Algebraic level sets for CAD/CAE integration and moving boundary problems

Boundary representation (B-rep) of CAD models obtained from solid modeling kernels are commonly used in design, and analysis applications outside the CAD systems. Boolean operations between interacting B-rep CAD models as well as analysis of such multi-body systems are fundamental operations on B-rep geometries in CAD/CAE applications. However, the boundary representation of B-rep solids is, in general, not a suitable representation for analysis operations which lead to CAD/CAE integration challenges due to the need for conversion from B-rep to volumetric approximations. The major challenges include intermediate mesh generation step, capturing CAD features and associated behavior exactly and recurring point containment queries for point classification as inside/outside the solid. Thus, an ideal analysis technique for CAD/CAE integration that can enable direct analysis operations on B-rep CAD models while overcoming the associated challenges is desirable. ^ Further, numerical surface intersection operations are typically necessary for boolean operations on B-rep geometries during the CAD and CAE phases. However, for non-linear geometries, surface intersection operations are non-trivial and face the challenge of simultaneously satisfying the three goals of accuracy, efficiency and robustness. In the class of problems involving multi-body interactions, often an implicit knowledge of the boolean operation is sufficient and explicit intersection computation may not be needed. Such implicit boolean operations can be performed by point containment queries on B-rep CAD models. However, for complex non-linear B-rep geometries, the point containment queries may involve numerical iterative point projection operations which are expensive. Thus, there is a need for inexpensive, non-iterative techniques to enable such implicit boolean operations on B-rep geometries. ^ Moreover, in analysis problems with evolving boundaries (ormoving boundary problems), interfaces or cracks, blending functions are used to enrich the underlying domain with the known behavior on the enriching entity. The blending functions are typically dependent on the distance from the evolving boundaries. For boundaries defined by free form curves or surfaces, the distance fields have to be constructed numerically. This may require either a polytope approximation to the boundary and/or an iterative solution to determine the exact distance to the boundary. ^ In this work a purely algebraic, and computationally efficient technique is described for constructing signed distance measures from Non-Uniform Rational B-Splines (NURBS) boundaries that retain the geometric exactness of the boundaries while eliminating the need for iterative and non-robust distance calculation. The proposed technique exploits the NURBS geometry and algebraic tools of implicitization. Such a signed distance measure, also referred to as the Algebraic Level Sets, gives a volumetric representation of the B-rep geometry constructed by purely non-iterative algebraic operations on the geometry. This in turn enables both the implicit boolean operations and analysis operations on B-rep geometries in CAD/CAE applications. Algebraic level sets ensure exactness of geometry while eliminating iterative numerical computations. Further, a geometry-based analysis technique that relies on hierarchical partition of unity field compositions (HPFC) theory and its extension to enriched field modeling is presented. The proposed technique enables direct analysis of complex physical problems without meshing, thus, integrating CAD and CAE. The developed techniques are demonstrated by constructing algebraic level sets for complex geometries, geometry-based analysis of B-rep CAD models and a variety of fracture examples culminating in the analysis of steady state heat conduction in a solid with arbitrary shaped three-dimensional cracks. ^ The proposed techniques are lastly applied to investigate the risk of fracture in the ultra low-k (ULK) dies due to copper (Cu) wirebonding process. Maximum damage induced in the interlayer dielectric (ILD) stack during the process steps is proposed as an indicator of the reliability risk. Numerical techniques based on enriched isogeometric approximations are adopted to model damage in the ULK stacks using a cohesive damage description. A damage analysis procedure is proposed to conduct damage accumulation studies during Cu wirebonding process. Analysis is carried out to identify weak interfaces and potential sites for crack nucleation as well as damage nucleation patterns. Further, the critical process condition is identified by analyzing the damage induced during the impact and ultrasonic excitation stages. Also, representative ILD stack designs with varying Cu percentage are compared for risk of fracture

