (2001)

A-patches are implicit surfaces in Bernstein-B'ezier(BB) form that are smooth and singlesheeted. In this paper, we present algorithms to utilize the extra degrees of freedom of each A-patch for local...

Fausto Bernardini, Chandrajit L. Bajaj, Jindong Chen, Daniel R. Schikore

this paper, and the accompanying video presentation, This research was partially supported by AFOSR grant F49620 -94-1-0080, NSF grant CCR 92-22467 and ONR grant N00014-94-1-0370 y Present address:...

Custom Prosthesis Design, Visualization, and Prototyping (2001)

Fast Isocontouring For Improved Interactivity (2001)

The design of a custom hip implant can be broken up into several distinct phases which can be carried out by separate toolkits which specialize in the service needed for each stage. We describe a...

Chandrajit L. Bajaj, Valerio Pascucci, Daniel R. Schikore

We present an isocontouringalgorithm which is near-optimal for real-time interaction and modification of isovalues in large datasets. A preprocessing step selects a subset S of the cells which are...

Regular Algebraic Curve Segments(I) --Definitions and Characteristics (2001)

Guoliang Xu, Chandrajit L. Bajaj, Weimin Xue

In this paper (part one of a trilogy), we introduce the concept of a discriminating family of regular algebraic curves (real, nonsingular and connected). Several discriminating families are obtained...

Smooth Low Degree Approximations of Polyhedra (2001)

Data Fitting with Cubic A-Splines (2001)

We present an efficient algorithm to construct an inner simplicial hull Sigma based on a given polyhedron P in three dimensional space. Piecewise smooth C 1 and C 2 A-patches can then be constructed...

Parameterization In Finite Precision (2001)

We present algorithms for constructing iso-contours from image data or fitting scattered point data C 1 , C 2 or C 3 piecewise smooth chains of single sheeted real cubic algebraic curve segments...

A-Splines: Local Interpolation and Approximation using (2001)

Certain classes of algebraic curves and surfaces admit both parametric and implicit representations. Such dual forms are highly useful in geometric modeling since they combine the strengths of the...

Error-bounded Reduction of Triangle Meshes with Multivariate Data (2001)

We provide sufficient conditions for the Bernstein-B'ezier (BB) form of an implicitly defined bivariate polynomial over a triangle, such that the zero contour of the polynomial defines a smooth and...

Multi-dimensional Hermite Interpolation and Approximation for Modelling and Visualization (2001)

Interactive visualization is complicated by the complexity of the objects being visualized. Sampled or computed scientific data is often dense, in order to capture high frequency components in...

Visualization of Scalar Topology for Structural Enhancement (2001)

In this paper we use some well known theorems of algebraic geometry in reducing polynomial Hermite interpolation and approximation in any dimension to the solution of linear systems. We present a mix...

Compression and Coding of Large CAD Models (2001)

Scalar fields arise in every scientific application.

Chandrajit L Bajaj, Valerio Pascucci, Guozhong Zhuang

In this paper we introduce a compression scheme suitable for large CAD (Computer Aided Design) models. We assume as input a large model in IGES 1 and VRML 2 formats that encode efficiently and...

Energy Formulations of A-Splines (2001)

Chandrajit L. Bajaj, Jindong Chen, Robert J. Holt, Arun N. Netravali

A-splines are implicit real algebraic curves in Bernstein-B'ezier (BB) form that are smooth. We develop A-spline curve models using various energy formulations, incorporating bending and stretching...

Regular Algebraic Curve Segments (III) - Applications in Interactive Design and Data Fitting (2000)

Energy Formulations of A-Splines (2000)

In this paper (part three of the trilogy) we use low degree G 1 and G 2 continuous regular algebraic spline curves dened within parallelograms, to interpolate an ordered set of data points in the...

Chandrajit L. Bajaj, Jindong Chen, Robert J. Holt, Arun N. Netravali

A-splines are implicit real algebraic curves in Bernstein-B'ezier (BB) form that are smooth. We develop A-spline curve models using various energy formulations, incorporating bending and stretching...

Rational Parametrizations of Non-singular Real Cubic Surfaces (2000)

Chandrajit L. Bajaj, Robert J. Holt, Arun N. Netravali

Real cubic algebraic surfaces may be described by either implicit or parametric equations. One particularly useful representation is the rational parametrization, where the three spatial coordinates...

Dynamic Maintenance and Visualization of Molecular Surfaces (2000)

Chandrajit L. Bajaj, Valerio Pascucci, Robert J. Holt, Arun N. Netravali

A method of modeling and animating objects that has gained much popularity recently is the use of molecular surfaces. A great deal of past work has included the combination of efficient data...

