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

Dimensions of spline spaces over unconstricted triangulations

AbstractOne of the puzzlingly hard problems in Computer Aided Geometric Design and Approximation Theory is that of finding the dimension of the spline space of Cr piecewise degree n polynomials over a 2D triangulation Ω. We denote such spaces by Snr(Ω). In this note, we restrict Ω to have a special structure, namely to be unconstricted. This will allow for several exact dimension formulas

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

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

On Approximating Contours of the Piecewise Trilinear Interpolant Using Triangular Rational-Quadratic Bezier Patches

Given a three-dimensional (3D) array of function values Fijk on a rectilinear grid, the marching cubes(MC) method is the most common technique used for computing a surface triangulation T approximating a contour (isosurface) F(x,y,z)=T. We describe the construction of a Co-continuous surface consisting of rational-quadratic surface patches interpolating the triangles in T. We determine the Bezier control points of a single rational-quadratic surface patch based on the coordinates of the vertices of the underlying triangle and the gradients and Hessians associated with the vertices

Curves and Surfaces for Computer Aided Geometric Design : A Practical Guide

444 tr.; 21 cm

Rational quadratic circles are parametrized by chord length

Abstract We show that the chord length parameter assignment is exact for circle segments in standard rational quadratic form. Keywords: chord length parametrization, rational quadratics, standard form. Rational Quadratic Circles An arc of a circle may be written as a rational quadratic: where the control points c 0 , c 1 , c 2 form an isosceles triangle with base c 0 , c 2 , see While the rational quadratic (1) does describe a circular arc, its parametrization is not the arc length one (for a proof, se

Curves and surfaces for CAGD: a practical guide

This fifth edition has been fully updated to cover the many advances made in CAGD and curve and surface theory since 1997, when the fourth edition appeared. Material has been restructured into theory and applications chapters. The theory material has been streamlined using the blossoming approach; the applications material includes least squares techniques in addition to the traditional interpolation methods. In all other respects, it is, thankfully, the same. This means you get the informal, friendly style and unique approach that has made Curves and Surfaces for CAGD: A Practical Gu