Curve network interpolation by C1C^1 quadratic B-spline surfaces

In this paper we investigate the problem of interpolating a B-spline curve network, in order to create a surface satisfying such a constraint and defined by blending functions spanning the space of bivariate $C^1$ quadratic splines on criss-cross triangulations. We prove the existence and uniqueness of the surface, providing a constructive algorithm for its generation. We also present numerical and graphical results and comparisons with other methods.Comment: With respect to the previous version, this version of the paper is improved. The results have been reorganized and it is more general since it deals with non uniform knot partitions. Accepted for publication in Computer Aided Geometric Design, October 201

Reverse Engineering Trimmed NURB Surfaces From Laser Scanned Data

A common reverse engineering problem is to convert several hundred thousand points collected from the surface of an object via a digitizing process, into a coherent geometric model that is easily transferred to a CAD software such as a solid modeler for either design improvement or manufacturing and analysis. These data are very dense and make data-set manipulation difficult and tedious. Many commercial solutions exist but involve time consuming interaction to go from points to surface meshes such as BSplines or NURBS (Non Uniform Rational BSplines). Our approach differs from current industry practice in that we produce a mesh with little or no interaction from the user. The user can produce degree 2 and higher BSpline surfaces and can choose the degree and number ofsegments as parameters to the system. The BSpline surface is both compact and curvature continuous. The former property reduces the large storage overhead, and the later implies a smooth can be created from noisy data. In addition, the nature ofthe BSpline allows one to easily and smoothly alter the surface, making re-engineering extremely feasible. The BSpline surface is created using the principle ofhigher orders least squares with smoothing functions at the edges. Both linear and cylindrical data sets are handled using an automated parameterization method. Also, because ofthe BSpline's continuous nature, a multiresolutional-triangulated mesh can quickly be produced. This last fact means that an STL file is simple to generate. STL files can also be easily used as input to the system.Mechanical Engineerin

Reverse Engineering Trimmed NURB Surfaces From Laser Scanned Data

A common reverse engineering problem is to convert several hundred thousand points collected from the surface of an object via a digitizing process, into a coherent geometric model that is easily transferred to a CAD software such as a solid modeler for either design improvement or manufacturing and analysis. These data are very dense and make data-set manipulation difficult and tedious. Many commercial solutions exist but involve time consuming interaction to go from points to surface meshes such as BSplines or NURBS (Non Uniform Rational BSplines). Our approach differs from current industry practice in that we produce a mesh with little or no interaction from the user. The user can produce degree 2 and higher BSpline surfaces and can choose the degree and number ofsegments as parameters to the system. The BSpline surface is both compact and curvature continuous. The former property reduces the large storage overhead, and the later implies a smooth can be created from noisy data. In addition, the nature ofthe BSpline allows one to easily and smoothly alter the surface, making re-engineering extremely feasible. The BSpline surface is created using the principle ofhigher orders least squares with smoothing functions at the edges. Both linear and cylindrical data sets are handled using an automated parameterization method. Also, because ofthe BSpline's continuous nature, a multiresolutional-triangulated mesh can quickly be produced. This last fact means that an STL file is simple to generate. STL files can also be easily used as input to the system.Mechanical Engineerin

Grid generation on trimmed Bezier and NURBS quilted surfaces

This paper presents some recently added capabilities to RAGGS, Rockwell Automated Grid Generation System. Included are the trimmed surface handling and display capability and structures and unstructured grid generation on trimmed Bezier and NURBS (non-uniform rational B-spline surfaces) quilted surfaces. Samples are given to demonstrate the new capabilities

Guaranteed passive parameterized model order reduction of the partial element equivalent circuit (PEEC) method

The decrease of IC feature size and the increase of operating frequencies require 3-D electromagnetic methods, such as the partial element equivalent circuit (PEEC) method, for the analysis and design of high-speed circuits. Very large systems of equations are often produced by 3-D electromagnetic methods. During the circuit synthesis of large-scale digital or analog applications, it is important to predict the response of the system under study as a function of design parameters, such as geometrical and substrate features, in addition to frequency (or time). Parameterized model order reduction (PMOR) methods become necessary to reduce large systems of equations with respect to frequency and other design parameters. We propose an innovative PMOR technique applicable to PEEC analysis, which combines traditional passivity-preserving model order reduction methods and positive interpolation schemes. It is able to provide parametric reduced-order models, stable, and passive by construction over a user-defined range of design parameter values. Numerical examples validate the proposed approach

Unstructured surface grid generation

Viewgraphs on unstructured surface grid generation are presented. Topics covered include: requirements for curves, surfaces, solids, and text; surface approximation; triangulation; advancing; projection; mapping; and parametric curves