NURBS Approximation of Surface/Surface Intersection Curves (1999)

Surface and 3D Triangular Meshes from Planar Cross Sections (1999)

We use a combination of both symbolic and numerical techniques to construct a degree bounded C k -continuous, rational B-spline -approximations of real algebraic surface-surface intersection curves....

Chandrajit L. Bajaj, Edward J. Coyle, Kwun-nan Lin

. This paper presents two unstructured mesh generation algorithms with a discussion of their implementation. One algorithm is for the generation of a surface triangular mesh from a parallel stack of...

Single Resolution Compression of Arbitrary Triangular Meshes with Properties (1999)

Chandrajit L Bajaj, Valerio Pascucci, Guozhong Zhuang

Triangular meshes are widely used as primary representation of surface models for networked gaming and for complex interactive design in manufacturing. Accurate traingulation of a surface with sharp...

Single Resolution Compression of Arbitrary Triangular Meshes with Properties (1999)

Chandrajit L Bajaj, Valerio Pascucci, Guozhong Zhuang

this paper, we propose a new layering structure to partition an arbitrary triangular mesh (non-manifold, arbitrary-genus amd possibly vertex irregularities) into generalized triangle strips. An...

Smooth Adaptive Reconstruction and Deformation of Free-Form Fat Surfaces (1999)

Regular Algebraic Curve Segments (III) - Applications in Interactive Design and Data Fitting (1999)

Most manufactured (airfoils)... In this paper we call such surfaces "fat surfaces" or "fat boundaries". We present an adaptive reconstruction algorithm to model the boundary of such fat surface...

Comprehensive Analysis of Joints From Patient Clinical Data (1999)

In this paper (part three of the trilogy) we use low degree G¹ and G² continuous regular algebraic spline curves defined within parallelograms, to interpolate an ordered set of data...

Chandrajit L. Bajaj, Fausto Bernardini, Steven M. Cutchin, Elisha Sacks, Daniel R. Schikore

write abstract 1 stress analysis part modeling validation visualization dynamical simulation contact analysis Figure 1: Modular structure of joint analysis system. 1 Introduction We are developing...

Smooth Multiresolution Reconstruction of Free-Form Fat Surfaces (1999)

Smooth Multiresolution Reconstruction of Free-Form Fat Surfaces (1999)

Most manufactured (airfoils) and several naturally occurring objects (sea shells) have shell like structures, that is the boundary consists of surfaces with thickness. In this paper we call such...

Single Resolution Compression of Arbitrary Triangular Meshes with Properties (1999)

Most manufactured (airfoils) and several naturally occurring objects (sea shells) have shell like structures, that is the boundary consists of surfaces with thickness. In this paper we call such...

Chandrajit L Bajaj, Valerio Pascucci, Guozhong Zhuang

this paper, we propose a new layering structure to partition an arbitrary triangular mesh (no-manifold and arbitrary-genus) into generalized triangle strips. An efficient and flexible encoding of the...

Active Contouring of Images with Physical A-splines (1999)

Chandrajit L. Bajaj, Valerio Pascucci, Robert J. Holt, Arun N. Netravali

A-splines are implicit real algebraic curves in Bernstein-B'ezier (BB) form that are smooth. We use these in an algorithm for active contouring of images. One advantage of A-splines is that any...

The Contour Spectrum (1999)

Chandrajit L. Bajaj, Valerio Pascucci, Daniel R. Schikore

We introduce the contour spectrum, a user interface component that improves qualitative user interaction and provides real-time exact quantification in the visualization of isocontours. The contour...

Fast Isocontouring For Improved Interactivity (1999)

Chandrajit L. Bajaj, Valerio Pascucci, Daniel R. Schikore

We present an isocontouringalgorithm which is near-optimal for real-time interaction and modification of isovalues in large datasets. A preprocessing step selects a subset S of the cells which are...

Single Resolution Compression of Arbitrary Triangular Meshes with Properties (1999)

Chandrajit L Bajaj, Valerio Pascucci, Guozhong Zhuang

this paper, we propose a new layering structure to partition an arbitrary triangular mesh (no-manifold and arbitrary-genus) into generalized triangle strips. An efficient and flexible encoding of the...

Single Resolution Compression of Arbitrary Triangular Meshes with Properties (1999)

Chandrajit L Bajaj, Valerio Pascucci, Guozhong Zhuang

this paper, we propose a new layering structure to partition an arbitrary triangular mesh (no-manifold and arbitrary-genus) into generalized triangle strips. An efficient and flexible encoding of the...

