A tension approach to controlling the shape of cubic spline surfaces on FVS triangulations

We propose a parametric tensioned version of the FVS macro-element to control the shape of the composite surface and remove artificial oscillations, bumps and other undesired behaviour. In particular, this approach is applied to C1 cubic spline surfaces over a four-directional mesh produced by two-stage scattered data fitting methods

Selected Algorithms of Quantitative Image Analysis for Measurements of Properties Characterizing Interfacial Interactions at High Temperatures.

In the case of every quantitative image analysis system a very important issue is to improve the quality of images to be analyzed, in other words, their pre-processing. As a result of pre-processing, the significant part of the redundant information and disturbances (which could originate from imperfect vision system components) should be removed from the image. Another particularly important problem to be solved is the right choice of image segmentation procedures. Segmentation essence is to divide an image into disjoint subsets that meet certain criteria for homogeneity (e.g. color, brightness or texture). The result of segmentation should allow the most precise determination of geometrical features of objects present in a scene with a minimum of computing effort. The measurement of geometric properties of objects present in the scene is the subject of image analysis

Polynomial cubic splines with tension properties

In this paper we present a new class of spline functions with tension properties. These splines are composed by polynomial cubic pieces and therefore are conformal to the standard, NURBS based CAD/CAM systems

Smooth path planning with Pythagorean-hodoghraph spline curves geometric design and motion control

This thesis addresses two significative problems regarding autonomous systems, namely path and trajectory planning. Path planning deals with finding a suitable path from a start to a goal position by exploiting a given representation of the environment. Trajectory planning schemes govern the motion along the path by generating appropriate reference (path) points. We propose a two-step approach for the construction of planar smooth collision-free navigation paths. Obstacle avoidance techniques that rely on classical data structures are initially considered for the identification of piecewise linear paths that do not intersect with the obstacles of a given scenario. In the second step of the scheme we rely on spline interpolation algorithms with tension parameters to provide a smooth planar control strategy. In particular, we consider Pythagorean\u2013hodograph (PH) curves, since they provide an exact computation of fundamental geometric quantities. The vertices of the previously produced piecewise linear paths are interpolated by using a G1 or G2 interpolation scheme with tension based on PH splines. In both cases, a strategy based on the asymptotic analysis of the interpolation scheme is developed in order to get an automatic selection of the tension parameters. To completely describe the motion along the path we present a configurable trajectory planning strategy for the offline definition of time-dependent C2 piece-wise quintic feedrates. When PH spline curves are considered, the corresponding accurate and efficient CNC interpolator algorithms can be exploited

Smooth path planning with Pythagorean-hodoghraph spline curves geometric design and motion control

This thesis addresses two significative problems regarding autonomous systems, namely path and trajectory planning. Path planning deals with finding a suitable path from a start to a goal position by exploiting a given representation of the environment. Trajectory planning schemes govern the motion along the path by generating appropriate reference (path) points. We propose a two-step approach for the construction of planar smooth collision-free navigation paths. Obstacle avoidance techniques that rely on classical data structures are initially considered for the identification of piecewise linear paths that do not intersect with the obstacles of a given scenario. In the second step of the scheme we rely on spline interpolation algorithms with tension parameters to provide a smooth planar control strategy. In particular, we consider Pythagorean–hodograph (PH) curves, since they provide an exact computation of fundamental geometric quantities. The vertices of the previously produced piecewise linear paths are interpolated by using a G1 or G2 interpolation scheme with tension based on PH splines. In both cases, a strategy based on the asymptotic analysis of the interpolation scheme is developed in order to get an automatic selection of the tension parameters. To completely describe the motion along the path we present a configurable trajectory planning strategy for the offline definition of time-dependent C2 piece-wise quintic feedrates. When PH spline curves are considered, the corresponding accurate and efficient CNC interpolator algorithms can be exploited

Model correlation and damage location for large space truss structures: Secant method development and evaluation

On-orbit testing of a large space structure will be required to complete the certification of any mathematical model for the structure dynamic response. The process of establishing a mathematical model that matches measured structure response is referred to as model correlation. Most model correlation approaches have an identification technique to determine structural characteristics from the measurements of the structure response. This problem is approached with one particular class of identification techniques - matrix adjustment methods - which use measured data to produce an optimal update of the structure property matrix, often the stiffness matrix. New methods were developed for identification to handle problems of the size and complexity expected for large space structures. Further development and refinement of these secant-method identification algorithms were undertaken. Also, evaluation of these techniques is an approach for model correlation and damage location was initiated

Convexity preserving interpolatory subdivision with conic precision

The paper is concerned with the problem of shape preserving interpolatory subdivision. For arbitrarily spaced, planar input data an efficient non-linear subdivision algorithm is presented that results in $G^1$ limit curves, reproduces conic sections and respects the convexity properties of the initial data. Significant numerical examples illustrate the effectiveness of the proposed method

Isogeometric Analysis in advection-diffusion problems: tension splines approximation

We present a novel approach, within the new paradigm of isogeometric analysis introduced by Hughes et al., to deal with advection dominated advection-diffusion problems. The key ingredient is the use of Galerkin approximating spaces of functions with high smoothness, as in IgA based on classical B-splines, but particularly well suited to describe sharp layers involving very strong gradients