In this paper we present a novel generic method for the fast and accurate computation of geometric features at multiple scales. The presented method works on arbitrarily complex models and operates in the parametric space. The majority of the existing methods compute local features directly on the geometric representation of the model. Our approach decouples the computational complexity from th...

New methods for D-decomposition analysis are presented. They are based on topology of real algebraic varieties and computational real algebraic geometry. The estimate of number of root invariant regions for polynomial parametric families of polynomial and matrices is given. For the case of two parametric family more sharp estimate is proven. Theoretic results are supported by various numerical ...

We develop a family of infinite-dimensional (i.e. non-parametric) manifolds of probability measures. The latter are defined on underlying Banach spaces, and have densities of class Ck b with respect to appropriate reference measures. The case k = ∞, in which the manifolds are modelled on Fréchet spaces, is included. The manifolds admit the Fisher-Rao metric and the dually flat geometry of Amari...

In this paper we address the design of large roof structures by integrating interdisciplinary performance evaluations in the early stages of the design process. Specific focus is given to structural and solar energy related performances. Geometry is stressed as a key interface between the different disciplines. Parametric modelling is used to automatically create geometric design alternatives. ...

Parametric X-ray radiation generated by a beam of relativistic electrons in single-crystal wafer is studied the Bragg geometry under conditions multiple electron scattering at target atoms. Expressions are obtained that describe spectral-angular and angular density scattering. An increase influence on demonstrated both with an thickness decrease energy electrons. It shown asymmetry electron-fie...

The Fisher information metric is an important foundation of information geometry, wherein it allows us to approximate the local geometry of a probability distribution. Recurrent neural networks such as the Sequence-to-Sequence (Seq2Seq) networks that have lately been used to yield state-of-the-art performance on speech translation or image captioning have so far ignored the geometry of the late...

In this paper, we present a method for time series analysis based on empirical intrinsic geometry (EIG). EIG enables one to reveal the low-dimensional parametric manifold as well as to infer the underlying dynamics of high-dimensional time series. By incorporating concepts of information geometry, this method extends existing geometric analysis tools to support stochastic settings and parametri...

The purpose of this study is to investigate a small centrifugal cooling fan applied on notebook computers, which is consisted of a forward-curved impeller and a centrifugal housing. First of all, a basic rotor impeller is designed with the cascade theory. To manufacture the mock-up for experimental verification, the design fan will be expressed in the CAD/CAM format for the CNC machine. All exp...

In this paper we present an experimental prototype called GEGROSS (GEsture & Geometric ReconstructiOn based Sketch System). This application allows using freehand sketches to create 3D parametric models onto a Tablet-PC. The modelling process consists of two stages. First, the user introduces the geometry of the 2D section using continuous sketches composed by line segments, circles and arcs, a...

The most important concepts for the handling and storage of freeform shapes in geometry processing applications are parametric representations and volumetric representations. Both have their specific advantages and drawbacks. While the algebraic complexity of volumetric representations S = {(x, y, z) | f(x, y, z) = 0} is independent from the shape complexity, the domain Ω of a parametric repres...