Fisheye Algorithm Research Articles

Planning-oriented optimization strategy for visualizing power distribution networks: from global to local

ABSTRACT The spatial distribution of power facilities is uneven, thereby making the topology of geographical wiring diagrams (GWDs) based on the actual coordinates unclear. A single-line diagram has the advantage of a clear topology but it lacks spatial locations. A GWD has the advantage of accurate spatial locations but it lacks a clear topology. Visualizing distribution networks for planning requires both features. We proposed a new planning-oriented method for optimizing the visualization of distribution networks. From the global perspective, we proposed an improved force-directed (FD) algorithm by introducing a space restriction strategy and node–edge repulsion strategy to promote the expansion of the distance between distribution facilities within a limited buffer. We then constructed the constrained Delaunay triangulation to identify the compact districts (CDs) and used a genetic algorithm to optimize the parameters for the improved FD algorithm. A novel visualization evaluation indicator was also proposed for quantitatively assessing the visualizations. From a local perspective, the fisheye algorithm was used to optimize the CDs to further improve the visualization of the distribution network. We verified the proposed methods with real-world data. We used limited spatial displacement in exchange for maximum topology clarity to balance the accurate spatial location and topology clarity.

RESEARCH FRACTAL STRUCTURES OF GENERALIZED M-J SETS USING THREE ALGORITHMS

Extreme modulus escaping time algorithm, decomposition algorithm and fisheye algorithm are analyzed in this thesis, and we construct a series of generalized Mandelbrot-Julia (M-J) sets using these three algorithms. By studying the structural character of generalized M-J sets, we find: (1) extreme modulus escaping time algorithm and decomposition algorithm are simple modifications of classic escaping time algorithm, they can both construct the structure of non-boundary areas of generalized M-J sets; (2) non-boundary areas of generalized M-J sets have fractal characters; (3) generalized M-J sets have symmetry, and the process of evolvement depends on range of phase angle; (4) we can observe not only the whole structure of generalized Mandelbrot sets but also the details of some parts by using fisheye algorithm.