Robust boolean set operations for manifold solids bounded by planar and natural quadric surfaces

Journal ArticleThis paper describes our latest effort in robust solid modeling. An algorithm for set operations on solids bounded by planar and natural quadric surfaces, that handles all geometrically degenerate cases robustly, is described. We identify as the main reason for the lack of robustness in geometric modeling, that dependent relations are handled inconsistently by disregarding the dependencies. Instead of using explicit reasoning to make dependent decisions consistent, we show that redundant computation can be avoided by correctly ordering the operations, and redundant data can be eliminated in the set operation algorithm, so that the result is guaranteed to be a valid two-manifold solid

Robustness in solid modeling - a tolerance based, intuitionistic approach

Journal ArticleThis paper presents a new robustness method for geometric modeling operations. It computes geometric relations from the tolerances defined for geometric objects and dynamically updates the tolerances to preserve the properties of the relations, using an intuitionistic self-validation approach. Geometric algorithms using this approach are proved to be robust. A robust Boolean set operation algorithm using this robustness approach has been implemented and test examples are described in this paper as well

A new approach to tolerance analysis

Journal ArticleTolerance analysis is seen as part of a more general problem, namely handling data with uncertainty. Uncertain geometric data arises when interpreting measured data, but also in solid modeling where floating point approximations are common, when representing design tolerances, or when dealing with limited manufacturing precision. The common question is whether parts with uncertain shape fulfill certain functional specification. The question is expressed as geometrical relationship between toleranced objects. Unfortunately, tolerance based relations are often inconsistent, unlike relations between exactly represented objects. In this paper we survey current tolerance representation and analysis methods. We then derive our method of intuitionistic tolerance handling from a method developed for robust solid modeling. A new representational framework is proposed, which serves as the basis for robust geometric modeling and tolerance analysis. We illustrate the framework with examples of assembly design

Robust solid modeling by avoiding redundancy for manifold objects in boundary representation

Journal ArticleThis paper describes a new approach to the robustness problem in solid modeling. We identify as t h e main cause of t h e lack of robustness that interdependent topological relations are derived from approximate data. Disregarding the interdependencies very likely violates basic properties, such as reflexivity, and transitivity, resulting in invalid data representations, such as dangling edges, missing faces, etc. We show that the boundary of manifold objects can be represented without redundant relations which avoids inconsistencies. An algorithm for regularized set operations for manifold solids which is based on the principle of avoiding and eliminating redundancy is described. This algorithm has been implemented for objects bounded by planar and natural quadric surfaces; it handles coincidence and incidence cases between surfaces and curves robustly

Trim Loop Closure for Enhanced CAD Interoperability

The transfer of design data among different CAD systems or subsequent downstream analysis applications is critically important to the acceleration of the product development cycle. Since each vendor has its own proprietary native file format, this transfer of data among differing systems is difficult at best. International standards such as IGES and STEP have evolved to address this challenge, but they are generally not sufficiently explicit. Each vendor writes its own “flavor” of the standard that other applications may not understand. This paper bridges a gap between disparate systems by developing a strategy to assess the completeness and robustness of models represented in IGES or STEP format, and a technique to either repair the representation or add missing information so that a downstream application can properly interpret it. The method ensures that the receiving system gets a full and accurate NURBS-based representation: the original surfaces, the corresponding full complement of model space trim curves, and the corresponding full complement of parameter space trim curves. With all the information present, the downstream system is more likely to receive the information it requires to interpret the model

ESOLID—a system for exact boundary evaluation

We present a system, ESOLID, that performs exact boundary evaluation of low-degree curved solids in reasonable amounts of time. ESOLID performs accurate Boolean operations using exact representations and exact computations throughout. The demands of exact computation require a different set of algorithms and efficiency improvements than those found in a traditional inexact floating point based modeler. We describe the system architecture, representations, and issues in implementing the algorithms. We also describe a number of techniques that increase the efficiency of the system based on lazy evaluation, use of floating point filters, arbitrary floating point arithmetic with error bounds, and lower dimensional formulation of subproblems. ESOLID has been used for boundary evaluation of many complex solids. These include both synthetic datasets and parts of a Bradley Fighting Vehicle designed using the BRL-CAD solid modeling system. It is shown that ESOLID can correctly evaluate the boundary of solids that are very hard to compute using a fixed-precision floating point modeler. In terms of performance, it is about an order of magnitude slower as compared to a floating point boundary evaluation system on most cases

Robustness in geometric modeling - an intuitionistic and tolerance-based approach

Journal ArticleAn intuitionistic geometry approach is taken to develop two tolerance-based methods for robust geometric computation. The so called analytic model method and the approximated model method are developed independently of a specific application or a geometric algorithm. Geometric robustness is formally defined. Geometric relations are computed based on tolerances defined for geometric objects. Dynamic tolerance updating rules are given to preserve properties of the geometric relations. The two methods differ in the definition of robustness and they use different tolerance updating rules, and hence, they preseve different properties and are suitable for different kinds of applications. To handle the possibly occuring ambiguities dynamic ambiguity handling methods are described as well

