An Efficient Trim Structure for Rendering Large B-Rep Models

International audienceWe present a multiresolution trim structure for fast and accurate B-Rep model visualization. To get a good tradeoff between performance and visual accuracy, we propose to use a vectorial but approximated representation of the model that allows efficient, real-time GPU exploitation. Our structure, based on a quadtree, enables us to do shallow lookups for distant fragments. For closeups, we leverage hardware tessellation. We get interactive frame rates for models that consists of hundreds of thousands of B-Rep faces, regardless of the zoom level

Rendu interactif de modèles B-Rep sur GPU

Les logiciels de modélisation géométrique utilisés dans la Conception Assistée par Ordinateur (CAO) servent aujourd'hui à concevoir des objets de toutes sortes, allant de simples lampes de bureau à des avions de lignes entiers. Les modèles de données B-Rep utilisés permettent de définir des formes de manière précise, et de créer des entités géométriques répondant à des critères divers et variés, qu'ils soient esthétiques, qu'ils reposent sur la résistance mécanique, ou encore sur des coûts de production. Au fur et à mesure des opérations de modélisation dans le logiciel de conception (i.e. CATIA, par exemple), les modèles doivent être affichés de la manière la plus fidèle possible à la représentation analytique, telle qu'elle a été explicitement définie par l'opérateur CAO. Les logiciels de modélisation existant discrétisent les formes définies au rythme des opérations de modélisation, et affichent des polygones approximant face par face les objects 3D résultant de cette discrétisation. Des jours ou "cracks" dûs à la tessellation apparaissent avec cette méthode de rendu et sont déplaisant voire gênant pour les opérateurs. Nous proposons dans nos travaux une manière de faire un rendu haute qualité et sans cracks des modèles, sans toucher à leur définition, et en conservant de bonnes performances à l'affichage. Notre méthode peut s'intégrer aux moteurs de rendu existant. Les sessions de modélisation manipulent des objets de petite ou moyenne envergure. Une fois assemblés, les objets définissant de grosses structures comme par exemple des bateaux ou des avions doivent parfois être visualisés dans leur totalité, et toujours avec une grande précision visuelle. C'est le cas par exemple pour les applications de tests statiques où des techniciens déposent sur une maquette virtuelle des capteurs servant à évaluer le comportement mécanique de centaines voire de milliers de parties localisées sur la structure. Ces capteurs, de la taille d'un ongle, sont physiquement placés sur un produit entièrement usiné et assemblé, tel qu'une section entière de fuselage, dans un hangar. La maquette virtuelle doit permettre de visualiser la structure exactement telle qu'elle est, dans ses moindres détails. Pour réaliser le rendu d'une telle quantité de données de manière interactive et ce, sans sacrifier les performances ou la qualité de rendu à fort niveau de zoom, nous nous appuyons sur les méthodes de rendu dites basées découpe. Nous proposons une structure de découpe rapide, avec laquelle le rendu de très grands modèles peut être effectué. Cette structure est associée à des routines de tessellation dédiées pour chaque type de face B-Rep, ce qui nous permet d'afficher en temps-réel une section entière d'un avion de ligne gros porteur, constituté de centaines de milliers de surfaces B-Rep, tessellées puis découpées à la volée.Modeling software applications dedicated to Computer Aided Design (CAD) are used to design objects of all sorts, ranging from small, simple desktop lamps to entire, complex aircrafts. The B-Rep models used during this design phase allow CAD operators to define shapes in a very precise manner, and create geometric entities meeting various design criteria, whether they are related to aesthetics, mechanical behavior, or production costs. As modeling operations are performed in the CAD software application (eg. CATIA, for instance), models must be rendered with a fidelity and accuracy as high as possible with regards to their analytical definition as it has specifically been defined by the CAD operator. Existing modeling software applications discretize shapes as they are being edited and render polygons approximating 3D objects resulting from this discretization, usually done on a face by face basis. Gaps or "cracks" caused by this tesselation show up with this rendering method and are very annoying for the operators. We propose a method to perform crack-free, high fidelity rendering of B-Rep models, with no model preprocess and with good performance, allowing interaction even for large-scale objects. Our method can easily be integrated into existing engines based on dynamic tesselation. Modeling sessions deal with small or medium scale object parts. Once assembled, these parts form large structures such as boats or aircrafts. These large assemblies may sometimes be interactively visualized as a whole, and once again high precision is strongly desired. Specifically, this is the case for static test applications where technicians place sensors on a virtual model called a Digital Mockup (or DMU) that is used to assess the mechanical strength of thousands of selected locations scattered throughout the model. These nail-sized sensors are then physically placed on a product entirely built and assembled in a hangar, such as an entire aircraft fuselage section. The DMU should represent as faithfully as possible the actual, physical model. For interactive rendering to take place with good frame rates and with high image quality, we rely on a trim-based rendering method with a custom, efficient, multi-resolution trim structure suitable for the rendering of large-scale models. This structure is used in conjunction with dedicated dynamic tesselation GPU routines for common types of B-Rep faces. This combination allows us to render in real-time and on current consumer hardware an entire wide-body aircraft fuselage section composed of hundreds of thousands of B-Rep faces that are dynamically tesselated and trimmed on the fly every time a rendering takes place