Active Contouring of Images with Physical A-splines (1998)

Chandrajit L. Bajaj, Valerio Pascucci, Robert J. Holt, Arun N. Netravali

A-splines are implicit real algebraic curves in Bernstein-B'ezier (BB) form that are smooth. We use these in an algorithm for active contouring of images. One advantage of A-splines is that any...

Parameterization In Finite Precision (1998)

Compression and Coding of Large CAD Models (1998)

Certain classes of algebraic curves and surfaces admit both parametric and implicit representations. Such dual forms are highly useful in geometric modeling since they combine the strengths of the...

Chandrajit L Bajaj, Valerio Pascucci, Guozhong Zhuang

We introduce a compression scheme suitable for large CAD (Computer Aided Design) models. We take as input IGES 1 or VRML 2 models efficiently encode and transmit to clients for remote interactive...

Image Compression: Multiple-Wavelet Approach (1998)

Chandrajit L Bajaj, Guozhong Zhuang

this paper we will construct wavelets on a bounded interval. Multiple scaling functions are used, instead of a single one. In this paper, there are taken as as a finite sequence of polynomials which...

An Efficient Algorithm and Implementation of Haar Wavelets (1998)

Chandrajit L. Bajaj, Guozhong Zhuang

this paper, our focus will be on the algorithm and implementation issue under the theoretic frame of the above paper. Compared to the algorithm in [1], our algorithm will provide two kinds of...

Compression and Coding of Large CAD Models (1998)

Chandrajit L Bajaj, Valerio Pascucci, Guozhong Zhuang

In this paper we introduce a compression scheme suitable for large CAD (Computer Aided Design) models. We assume as input a large model in IGES 1 and VRML 2 formats that encode efficiently and...

Efficient Algorithms and Data Structures in Geometric Design. (1998)

Efficient Algorithms and Data Structures in Geometric Design. (1998)

Research has been conducted on the design of a numerically stable and topologically robust algorithm for boolean set operations between solids with algorithms surface patches of arbitrary degree.

Modeling and Visualization for Polymers, Surfaces and Biomolecules (1998)

An efficient and uniform approach for the automatic reconstruction of surfaces of CAD models, and scalar field defined on them, from an unorganized collection of scanned point data has been...

Modeling and Visualization for Polymers, Surfaces and Biomolecules. (1998)

Our research emphasizes efficient algorithms and data structures for biomolecular modeling and visualization. The main research thrusts of this contract are: The computation of the topological,...

Visualization and Querying of Scalar, Vector, and Tensor Field Data (1998)

Problems in the representation of molecular surfaces using different spline representations have been studied. The suitability of these patch representations for visualizing scalar functions has been...

Modeling Scattered Function Data On Curved Surfaces (1998)

Interactive visualization allows scientists and engineers to analyze massive data sets in new ways. They can prune useless data, identify important features, and see the science behind the data. We...

Smooth Low Degree Approximations of Polyhedra (1998)

We present efficient algorithms to model a collection of scattered function data defined on a given smooth domain surface D in three dimensional real space (IR 3 ), by a C 1 cubic or a C 2 quintic...

Data Fitting with Cubic A-Splines (1998)

We present an efficient algorithm to construct an inner simplicial hull Sigma based on a given polyhedron P in three dimensional space. Piecewise smooth C 1 and C 2 A-patches can then be constructed...

Triangulation and Display of Rational Parametric Surfaces (1998)

We present algorithms for constructing iso-contours from image data or fitting scattered point data C 1 , C 2 or C 3 piecewise smooth chains of single sheeted real cubic algebraic curve segments...

Collaborative Multimedia in Scientific Design (1998)

We present a comprehensive algorithm to construct a topologically correct triangulation of the real affine part of a rational parametric surface with few restrictions on the defining rational...

Multi-dimensional Hermite Interpolation and Approximation for Modelling and Visualization (1998)

We discuss the application of multimedia in scientific design, and describe a multi-user distributed and collaborative scientific manipulation environment, Shastra, implemented on the multimedia...

Decimation of 2D Scalar Data with Error Control (1998)

In this paper we use some well known theorems of algebraic geometry in reducing polynomial Hermite interpolation and approximation in any dimension to the solution of linear systems. We present a mix...

Daniel R. Schikore, Chandrajit L. Bajaj

Scientific applications frequently use dense scalar data defined over a 2D mesh. Often these meshes are created at a high density in order to capture the high frequency components of sampled data or...

Custom Prosthesis Design, Visualization, and Prototyping (1998)

The SHILP solid modeling and display toolkit V 1.1 (1998)

The design of a custom hip implant can be broken up into several distinct phases which can be carried out by separate toolkits which specialize in the service needed for each stage. We describe a...