In spite of the widespread use of CAD systems for design and CAE systems for analysis, the two processes are not well integrated because CAD and CAE models inherently use different types of geometric models and there currently exists no generic, unified model that allows both design and analysis information to be specified and shared. In this paper, a new approach called the CAD/CAE-integrated approach is proposed and implemented by a feature-based non-manifold modelling system. The system creates and manipulates a single master model containing different types of all of the geometric models required for CAD and CAE. Both a solid model (for CAD) and a non-manifold model (for CAE) are immediately extracted from the master model through a selection process. If a design change is required, the master model is modified by the feature modelling capabilities of the system. As a result, the design and analysis models are modified simultaneously and maintained consistently. This system also supports feature-based multi-resolution and multi-abstraction modelling capabilities providing the CAD model at different levels of detail and the CAE model at various levels of abstraction.

A CAD-CAE integration approach using feature-based multi-resolution and multi-abstraction modelling techniques

Interestingly, constraint programming languages their specification and generation that you really wait for now is coming. It's significant to wait for the representative and beneficial books to read. Every book that is provided in better way and utterance will be expected by many peoples. Even you are a good reader or not, feeling to read this book will always appear when you find it. But, when you feel hard to find it as yours, what to do? Borrow to your friends and don't know when to give back it to her or him.

Constraint programming languages: their specification and generation

https://www.cs.purdue.edu/homes/cmh/distribution/PapersChron/decompJSC01a.pdf

Decomposition Plans for Geometric Constraint Systems, Part I: Performance Measures for CAD

Analysis plays a significant role during product design. Thanks to computational tools; it contributes highly in product optimisation while decreasing design cost and time. For analysis applications, the adaptation of the product geometry is required and consists of producing an idealised model out of a product solid one. This paper presents a form of features based tool to aid the integration of analysis during the design process. It allows producing an analysis model out of a part solid model. This tool is based on a morphological analysis of the solid model followed by a two-phase process: simplification and idealisation. The tool provides an easy way to make computer-aided design model modifications implied by the analysis results; thanks to features parameterisation and a reconstruction process. Both allow us to create a solid model on the basis of the idealised one, by using parameterised reconstruction operators.

Morphological analysis for product design

https://www.cs.purdue.edu/homes/cmh/distribution/papers/Constraints/JSC01b.pdf

Decomposition Plans for Geometric Constraint Problems, Part II

This paper provides a rationale for its abstract data definitions of geometric features. These definitions are used as the basis of a suite of functions to support feature modelling. It assumes that implementations of the proposed functions will make use of a solid modelling kernel that supports objects with a disjoint cellular structure and persistent cell identifiers. It is intended that most of the functions required for the manipulation of features can be provided by overloaded kernel functions; new functions are necessary only to provide feature specific operations. Unlike most features in the literature, the features of this paper are not design features, manufacturing features or features for any other specific application. They are geometric structures that support such applications. Thus, the disjoint cellular structure of a modern solid modelling kernel is enhanced to include a hierarchy of geometrically overlapping features. A feature at any node in the hierarchy is defined in terms of instances of multiple sub-features combined using any object construction function of the kernel. Such instancing allows multiple versions of any feature to be modified simultaneously via the master.

A kernel for geometric features

The major purpose of this paper is to introduce a general theory within which previous boundary representations (Breps) are a special case. Basically, this theory combines sub-analyt,ic geometry and theory of stratifications. The sub-analyt,ic geometry covers almost, all geometric engineering artefacts, and it is a generalisation of the semi-analytic geometry, which in turn is a generalisation of the semialgebraic geometry used by most geometric kernels. On the other hand, the theory of stratifications provides the most general manifold structures for geometric objects that it is possible to consider in geometric modelling. Whitney stratifications are particularly useful in geometric modelling because they provide a general abstraction for the #structure of boundary representations of objects in IV’. Remarkably, it is well-known in mathematics that sub-analytic objects are Whitney stratifiable, and this mathematically matches and validates the usual geometry-structure design of boundary representation data structures. Thus, the general B-rep introduced here represents Whitney-stratified sub-analytic objects, though the global design of the data structure is classical: the geometry (sub-analytic geometry) separated from the structure (Whitney stratification). 1 Theoretical evolution of boundary repre-

A mathematical model for boundary representations of n-dimensional geometric objects

This paper is concerned with the mathematics and formal specification of “set-like” operations for the mixed dimension cellular geometric objects of the Djinn Application Programming Interface. The relationships between these operations and stratifications of dimensionally heterogeneous semianalytic point-sets are uncovered and formalised. Semianalytic geometry is central to the algebraic model discussed in this paper, but multi-disciplinary concepts from topology, differential geometry and computer-aided geometric design have been used also. In particular, the use of strong relative topological stratifications enables Djinn to satisfy significant industrial requirements.

Set-combinations of the mixed-dimension cellular objects of the Djinn API

The medial axis transform of a 2D region was introduced by Blum in the 1960's as an aid to the description of biological shape. It is an alternative representation of a region which is often more amenable to analysis. This property has led to its use in diverse fields including pattern recognition and automatic finite element mesh generation. There are two widely agreed mathematical definitions for the medial axis transform which are closely related. It is shown that these definitions are not in general equivalent, despite being so far many types of region. In this paper, precise mathematical definitions of the medial axis transform and its key points (atoms) are given, and an O(n2) algorithm for its computation via those atoms presented. This algorithm is described in terms of simple polygons whose sole boundary consists of circular arcs and straight line segments, then extended to polygons with holes. It is shown how more complex edges could be accommodated. In comparison with existing algorithms it is simple to implement and stable in the presence of geometric degeneracy.

Stable Computation of the 2D Medial Axis Transform

Several fields of mathematics are relevant to computer aided design and other software systems involving solid object geometry, topology, differential and algebraic geometry being particularly important. This paper discusses some of this mathematics in order to provide a theoretical foundation for geometric modelling kernels that support non-manifold objects with an internal cellular structure and subsets of different dimensions. The paper shows relationships between relevant concepts from topology, differential geometry and computer aided geometric design that are not widely known in the CAD community. It also discusses semialgebraic, semianalytic and subanalytic sets as candidates for object representation. Stratifications of such sets are proposed for an object's cellular structure and new stratification concepts are introduced to support candidate applications.

Point-sets and cell structures relevant to computer aided design

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