A Survey of Methods for Converting Unstructured Data to CSG Models

The goal of this document is to survey existing methods for recovering CSG representations from unstructured data such as 3D point-clouds or polygon meshes. We review and discuss related topics such as the segmentation and fitting of the input data. We cover techniques from solid modeling and CAD for polyhedron to CSG and B-rep to CSG conversion. We look at approaches coming from program synthesis, evolutionary techniques (such as genetic programming or genetic algorithm), and deep learning methods. Finally, we conclude with a discussion of techniques for the generation of computer programs representing solids (not just CSG models) and higher-level representations (such as, for example, the ones based on sketch and extrusion or feature based operations).Comment: 29 page

Quantifying Geometric Changes in BIM-GIS Conversion

Abstract. A conversion process is often carried out to migrate data during BIM and GIS integration, often from the highly detailed BIM to the less detailed GIS environment. Due to the differences between the two systems, information loss occurs during conversion. While research has been focusing on addressing information loss on the semantics, it is also necessary to quantify geometric changes resulted from converting geometry representations used in the two systems. This paper describes a preliminary study which evaluates the geometric changes during conversion for a list of primitives. The outcome shows that the metrics are useful both to those carrying out the conversion to balance between potential information loss and resulting data complexity, and to end users of the converted information to assess the fitness for purpose and impact of the conversion results

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

D2^2CSG: Unsupervised Learning of Compact CSG Trees with Dual Complements and Dropouts

We present D$^2$CSG, a neural model composed of two dual and complementary network branches, with dropouts, for unsupervised learning of compact constructive solid geometry (CSG) representations of 3D CAD shapes. Our network is trained to reconstruct a 3D shape by a fixed-order assembly of quadric primitives, with both branches producing a union of primitive intersections or inverses. A key difference between D$^2$CSG and all prior neural CSG models is its dedicated residual branch to assemble the potentially complex shape complement, which is subtracted from an overall shape modeled by the cover branch. With the shape complements, our network is provably general, while the weight dropout further improves compactness of the CSG tree by removing redundant primitives. We demonstrate both quantitatively and qualitatively that D$^2$CSG produces compact CSG reconstructions with superior quality and more natural primitives than all existing alternatives, especially over complex and high-genus CAD shapes.Comment: 9 page

Procedural function-based modelling of volumetric microstructures

We propose a new approach to modelling heterogeneous objects containing internal volumetric structures with size of details orders of magnitude smaller than the overall size of the object. The proposed function-based procedural representation provides compact, precise, and arbitrarily parameterised models of coherent microstructures, which can undergo blending, deformations, and other geometric operations, and can be directly rendered and fabricated without generating any auxiliary representations (such as polygonal meshes and voxel arrays). In particular, modelling of regular lattices and cellular microstructures as well as irregular porous media is discussed and illustrated. We also present a method to estimate parameters of the given model by fitting it to microstructure data obtained with magnetic resonance imaging and other measurements of natural and artificial objects. Examples of rendering and digital fabrication of microstructure models are presented

ExtrudeNet: Unsupervised Inverse Sketch-and-Extrude for Shape Parsing

Sketch-and-extrude is a common and intuitive modeling process in computer aided design. This paper studies the problem of learning the shape given in the form of point clouds by inverse sketch-and-extrude. We present ExtrudeNet, an unsupervised end-to-end network for discovering sketch and extrude from point clouds. Behind ExtrudeNet are two new technical components: 1) an effective representation for sketch and extrude, which can model extrusion with freeform sketches and conventional cylinder and box primitives as well; and 2) a numerical method for computing the signed distance field which is used in the network learning. This is the first attempt that uses machine learning to reverse engineer the sketch-and-extrude modeling process of a shape in an unsupervised fashion. ExtrudeNet not only outputs a compact, editable and interpretable representation of the shape that can be seamlessly integrated into modern CAD software, but also aligns with the standard CAD modeling process facilitating various editing applications, which distinguishes our work from existing shape parsing research. Code is released at https://github.com/kimren227/ExtrudeNet.Comment: Accepted to ECCV 202