scholarly journals Evenly spaced data points and radial basis functions

2011 ◽  
Author(s):  
L. T. Luh
Keyword(s):  
Radial Basis Functions ◽  
Basis Functions ◽  
Radial Basis ◽  
Data Points

GPU-Based Sphere Tracing for Radial Basis Function Implicits

2014 ◽  
Vol 14 (01n02) ◽  
pp. 1450004
Author(s):  
Harlen Costa Batagelo ◽  
João Paulo Gois
Keyword(s):  
Ray Tracing ◽  
Radial Basis Functions ◽  
Computational Cost ◽  
Partition Of Unity ◽  
Basis Functions ◽  
Regular Partition ◽  
Ambient Occlusion ◽  
Radial Basis ◽  
Data Points ◽  
Normal Vectors

Ray tracing of implicit surfaces based on radial basis functions can demand high computational cost in the presence of a large number of radial centers. Recently, it was presented the least squares hermite radial basis functions (LS-HRBF) Implicits, a method for implicit surface reconstruction from Hermitian data (points equipped with their normal vectors) which makes use of iterative center selection in order to reduce the number of centers. In the present work, we propose an antialiazed sphere tracing algorithm fully implemented in OpenGL Shader Language for ray tracing LS-HRBF Implicits, which exploits a regular partition of unity for strong parallelization. We show that interactive frame rates can be achieved for surfaces composed of thousands of centers even when rendering effects such as cube mapping, soft shadows and ambient occlusion are used.

Characterization of a two-dimensional static wind field using Radial Basis Functions

SIMULATION ◽  
2018 ◽  
Vol 95 (6) ◽  
pp. 561-567
Author(s):  
Brandon Troub ◽  
Rockwell Garrido ◽  
Carlos Montalvo ◽  
JD Richardson
Keyword(s):  
Regression Model ◽  
Radial Basis Functions ◽  
Basis Function ◽  
Wind Field ◽  
Basis Functions ◽  
Two Dimensional ◽  
Sampled Data ◽  
Radial Basis ◽  
Data Points ◽  
Spatially Varying

Radial Basis Functions are a modern way of creating a regression model of a multivariate function when sampled data points are not uniformly distributed in a perfect grid. Radial Basis Functions are well suited to atmospheric characterization when unmanned aerial vehicles (UAVs) are used to sample the given space. Multiple UAVs reduce the time for the Radial Basis Functions to yield a suitable solution to the measured data while data from all aircraft are aggregated and sent to Radial Basis Functions to fit the data. The research presented here focuses on the requirements for a high correlation value between the sampled data and the actual data. It is found that the number of centers is a large driver of the goodness of fit in the Radial Basis Function routine, much like aliasing is an issue in sampling a sinusoidal function. These centers act like a sampling rate for the spatially varying wind field. If the centers are dense enough to fully capture the spatial frequency of the wind field, the Radial Basis Functions will produce a suitable fit. This also requires the number of data points to be larger than the number of centers. The ratio between the number of centers and number of sampled data points declines as the number of centers increases. The results presented here are revealed using a two-dimensional Fourier series analysis coupled to a spatially varying atmospheric wind model and a Radial Basis Function regression model.

Biharmonic navigation using radial basis functions

Robotica ◽  
2021 ◽  
pp. 1-12
Author(s):  
Xu-Qian Fan ◽  
Wenyong Gong
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Radial Basis Functions ◽  
Real World ◽  
Biharmonic Equation ◽  
Finite Difference Methods ◽  
Basis Functions ◽  
Large Size ◽  
Radial Basis ◽  
Difference Methods

Abstract Path planning has been widely investigated by many researchers and engineers for its extensive applications in the real world. In this paper, a biharmonic radial basis potential function (BRBPF) representation is proposed to construct navigation fields in 2D maps with obstacles, and it therefore can guide and design a path joining given start and goal positions with obstacle avoidance. We construct BRBPF by solving a biharmonic equation associated with distance-related boundary conditions using radial basis functions (RBFs). In this way, invalid gradients calculated by finite difference methods in large size grids can be preventable. Furthermore, paths constructed by BRBPF are smoother than paths constructed by harmonic potential functions and other methods, and plenty of experimental results demonstrate that the proposed method is valid and effective.

Sign in / Sign up

Export Citation Format

Share Document