Visualizing planar vector fields with normal component using line integral convolution

2003 ◽  
Author(s):  
G. Scheuermann ◽  
H. Barbach ◽  
H. Hagen
Keyword(s):  
Vector Fields ◽  
Normal Component ◽  
Line Integral ◽  
Integral Convolution ◽  
Planar Vector Fields ◽  
Line Integral Convolution ◽  
Planar Vector

scholarly journals A Vector Field Texture Generation Method without Convolution Calculation

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 724
Author(s):  
Xiaofu Du ◽  
Huilin Liu ◽  
Hsien-Wei Tseng ◽  
Teen-Hang Meen
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Special Kind ◽  
Line Integral ◽  
Time Consumption ◽  
Integral Convolution ◽  
Line Integral Convolution ◽  
Texture Generation ◽  
Novel Method ◽  
Streamline Tracing

In the LIC algorithm process, symmetrical streamline tracing is used to symmetrically convolve the original values of all the primitive values that pass by to obtain the resulting texture. In this process, streamline tracking and convolution consume a lot of computing resources. To generate more expressive textures for vector fields with less time consumption, a novel method named random increment streamline (RIS) is put forward, which can generate streamline textures without convolution calculations. First, the mesh unit filling preprocessing (MUFP) method is presented to transform an undressed irregular grid into a special kind of regular grid named a “texture pixel”, and the point location and interpolation processes of all sampling points in the texture pixels are calculated before streamline tracking. Second, the random increment streamline method is used to generate line integral convolution style textures without any convolution calculations, thus greatly reducing the algorithm’s time consumption. Third, the vector directions at each point in the static vector field are clearly expressed using the periodic cyclic animation method. Finally, several simplifications of the RIS algorithm are discussed, which help to achieve a better visual effect with faster speed. The programming results show that the method is faster and more applicable than the traditional LIC method and provides clearer expression of the vector field.

scholarly journals A New Normal Form for Monodromic Nilpotent Singularities of Planar Vector Fields

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
Antonio Algaba ◽  
Cristóbal García ◽  
Jaume Giné
Keyword(s):  
Normal Form ◽  
Vector Fields ◽  
New Technique ◽  
Center Problem ◽  
New Normal ◽  
Planar Vector Fields ◽  
Planar Vector ◽  
A New Technique

AbstractIn this work, we present a new technique for solving the center problem for nilpotent singularities which consists of determining a new normal form conveniently adapted to study the center problem for this singularity. In fact, it is a pre-normal form with respect to classical Bogdanov–Takens normal formal and it allows to approach the center problem more efficiently. The new normal form is applied to several examples.

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