NDLI: Injectivity of 2D Toric Bézier Patches

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2013 International Conference on Computer-Aided Design and Computer Graphics

2011 12th International Conference on Computer-Aided Design and Computer Graphics

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A "Change 'n Play" Software Architecture Integrating CAD, CAE and Immersive Real-Time Environments

Detecting Ambiguities in 3D Polygons with Self-Intersecting Projections

Automatic Generation of Canonical Views for CAD Models

Direct Rendering of Solid CAD Models on the GPU

An Example-Driven Symbol Recognition Approach Based on Key Features in Engineering Drawings

Knowledge Management for Product Development: A Review

DMML: A Design Thinking Process Modeling Language

Niche Improved Particle Swarm Optimization on Geometric Constraint Solving

Finite Element Mesh Editing through CAD Operations

An Accurate and Practical Camera Lens Model for Rendering Realistic Lens Effects

Real-Time Volume Caustics with Image-Based Photon Tracing

Importance-Driven Composition of Multiple Rendering Styles

SIMD Friendly Ray Tracing on GPU

Fast Point Based Global Illumination

A New Foveation Ray Casting Approach for Real-Time Rendering of 3D Scenes

Multi-GPU Compositeless Parallel Rendering Algorithm

Spherical Projective Displacement Mesh

The Spherical Images of Triangular Mesh Surfaces

Structure Preserving Mesh Parameterization

Tetrahedral Mesh Editing with Local Feature Manipulations

Real-Time Image Smoothing Based on True Edges

A 2D-3D Hybrid Approach to Video Stabilization

Color-Mood-Aware Clothing Re-texturing

Image Mosaics with Irregular Tiling

Automatic Segmentation of Head-and-Shoulder Images by Combining Edge Feature and Shape Prior

Creating Cylindrical Panoramic Mosaic from a Pipeline Video

iFrames: A Multi-level Keyframe Extraction and Navigation Tool for Videos

Automatic Compositing Soccer Video Highlights with Core-Around Event Model

Fast Patch-Based Image Hybrids Synthesis

Detection Geometric Object in the Conformal Geometric Algebra Framework

Scale Adaptation of Mean Shift Based on Graph Cuts Theory

A Unified Framework for Alpha Matting

Constructing an Interpolatory Subdivision Scheme from Doo-Sabin Subdivision

Variational Harmonic Method for Parameterization of Computational Domain in 2D Isogeometric Analysis

Convergence of Geometric Interpolation Using Uniform B-splines

Injectivity of 2D Toric Bézier Patches

The PIA Property of Low Degree Non-uniform Triangular B-B Patches

CurveNetSurf: Creating Surfaces from Curve Networks

Multi-resolution Mesh Fitting by B-spline Surfaces for Reverse Engineering

Variational Progressive-iterative Approximation for Fairing Curve and Surface Generation

A Hierarchical Approach to 3D Scattered Data Interpolation with Radial Basis Functions

A Tangent Vector Based Nonlinear Subdivision Scheme without Self-Intersection for Curve Design

A Local Behavior Model for Small Pedestrian Groups

Human Motion Synthesis Using Window-Based Local Principal Component Analysis

Parallel Spatial Hashing for Collision Detection of Deformable Surfaces

Controlling Simulated Explosions by Optimization and Prediction

Robust Deformation Transfer via Dual Domain

Lattice-Based Skinning and Deformation for Real-Time Skeleton-Driven Animation

A Rapid Method of 3D Character Models' Diversity Used Micro-deformation

An Efficient Adaptive Vortex Particle Method for Real-Time Smoke Simulation

Orthognathic Soft-Tissue Prediction Based on Three-Dimensional Graphics Model Recovery

Realistic Fire Simulation: A Survey

An Improved Cellular Genetic Algorithm with Evolutionary Rules for 3D Animation Modeling Design

Anisotropic Kernels for Meshless Elastic Solids

MCA-Based Animation of Fracturing Heterogeneous Objects

IdiotPencil: An Interactive System for Generating Pencil Drawings from 3D Polygonal Models

Application of Pen-Based Planar Haptic Interface in Physics Education

Depth-Based Feature Enhancement for Volume Visualization

2.5D Focus+Context Map Visualization

Feature-Preserving Quantization for 3D Seismic Visualization

Interactive Expressive Illustration of 3D City Scenes

An Optimal Color Mapping Strategy Based on Energy Minimization for Time-Varying Data

Opacity Volume Based Halo Generation for Enhancing Depth Perception

A Kind of Shape-Color Moment Invariants

The Multi-layer Spherical Helix Curve-Based 3-D Fourier Feature

On-line Illumination Estimation of Outdoor Scenes Based on Area Selection for Augmented Reality

An Interactive 3D Preoperative Planning and Training System for Minimally Invasive Vascular Surgery

Single Image Based Illumination Estimation for Lighting Virtual Object in Real Scene

Behavior-Based Simulation of Real-Time Crowd Evacuation

Tree-Based Partitioning Approach for Network-on-Chip Synthesis

A Fast Retiming Algorithm Integrated with Rewiring for Flip-Flop Reductions

Row-Based Analysis of Structure Power/Ground Grids with General Purpose GPU

A Residential Building Reconstruction Method and Its Evaluation

Delaunay/Voronoi Dual Representation of Smooth 2-Manifolds

Modeling Expressions of Peking Opera Facial Make-Ups

Implicit Surface Reconstruction Based on Adaptive Clustering

2009 11th IEEE International Conference on Computer-Aided Design and Computer Graphics

2007 10th IEEE International Conference on Computer-Aided Design and Computer Graphics

Ninth International Conference on Computer Aided Design and Computer Graphics (CAD-CG'05)

Injectivity of 2D Toric Bézier Patches

Content Provider	IEEE Xplore Digital Library
Author	Sottile, F. Chun-Gang Zhu
Copyright Year	2011
Abstract	Rational Bezier functions are widely used as mapping functions in surface reparameterization, finite element analysis, image warping and morphing. The injectivity (one-to-one property) of a mapping function is typically necessary for these applications. Toric B´ezier patches are generalizations of classical patches (triangular, tensor product) which are defined on the convex hull of a set of integer lattice points. We give a geometric condition on the control points that we show is equivalent to the injectivity of every 2D toric B´ezier patch with those control points for all possible choices of weights. This condition refines that of Craciun, et al., which only implied injectivity on the interior of a patch.
Starting Page	235
Ending Page	238
File Size	172231
Page Count	4
File Format	PDF
ISBN	9781457710797
DOI	10.1109/CAD/Graphics.2011.13
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-09-15
Publisher Place	Colombia
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Tensile stress mapping injectivity Image edge detection Lattices Bézier patches Educational institutions Polynomials Three dimensional displays toric patches
Content Type	Text
Resource Type	Article

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