Direct immersogeometric fluid flow analysis using B-rep CAD models

We present a new method for immersogeometric fluid flow analysis that directly uses the CAD boundary representation (B-rep) of a complex object and immerses it into a locally refined, non-boundary-fitted discretization of the fluid domain. The motivating applications include analyzing the flow over complex geometries, such as moving vehicles, where the detailed geometric features usually require time-consuming, labor-intensive geometry cleanup or mesh manipulation for generating the surrounding boundary-fitted fluid mesh. The proposed method avoids the challenges associated with such procedures. A new method to perform point membership classification of the background mesh quadrature points is also proposed. To faithfully capture the geometry in intersected elements, we implement an adaptive quadrature rule based on the recursive splitting of elements. Dirichlet boundary conditions in intersected elements are enforced weakly in the sense of Nitsche\u27s method. To assess the accuracy of the proposed method, we perform computations of the benchmark problem of flow over a sphere represented using B-rep. Quantities of interest such as drag coefficient are in good agreement with reference values reported in the literature. The results show that the density and distribution of the surface quadrature points are crucial for the weak enforcement of Dirichlet boundary conditions and for obtaining accurate flow solutions. Also, with sufficient levels of surface quadrature element refinement, the quadrature error near the trim curves becomes insignificant. Finally, we demonstrate the effectiveness of our immersogeometric method for high-fidelity industrial scale simulations by performing an aerodynamic analysis of an agricultural tractor directly represented using B-rep

Efficient and High-Quality Rendering of Higher-Order Geometric Data Representations

Computer-Aided Design (CAD) bezeichnet den Entwurf industrieller Produkte mit Hilfe von virtuellen 3D Modellen. Ein CAD-Modell besteht aus parametrischen Kurven und Flächen, in den meisten Fällen non-uniform rational B-Splines (NURBS). Diese mathematische Beschreibung wird ebenfalls zur Analyse, Optimierung und Präsentation des Modells verwendet. In jeder dieser Entwicklungsphasen wird eine unterschiedliche visuelle Darstellung benötigt, um den entsprechenden Nutzern ein geeignetes Feedback zu geben. Designer bevorzugen beispielsweise illustrative oder realistische Darstellungen, Ingenieure benötigen eine verständliche Visualisierung der Simulationsergebnisse, während eine immersive 3D Darstellung bei einer Benutzbarkeitsanalyse oder der Designauswahl hilfreich sein kann. Die interaktive Darstellung von NURBS-Modellen und -Simulationsdaten ist jedoch aufgrund des hohen Rechenaufwandes und der eingeschränkten Hardwareunterstützung eine große Herausforderung. Diese Arbeit stellt vier neuartige Verfahren vor, welche sich mit der interaktiven Darstellung von NURBS-Modellen und Simulationensdaten befassen. Die vorgestellten Algorithmen nutzen neue Fähigkeiten aktueller Grafikkarten aus, um den Stand der Technik bezüglich Qualität, Effizienz und Darstellungsgeschwindigkeit zu verbessern. Zwei dieser Verfahren befassen sich mit der direkten Darstellung der parametrischen Beschreibung ohne Approximationen oder zeitaufwändige Vorberechnungen. Die dabei vorgestellten Datenstrukturen und Algorithmen ermöglichen die effiziente Unterteilung, Klassifizierung, Tessellierung und Darstellung getrimmter NURBS-Flächen und einen interaktiven Ray-Casting-Algorithmus für die Isoflächenvisualisierung von NURBSbasierten isogeometrischen Analysen. Die weiteren zwei Verfahren beschreiben zum einen das vielseitige Konzept der programmierbaren Transparenz für illustrative und verständliche Visualisierungen tiefenkomplexer CAD-Modelle und zum anderen eine neue hybride Methode zur Reprojektion halbtransparenter und undurchsichtiger Bildinformation für die Beschleunigung der Erzeugung von stereoskopischen Bildpaaren. Die beiden letztgenannten Ansätze basieren auf rasterisierter Geometrie und sind somit ebenfalls für normale Dreiecksmodelle anwendbar, wodurch die Arbeiten auch einen wichtigen Beitrag in den Bereichen der Computergrafik und der virtuellen Realität darstellen. Die Auswertung der Arbeit wurde mit großen, realen NURBS-Datensätzen durchgeführt. Die Resultate zeigen, dass die direkte Darstellung auf Grundlage der parametrischen Beschreibung mit interaktiven Bildwiederholraten und in subpixelgenauer Qualität möglich ist. Die Einführung programmierbarer Transparenz ermöglicht zudem die Umsetzung kollaborativer 3D Interaktionstechniken für die Exploration der Modelle in virtuellenUmgebungen sowie illustrative und verständliche Visualisierungen tiefenkomplexer CAD-Modelle. Die Erzeugung stereoskopischer Bildpaare für die interaktive Visualisierung auf 3D Displays konnte beschleunigt werden. Diese messbare Verbesserung wurde zudem im Rahmen einer Nutzerstudie als wahrnehmbar und vorteilhaft befunden.In computer-aided design (CAD), industrial products are designed using a virtual 3D model. A CAD model typically consists of curves and surfaces in a parametric representation, in most cases, non-uniform rational B-splines (NURBS). The same representation is also used for the analysis, optimization and presentation of the model. In each phase of this process, different visualizations are required to provide an appropriate user feedback. Designers work with illustrative and realistic renderings, engineers need a comprehensible visualization of the simulation results, and usability studies or product presentations benefit from using a 3D display. However, the interactive visualization of NURBS models and corresponding physical simulations is a challenging task because of the computational complexity and the limited graphics hardware support. This thesis proposes four novel rendering approaches that improve the interactive visualization of CAD models and their analysis. The presented algorithms exploit latest graphics hardware capabilities to advance the state-of-the-art in terms of quality, efficiency and performance. In particular, two approaches describe the direct rendering of the parametric representation without precomputed approximations and timeconsuming pre-processing steps. New data structures and algorithms are presented for the efficient partition, classification, tessellation, and rendering of trimmed NURBS surfaces as well as the first direct isosurface ray-casting approach for NURBS-based isogeometric analysis. The other two approaches introduce the versatile concept of programmable order-independent semi-transparency for the illustrative and comprehensible visualization of depth-complex CAD models, and a novel method for the hybrid reprojection of opaque and semi-transparent image information to accelerate stereoscopic rendering. Both approaches are also applicable to standard polygonal geometry which contributes to the computer graphics and virtual reality research communities. The evaluation is based on real-world NURBS-based models and simulation data. The results show that rendering can be performed directly on the underlying parametric representation with interactive frame rates and subpixel-precise image results. The computational costs of additional visualization effects, such as semi-transparency and stereoscopic rendering, are reduced to maintain interactive frame rates. The benefit of this performance gain was confirmed by quantitative measurements and a pilot user study

