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

Flexible G1 Interpolation of Quad Meshes

International audienceTransforming an arbitrary mesh into a smooth G1 surface has been the subject of intensive research works. To get a visual pleasing shape without any imperfection even in the presence of extraordinary mesh vertices is still a challenging problem in particular when interpolation of the mesh vertices is required. We present a new local method, which produces visually smooth shapes while solving the interpolation problem. It consists of combining low degree biquartic Bézier patches with minimum number of pieces per mesh face, assembled together with G1-continuity. All surface control points are given explicitly. The construction is local and free of zero-twists. We further show that within this economical class of surfaces it is however possible to derive a sufficient number of meaningful degrees of freedom so that standard optimization techniques result in high quality surfaces

Smooth Subdivision Surfaces: Mesh Blending and Local Interpolation

Subdivision surfaces are widely used in computer graphics and animation. Catmull-Clark subdivision (CCS) is one of the most popular subdivision schemes. It is capable of modeling and representing complex shape of arbitrary topology. Polar surface, working on a triangle-quad mixed mesh structure, is proposed to solve the inherent ripple problem of Catmull-Clark subdivision surface (CCSS). CCSS is known to be C1 continuous at extraordinary points. In this work, we present a G2 scheme at CCS extraordinary points. The work is done by revising CCS subdivision step with Extraordinary-Points-Avoidance model together with mesh blending technique which selects guiding control points from a set of regular sub-meshes (named dominative control meshes) iteratively at each subdivision level. A similar mesh blending technique is applied to Polar extraordinary faces of Polar surface as well. Both CCS and Polar subdivision schemes are approximating. Traditionally, one can obtain a CCS limit surface to interpolate given data mesh by iteratively solving a global linear system. In this work, we present a universal interpolating scheme for all quad subdivision surfaces, called Bezier Crust. Bezier Crust is a specially selected bi-quintic Bezier surface patch. With Bezier Crust, one can obtain a high quality interpolating surface on CCSS by parametrically adding CCSS and Bezier Crust. We also show that with a triangle/quad conversion process one can apply Bezier Crust on Polar surfaces as well. We further show that Bezier Crust can be used to generate hollowed 3D objects for applications in rapid prototyping. An alternative interpolating approach specifically designed for CCSS is developed. This new scheme, called One-Step Bi-cubic Interpolation, uses bicubic patches only. With lower degree polynomial, this scheme is appropriate for interpolating large-scale data sets. In sum, this work presents our research on improving surface smoothness at extraordinary points of both CCS and Polar surfaces and present two local interpolating approaches on approximating subdivision schemes. All examples included in this work show that the results of our research works on subdivision surfaces are of high quality and appropriate for high precision engineering and graphics usage

Multiple Representation Approach to Geometric Model Construction From Range Data

A method is presented for constructing geometric design data from noisy 3-D sensor measurements of physical parts. In early processing phase, RLTS regression filters stemming from robust estimation theory are used for separating the desired part of the signal in contaminated sensor data from undesired part. Strategies for producing a complete 3-D data set from partial views are studied. Multiple representations are used in model construction because there is no single representation that would be most appropriate in all situations. In particular, surface triangulation, NURBS, and super-ellipsoids are employed in order to represent efficiently polygonal and irregular shapes, free form surfaces and standard primitive solids. The size of the required control point mesh for spline description is estimated using a surface characterization process. Surfaces of arbitrary topology are modeled using triangulation and trimmed NURBS. A user given tolerance value is driving refinement of the obtained surface model. The resulting model description is a procedural CAD model which can convey structural information in addition to low level geometric primitives. The model is translated to IGES standard product data exchange format to enable data sharing with other processes in concurrent engineering environment. Preliminary results on view registration using simulated data are shown. Examples of model construction using both real and simulated data are also given

Data-driven quasi-interpolant spline surfaces for point cloud approximation

In this paper we investigate a local surface approximation, the Weighted Quasi Interpolant Spline Approximation (wQISA), specifically designed for large and noisy point clouds. We briefly describe the properties of the wQISA representation and introduce a novel data-driven implementation, which combines prediction capability and complexity efficiency. We provide an extended comparative analysis with other continuous approximations on real data, including different types of surfaces and levels of noise, such as 3D models, terrain data and digital environmental data

Cad-based adaptive shape parameterisation for aerodynamic shape optimisation

Non-Uniform Rational B-Splines (NURBS) have become the industrial standard to represent and exchange a CAD geometry between CAD/CAE systems. CAD-based shape parameterisation uses parameters of a CAD model to modify the shape which allows to integrate a CAD model into the design loop. However, feature-trees of typical commercial CAD systems are not open and obtaining exact derivatives for gradient-based optimisation methods is not possible. Using the CAD-based NSPCC approach a designer can deform multiple NURBS patches in the design loop without violating geometric and/or thickness constraints. The NSPCC approach takes CAD descriptions as input and perturbs the control points of the NURBS boundary representation to modify the shape. In this work, an adaptive NSPCC method is proposed where the optimisation begins with a coarser design space and adapts to finer parametrisation during the design process where more shape control is needed. The refinement sensor is based on a comparison of smoothed node-based sensitivity compared to its projection onto the shape modes of the current parametrisation. Both static and adaptive parametrisation methods are coupled in the adjoint-based shape optimisation process to reduce the total pressure loss of a turbine blade internal cooling channel. The discrete adjoint flow solver STAMPS is used to compute the flow fields and their derivatives w.r.t. surface node displacements. The shape derivatives for gradient-based optimisation are obtained by application of reverse mode AD to the NSPCC CAD kernel. Since a CAD model is kept inside the design loop, the resulting optimal shape is directly available in CAD for further analysis or manufacturing. Based on the analysis regarding quality of the optima and rate of convergence of the design process adaptive NSPCC method outperforms static NSPCC approach