Visualizing planar vector fields with normal component using line integral convolution

Author(s):  
G. Scheuermann ◽  
H. Barbach ◽  
H. Hagen
Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 724
Author(s):  
Xiaofu Du ◽  
Huilin Liu ◽  
Hsien-Wei Tseng ◽  
Teen-Hang Meen

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.


2021 ◽  
Vol 18 (5) ◽  
Author(s):  
Antonio Algaba ◽  
Cristóbal García ◽  
Jaume Giné

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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