A geometric framework for immersogeometric analysis

The purpose of this dissertation is to develop a geometric framework for immersogeometric analysis that directly uses the boundary representations (B-reps) of a complex computer-aided design (CAD) model and immerses it into a locally refined, non-boundary-fitted discretization of the fluid domain. Using the non-boundary-fitted mesh which does not need to conform to the shape of the object can alleviate the challenge of mesh generation for complex geometries. This also reduces the labor-intensive and time-consuming work of geometry cleanup for the purpose of obtaining watertight CAD models in order to perform boundary-fitted mesh generation. The Dirichlet boundary conditions in the fluid domain are enforced weakly over the immersed object surface in the intersected elements. The surface quadrature points for the immersed object are generated on the parametric and analytic surfaces of the B-rep models. In the case of trimmed surfaces, adaptive quadrature rule is considered to improve the accuracy of the surface integral. For the non-boundary-fitted mesh, a sub-cell-based adaptive quadrature rule based on the recursive splitting of quadrature elements is used to faithfully capture the geometry in intersected elements. The point membership classification for identifying quadrature points in the fluid domain is based on a voxel-based approach implemented on GPUs. A variety of computational fluid dynamics (CFD) simulations are performed using the proposed method to assess its accuracy and efficiency. Finally, a fluid--structure interaction (FSI) simulation of a deforming left ventricle coupled with the heart valves shows the potential advantages of the developed geometric framework for the immersogeomtric analysis with complex moving domains

Doctor of Philosophy

dissertationWhile boundary representations, such as nonuniform rational B-spline (NURBS) surfaces, have traditionally well served the needs of the modeling community, they have not seen widespread adoption among the wider engineering discipline. There is a common perception that NURBS are slow to evaluate and complex to implement. Whereas computer-aided design commonly deals with surfaces, the engineering community must deal with materials that have thickness. Traditional visualization techniques have avoided NURBS, and there has been little cross-talk between the rich spline approximation community and the larger engineering field. Recently there has been a strong desire to marry the modeling and analysis phases of the iterative design cycle, be it in car design, turbulent flow simulation around an airfoil, or lighting design. Research has demonstrated that employing a single representation throughout the cycle has key advantages. Furthermore, novel manufacturing techniques employing heterogeneous materials require the introduction of volumetric modeling representations. There is little question that fields such as scientific visualization and mechanical engineering could benefit from the powerful approximation properties of splines. In this dissertation, we remove several hurdles to the application of NURBS to problems in engineering and demonstrate how their unique properties can be leveraged to solve problems of interest