A Framework for n-dimension Visibility Calculation

4 pagesVisibility computation is a fundamental task in computer graphics, as in many other scientific domains. While it is well understood in two dimensions, this does not remain true in high dimensional spaces. Using Grassmann Algebra, we propose a framework for solving visibility problems in any n-dimensional spaces, for n ≥ 2. Our presentation recalls the problem statement, in two and three dimensions. Then, we formalize the space of n-dimensional lines. Finally, we show how this leads to a global framework for visibility computations, giving an example of use with exact soft shadows

An Algebraic Framework for the Real-Time Solution of Inverse Problems on Embedded Systems

This article presents a new approach to the real-time solution of inverse problems on embedded systems. The class of problems addressed corresponds to ordinary differential equations (ODEs) with generalized linear constraints, whereby the data from an array of sensors forms the forcing function. The solution of the equation is formulated as a least squares (LS) problem with linear constraints. The LS approach makes the method suitable for the explicit solution of inverse problems where the forcing function is perturbed by noise. The algebraic computation is partitioned into a initial preparatory step, which precomputes the matrices required for the run-time computation; and the cyclic run-time computation, which is repeated with each acquisition of sensor data. The cyclic computation consists of a single matrix-vector multiplication, in this manner computation complexity is known a-priori, fulfilling the definition of a real-time computation. Numerical testing of the new method is presented on perturbed as well as unperturbed problems; the results are compared with known analytic solutions and solutions acquired from state-of-the-art implicit solvers. The solution is implemented with model based design and uses only fundamental linear algebra; consequently, this approach supports automatic code generation for deployment on embedded systems. The targeting concept was tested via software- and processor-in-the-loop verification on two systems with different processor architectures. Finally, the method was tested on a laboratory prototype with real measurement data for the monitoring of flexible structures. The problem solved is: the real-time overconstrained reconstruction of a curve from measured gradients. Such systems are commonly encountered in the monitoring of structures and/or ground subsidence.Comment: 24 pages, journal articl

Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package

We introduce the \texttt{pyunicorn} (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. \texttt{pyunicorn} is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics or network surrogates. Additionally, \texttt{pyunicorn} provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis (RQA), recurrence networks, visibility graphs and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology.Comment: 28 pages, 17 figure

ADAM: a general method for using various data types in asteroid reconstruction

We introduce ADAM, the All-Data Asteroid Modelling algorithm. ADAM is simple and universal since it handles all disk-resolved data types (adaptive optics or other images, interferometry, and range-Doppler radar data) in a uniform manner via the 2D Fourier transform, enabling fast convergence in model optimization. The resolved data can be combined with disk-integrated data (photometry). In the reconstruction process, the difference between each data type is only a few code lines defining the particular generalized projection from 3D onto a 2D image plane. Occultation timings can be included as sparse silhouettes, and thermal infrared data are efficiently handled with an approximate algorithm that is sufficient in practice due to the dominance of the high-contrast (boundary) pixels over the low-contrast (interior) ones. This is of particular importance to the raw ALMA data that can be directly handled by ADAM without having to construct the standard image. We study the reliability of the inversion by using the independent shape supports of function series and control-point surfaces. When other data are lacking, one can carry out fast nonconvex lightcurve-only inversion, but any shape models resulting from it should only be taken as illustrative global-scale ones.Comment: 11 pages, submitted to A&