Détection, visualisation et communication de défauts dans les modèles géométriques et les maillages

Résumé Ce mémoire traite de problèmes rencontrés dans le cadre des premières étapes de la conception de pièces en lien avec la mécanique des fluides. En particulier, on s'attardera sur la méthodologie utilisée afin de détecter et communiquer des erreurs que peuvent rencontrer les concepteurs de pièces mécaniques, et en particulier de composantes de turbines hydroélectriques, lors du design préliminaire et des premières simulations numériques. En effet, lors des premières phases de design, il est souvent nécessaire d'obtenir un modèle mathématique complet de la pièce conçue afin de pouvoir évaluer son comportement final sans avoir à en réaliser un prototype. Ces modèles sont le plus souvent réalisés selon les normes de la représentation frontière (Boundary REPresentation, BREP) où les volumes ne sont définis que par les surfaces qui les délimitent. Cette méthode de modélisation, associée aux courbes paramétriques (en général de type Non Uniform Rational B-Spline (NURBS) ), permet de modéliser des géométries extrêmement complexes tout en utilisant des entités mathématiques (courbes, surfaces) assez simples. Cela permettra, par la suite, de réduire les temps de calcul nécessaires pour les simulations ou les rendus graphiques. Cette simplification des entités utilisées entraîne par contre des approximations, notamment au niveau des jonctions entre entités de même dimension (par exemple, deux surfaces jointives peuvent ne pas se suivre exactement le long de l'arête commune). Afin d'assurer l'étanchéité des volumes, différentes solutions sont utilisées. Celle qui a été choisie au sein de la série de logiciels basés sur la librairie Pirate est l'utilisation d'une topologie afin de spécifier quelles sont les entités coïncidentes. Mais ces solutions peuvent présenter des erreurs, par exemple si deux entités déclarées correspondantes sont en réalité géométriquement éloignées. Ces erreurs, si non corrigées, se retrouvent généralement dans les maillages générés à partir de ces modèles BREP, et donc ont une influence sur la qualité des simulations qui peuvent être effectuées ensuite. Le premier aspect de ce mémoire traite des moyens qui ont été mis en place au sein du logiciel TopoVisu afin de détecter et de visualiser les erreurs présentes au sein des modèles BREP et des maillages utilisés lors de l'étape de conception. Le second aspect de ce mémoire traite d'une des origines principales des erreurs citées précédemment : la conservation et le transfert des données. C'est à ce niveau que de nombreuses erreurs apparaissent. En effet, le passage d'un format de fichiers à un autre peut s'avérer extrêmement néfaste pour un modèle, et cela peut poser problème si on change d'application, mais aussi si on passe à une autre version d'une même application. La solution proposée ici est l'exportation native vers un format de données ayant un bon niveau de maintenance et d'utilisation qui permettra de favoriser sa pérennité. Le format qui a été choisi pour cette fonction est le Portable Document Format, avec inclusion de modèles en trois dimensions (PDF 3D). Les éléments 3D sont inclus dans le format Product Representation Compact (PRC), car ce format est compatible avec la norme ISO 10303 (Standard for the Exchange of Product model data, STEP) qui est au cœur de beaucoup de modélisations BREP, dont celle de la librairie Pirate.----------Abstract This master thesis addresses some of the problems encountered during the first design stages of engineered object related to fluid mechanics. More precisely, we will focus on the problems that can be encountered in the early modeling and simulations of hydroelectric turbines. During the first steps of design, a mathematical model of the engineered item is realized in order to evaluate its properties in simulations, and without building a prototype. The methodology used to build those models is generally based on the boundary representation (BREP) rules : Volumes are defined through the faces that delimit them; faces are defined through a geometric support (a surface) and through the edges that delimit them and so on. BREP models generally use parametric curves and surfaces (and Non Uniform Rational B-Spline (NURBS) in most cases). This type of models allows a great complexity in geometries while keeping reasonably simple mathematical entities, and thus reasonably low computing time in simulations or graphic rendering. But the simplification of models implied by BREP results in approximations, which lead to small gaps or overlaps near the border of the entities (e.g. between two faces of a shell). In order to solve those small errors, the Pirate library and its software suite use topology to identify which entities are connected. But this isn't sufficient, if two surfaces are declared connected, but are separated by a non negligible gap, errors can appear later in the design process, often with bad quality meshes and simulation results. The beginning of this master thesis will treat the methods used to find and highlight the errors in BREP models and meshes, and particularly how they have been implemented in TopoVisu. The second main aspect of this work is to treat the errors at their source. Most of the errors in BREP models and meshes are generated when data is transferred, either to another CAD application, or to a more recent version of the same software. The solution proposed in TopoVisu is to natively export data to a highly maintained, widespread file format, which has a good chance to stay viable in the future. The format we chose is the Portable Document Format (PDF) with 3D models included in Product Representation Compact (PRC) format. This choice is based upon the ISO-10303 standard (Standard for the Exchange of Product model data, STEP) compatibility of the PDF 3D format, this standard being at the heart of most CAD engines, including the Pirate library