2007
DOI: 10.1109/tvcg.2007.1021
|View full text |Cite
|
Sign up to set email alerts
|

Vector Field Editing and Periodic Orbit Extraction Using Morse Decomposition

Abstract: Abstract-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 … Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1

Citation Types

0
1
0

Year Published

2014
2014
2021
2021

Publication Types

Select...
5
2
1

Relationship

0
8

Authors

Journals

citations
Cited by 105 publications
(3 citation statements)
references
References 47 publications
(90 reference statements)
0
1
0
Order By: Relevance
“…13 Theisel et al 14 proposed a grid-independent method for the location of periodic orbits. Chen et al 3 introduced an efficient method for periodic orbit detection from 2D/2.5D vector fields and defined a more complete vector field topology by including periodic orbits into the topology construction. In the meantime, saddle-saddle connector has been introduced by Theisel et al 15 for 3D vector field topology visualization to reduce the occlusion issue.…”
Section: Related Workmentioning
confidence: 99%
“…13 Theisel et al 14 proposed a grid-independent method for the location of periodic orbits. Chen et al 3 introduced an efficient method for periodic orbit detection from 2D/2.5D vector fields and defined a more complete vector field topology by including periodic orbits into the topology construction. In the meantime, saddle-saddle connector has been introduced by Theisel et al 15 for 3D vector field topology visualization to reduce the occlusion issue.…”
Section: Related Workmentioning
confidence: 99%
“…[37]), and also in an automatized method for the computation of the Conley index from index pairs constructed as cubical sets in R n [41,48], used e.g. in a method for editing vector fields and extraction of periodic orbits [8], and also very helpful in an automatic method for classification of dynamics in multi-parameter systems [4,7], which found applications e.g. in population biology [38] and in physics of plasmas [49].…”
Section: Introductionmentioning
confidence: 99%
“…First, the decomposition establishes a clear, deterministic notion of steady state behavior that, no matter how complicated its temporal manifestation [44,62,65], imposes a computationally effective [51] spatial partition into attractor basins [69] whose topology persists under small perturbations. The passage from signal to symbol afforded by such partitions has great value for analyzing natural systems [6,33], and has encouraged slowly growing use in the synthesis of engineered systems as well [1,22,41,42]. Second, interpreted as a universal converse Lyapunov theorem, and a global analogue to the classical counterpart addressing a specific basin [52], the long-established value for classical [88], multistable [30], and hybrid control systems theory [36] is leveraged by a steadily advancing literature on constructive methods for their eventual feedback closed loops [10,34].…”
mentioning
confidence: 99%