A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides
ACM Transactions on Mathematical Software (TOMS)
Introduction to algorithms
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Automatic detection of open and closed separation and attachment lines
Proceedings of the conference on Visualization '98
The “parallel vectors” operator: a vector field visualization primitive
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Texture synthesis over arbitrary manifold surfaces
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
A flow-guided streamline seeding strategy
Proceedings of the conference on Visualization '00
Image based flow visualization
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Continuous topology simplification of planar vector fields
Proceedings of the conference on Visualization '01
Visualizing Nonlinear Vector Field Topology
IEEE Transactions on Visualization and Computer Graphics
Detection and Visualization of Closed Streamlines in Planar Flows
IEEE Transactions on Visualization and Computer Graphics
Visualizing Vector Field Topology in Fluid Flows
IEEE Computer Graphics and Applications
Computer Aided Geometric Design
Morse-smale complexes for piecewise linear 3-manifolds
Proceedings of the nineteenth annual symposium on Computational geometry
Discrete multiscale vector field decomposition
ACM SIGGRAPH 2003 Papers
Anisotropic polygonal remeshing
ACM SIGGRAPH 2003 Papers
Flows on surfaces of arbitrary topology
ACM SIGGRAPH 2003 Papers
Exploring global dynamics: a numerical algorithm based on the conley index theory
Exploring global dynamics: a numerical algorithm based on the conley index theory
The topology of symmetric, second-order tensor fields
VIS '94 Proceedings of the conference on Visualization '94
Investigating Swirl and Tumble Flow with a Comparison of Visualization Techniques
VIS '04 Proceedings of the conference on Visualization '04
Visualization of Intricate Flow Structures for Vortex Breakdown Analysis
VIS '04 Proceedings of the conference on Visualization '04
Image Based Flow Visualization for Curved Surfaces
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Image Space Based Visualization of Unsteady Flow on Surfaces
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
An Algorithmic Approach to Chain Recurrence
Foundations of Computational Mathematics
Vector field design on surfaces
ACM Transactions on Graphics (TOG)
Interactive Tensor Field Design and Visualization on Surfaces
IEEE Transactions on Visualization and Computer Graphics
Rotational symmetry field design on surfaces
ACM SIGGRAPH 2007 papers
Interactive procedural street modeling
ACM SIGGRAPH 2008 papers
Evolving heterochrony for cellular differentiation using vector field embryogeny
Proceedings of the 12th annual conference on Genetic and evolutionary computation
TADD: a computational framework for data analysis using discrete Morse theory
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
Surface curvature line clustering for polyp detection in CT colonography
EG VCBM'08 Proceedings of the First Eurographics conference on Visual Computing for Biomedicine
Topology-based smoothing of 2D scalar fields with C1-continuity
EuroVis'10 Proceedings of the 12th Eurographics / IEEE - VGTC conference on Visualization
Stable morse decompositions for piecewise constant vector fields on surfaces
EuroVis'11 Proceedings of the 13th Eurographics / IEEE - VGTC conference on Visualization
SMI 2013: Steepest descent paths on simplicial meshes of arbitrary dimensions
Computers and Graphics
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Design and control of vector fields is critical for many visualization and graphics tasks such as vector field visualization, fluid simulation, and texture synthesis. The fundamental qualitative structures associated with vector fields are fixed points, periodic orbits, and separatrices. In this paper, we provide a new technique that allows for the systematic creation and cancellation of fixed points and periodic orbits. This technique enables vector field design and editing on the plane and surfaces with desired qualitative properties. The technique is based on Conley theory, which provides a unified framework that supports the cancellation of fixed points and periodic orbits. We also introduce a novel periodic orbit extraction and visualization algorithm that detects, for the first time, periodic orbits on surfaces. Furthermore, we describe the application of our periodic orbit detection and vector field simplification algorithms to engine simulation data demonstrating the utility of the approach. We apply our design system to vector field visualization by creating data sets containing periodic orbits. This helps us understand the effectiveness of existing visualization techniques. Finally, we propose a new streamline-based technique that allows vector field topology to be easily identified.