A univariate rational quadratic trigonometric interpolating spline to visualize shaped data

This study was concerned with shape preserving interpolation of 2D data. A piecewise C1 univariate rational quadratic trigonometric spline including three positive parameters was devised to produce a shaped interpolant for given shaped data. Positive and monotone curve interpolation schemes were presented to sustain the respective shape features of data. Each scheme was tested for plentiful shaped data sets to substantiate the assertion made in their construction. Moreover, these schemes were compared with conventional shape preserving rational quadratic splines to demonstrate the usefulness of their construction

Parametric Interpolation To Scattered Data [QA281. A995 2008 f rb].

Dua skema interpolasi berparameter yang mengandungi interpolasi global untuk data tersebar am dan interpolasi pengekalan-kepositifan setempat data tersebar positif dibincangkan. Two schemes of parametric interpolation consisting of a global scheme to interpolate general scattered data and a local positivity-preserving scheme to interpolate positive scattered data are described

04131 Abstracts Collection -- Geometric Properties from Incomplete Data

From 21.03.04 to 26.03.04, the Dagstuhl Seminar 04131 ``Geometric Properties from Incomplete Data\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Arbitrary topology meshes in geometric design and vector graphics

Meshes are a powerful means to represent objects and shapes both in 2D and 3D, but the techniques based on meshes can only be used in certain regular settings and restrict their usage. Meshes with an arbitrary topology have many interesting applications in geometric design and (vector) graphics, and can give designers more freedom in designing complex objects. In the first part of the thesis we look at how these meshes can be used in computer aided design to represent objects that consist of multiple regular meshes that are constructed together. Then we extend the B-spline surface technique from the regular setting to work on extraordinary regions in meshes so that multisided B-spline patches are created. In addition, we show how to render multisided objects efficiently, through using the GPU and tessellation. In the second part of the thesis we look at how the gradient mesh vector graphics primitives can be combined with procedural noise functions to create expressive but sparsely defined vector graphic images. We also look at how the gradient mesh can be extended to arbitrary topology variants. Here, we compare existing work with two new formulations of a polygonal gradient mesh. Finally we show how we can turn any image into a vector graphics image in an efficient manner. This vectorisation process automatically extracts important image features and constructs a mesh around it. This automatic pipeline is very efficient and even facilitates interactive image vectorisation

08221 Abstracts Collection -- Geometric Modeling

From May 26 to May 30 2008 the Dagstuhl Seminar 08221 ``Geometric Modeling\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Algorithms for curve design and accurate computations with totally positive matrices

Esta tesis doctoral se enmarca dentro de la teoría de la Positividad Total. Las matrices totalmente positivas han aparecido en aplicaciones de campos tan diversos como la Teoría de la Aproximación, la Biología, la Economía, la Combinatoria, la Estadística, las Ecuaciones Diferenciales, la Mecánica, el Diseño Geométrico Asistido por Ordenador o el Álgebra Numérica Lineal. En esta tesis nos centraremos en dos de los campos que están relacionados con matrices totalmente positivas.This doctoral thesis is framed within the theory of Total Positivity. Totally positive matrices have appeared in applications from fields as diverse as Approximation Theory, Biology, Economics, Combinatorics, Statistics, Differential Equations, Mechanics, Computer Aided Geometric Design or Linear Numerical Algebra. In this thesis, we will focus on two of the fields that are related to totally positive matrices.<br /

Fungsi Ball Teritlak Nisbah Untuk Lengkung Interpolasi Cembung Dan Berekanada [QA603. S193 2008 f rb].

Tesis ini membincangkan skema interpolasi lengkung yang berasaskan fungsi asas Ball teritlak (Said-Ball) untuk menampakkan data saintifik. Skema menggunakan fungsi nisbah cebis demi cebis Ball teritlak dengan pengangka kuartik dan penyebut linear, yang melibatkan dua parameter bentuk. This thesis discusses a curve interpolation scheme based on the generalized Ball basis functions (Said-Ball) to visualize the scientific data. The scheme uses piecewise generalized Ball functions with quartic numerator and linear denominator involving two shape parameters

Sobre algunas técnicas de aproximación usadas en diseño asistido por computador

Las conclusiones de este TFG indican que los nuevos esquemas de subdivisión no lineal que se han presentado tienen las siguientes propiedades:1.son esquemas de interpolación ternarios , que convergen hacia funciones de regularidad superior a uno. 2.si los datos iniciales provienen de discretizar una función discontinua, las funciones límite no oscilan, a diferencia de lo que ocurre en los clásicos esquemas interpolatorios lineales. 3.las transformadas multiresolución asociadas son estables. Y constituyen la primera familia de esquemas que comparten simultáneamente esas propiedades tan deseables.Escuela Técnica Superior de Ingeniería de TelecomunicaciónUniversidad Politécnica de Cartagen

2D and 3D surface image processing algorithms and their applications

This doctoral dissertation work aims to develop algorithms for 2D image segmentation application of solar filament disappearance detection, 3D mesh simplification, and 3D image warping in pre-surgery simulation. Filament area detection in solar images is an image segmentation problem. A thresholding and region growing combined method is proposed and applied in this application. Based on the filament area detection results, filament disappearances are reported in real time. The solar images in 1999 are processed with this proposed system and three statistical results of filaments are presented. 3D images can be obtained by passive and active range sensing. An image registration process finds the transformation between each pair of range views. To model an object, a common reference frame in which all views can be transformed must be defined. After the registration, the range views should be integrated into a non-redundant model. Optimization is necessary to obtain a complete 3D model. One single surface representation can better fit to the data. It may be further simplified for rendering, storing and transmitting efficiently, or the representation can be converted to some other formats. This work proposes an efficient algorithm for solving the mesh simplification problem, approximating an arbitrary mesh by a simplified mesh. The algorithm uses Root Mean Square distance error metric to decide the facet curvature. Two vertices of one edge and the surrounding vertices decide the average plane. The simplification results are excellent and the computation speed is fast. The algorithm is compared with six other major simplification algorithms. Image morphing is used for all methods that gradually and continuously deform a source image into a target image, while producing the in-between models. Image warping is a continuous deformation of a: graphical object. A morphing process is usually composed of warping and interpolation. This work develops a direct-manipulation-of-free-form-deformation-based method and application for pre-surgical planning. The developed user interface provides a friendly interactive tool in the plastic surgery. Nose augmentation surgery is presented as an example. Displacement vector and lattices resulting in different resolution are used to obtain various deformation results. During the deformation, the volume change of the model is also considered based on a simplified skin-muscle model