We present octree-embedded BSPs, a volumetric mesh data structure suited for performing a sequence of Boolean operations (iterated CSG) efficiently. At its core, our data structure leverages a plane-based geometry representation and integer arithmetics to guarantee unconditionally robust operations. These typically present considerable performance challenges which we overcome by using custom-tailored

The published literature on topology optimization has exploded over the last two decades to include methods that use shape and topological derivatives or evolutionary algorithms formulated on various geometric representations and parametrizations. One of the key challenges of all these methods is the massive computational cost associated with 3D topology optimization problems. We introduce a transfer

Complex physical problems with emerging topologies such as phase nucleation and growth during solidification or electromigration, as well as design problems such as topology optimization are commonly modeled using phase field or level set methods. However, the implicit representations of the evolving interfaces in these methods implicitize geometrical parameters such as normals and curvatures that

Real-time CNC interpolators achieving a constant or variable feedrate V along a parametric curve r(ξ) are usually based on truncated Taylor series expansions defining the time-dependence of the curve parameter ξ. Since the feedrate should be specified as a function of a physically meaningful variable (such as time t, path arc length s, or curvature κ) rather than ξ, successive applications of the differentiation

Semantics-based approaches – founded on the idea of explicitly encoding meaning separately from the data or the application code – are being applied to manufacturing, for example, to enable early manufacturability feedback. These approaches rely on formal, i.e., computer-interpretable, knowledge and rules along with the context or semantics, which facilitates the reuse and sharing of the knowledge

Feature recognition is an important stage in digital manufacturing as it supports activities such as automated process planning and part re-design. This paper describes a two-stage algorithm for recognising features in sheet metal parts which are manufactured using progressive dies. Representation of the part in neutral format (STEP AP203) facilitates the first stage of this algorithm in which the

Beam-based Compliant Mechanisms (CMs) are increasingly studied and implemented in precision engineering. Straight beams with uniform cross section are the basic modules in several design concepts, which can be deemed as standard CMs. Their behavioral analysis can be addressed with a large variety of techniques, including the Euler–Bernoulli beam theory, the Pseudo-Rigid Body (PRB) method, the beam

In this paper, we introduce a structural form finding plugin called PolyFrame for the Rhinoceros software. This plugin is developed based on the methods of 3D Graphic Statics and Polyhedral Reciprocal Diagrams. The computational framework of this plugin uses new robust and efficient algorithms for the creation and modification of complex funicular, compression-only structural forms and is freely available

The assemblability, which is the feasibility and difficulty of assembly, will greatly affect the efficiency and quality of assembly process, so assemblability analysis plays an important role during the design stage of products. Cylindrical parts assembly is a common structure with wide applications, whose assemblability can be affected by surface deviations, especially in some precision assemblies

A method is presented for generating a discrete piecewise constant Gaussian curvature (CGC) surface. An energy functional is first formulated so that its stationary point is the linear Weingarten (LW) surface, which has a property such that the weighted sum of mean and Gaussian curvatures is constant. The CGC surface is obtained using the gradient derived from the first variation of a special type

Turbomachinery design is increasingly carried out by means of automated workflows based on high-fidelity physical models and optimization algorithms. The parametrization of the blade geometry is an essential aspect of such workflows because it defines the design space in which an optimal solution can be found. Currently, parametrization methods used for this purpose are often tailored to one particular

Mesh models have been widely employed in current CAD/CAM systems, where the workpiece is considered as made up of a number of features limited by natural boundaries. The natural boundaries among features are in most cases edges where an abrupt change of point differential geometry properties occurs. However, such features and underlying surface portions could also be connected smoothly without an abrupt

In additive manufacturing, infill structures are commonly used to reduce the weight and cost of a solid part. Currently, most infill structure generation methods are based on the conventional 2.5-axis printing configuration, which, although able to satisfy the self-supporting condition on the infills, suffer from the well-known stair-case effect on the finished surface and the need of extensive support

This paper presents a hardware-adaptive feature modeling framework to automatically generate and optimize deep neural networks to support real-time feature extraction and matching on a given hardware platform. This framework consists of a deep feature extraction and matching pipeline and a neural architecture search scheme, with which deep neural networks can be automatically generated and optimized

Automated fiber placement (AFP) is an advanced composite manufacturing technology which is widely used in the production of complex shaped aircraft components. However, on the surface with large curvature, the fiber compaction performance is poor, and the direction deviation and the geodesic curvature of the path increase sharply with the offset distance, resulting in various placement defects. To

In this paper, we describe a general class of C1 smooth rational splines that enables, in particular, exact descriptions of ellipses and ellipsoids — some of the most important primitives for CAD and CAE. The univariate rational splines are assembled by transforming multiple sets of NURBS basis functions via so-called design-through-analysis compatible extraction matrices; different sets of NURBS are

Truss lattices are common in a wide variety of engineering applications, due to their high ratio of strength versus relative density. They are used both as the interior support for other structures, and as structures on their own. Using 3D sphere packing, we propose a set of methods for generating truss lattices that fill the interior of B-rep models, polygonal or (trimmed) NURBS based, of arbitrary

Providing additional information for parts or items usually means to enclose it next to the object or affix it on the component when that is possible. However, another solution is available by gaining the benefits of an additive manufacturing technology, 3D printing. This technology makes it possible to embed the additional information onto the surface of the items, for example, in the forms of QR

Extending (Sati et al., 2016) to 3D, we propose definitions and closed-form expressions for what we call the Valley Average of Directions (VAD), T→, of a set {T→i} of directions (unit vectors) and for what we call the Valley Average of Lines (VAL), L, of a set {Li} of lines. L is independent of the input order. When the {Li} are parallel, L is parallel to them and passes through the centroid of their

Meaningful feature curves provide high-level shape representation of the geometrical shapes and are useful in various applications. In this paper, we propose an automatic method on the basis of the quadric surface fitting technique to extract complete feature curve networks (FCNs) from 3D surface meshes, as well as finding cycles and generating a high-quality segmentation. In the initial collection

Most mechatronic systems have becoming software-intensive. Even in their early design, the software and physical domains intersect with each other deeply. It is significant to capture and process the cross-domain influences automatically to avoid design defects in late stages. Semantic web technologies have been recognized as effective enabling technologies to support cross-domain knowledge representation

In this paper, we propose an improved singularity structure simplification method for hexahedral (hex) meshes using a weighted ranking approach. In previous work, the selection of to-be-collapsed base complex sheets/chords is only based on their thickness, which will introduce a few closed-loops and cause an early termination of simplification and a slow convergence rate. In this paper, a new weighted

We present a machine learning framework for predicting the optimized structural topology designs using multiresolution data. Our approach primarily uses optimized designs from inexpensive coarse mesh finite element simulations for model training and generates high resolution images associated with simulation parameters that are not previously used. Our cost-efficient approach enables the designers

Geometrically smooth spline surfaces, generalized to include n-sided facets or configurations of n≠4 quads, can exhibit a curious lack of additional degrees of freedom for modeling or engineering analysis when refined. This paper establishes a minimal polynomial degree for smooth constructions of multi-sided surfaces that guarantees more flexibility in all directions under refinement. Degree bi-4 is

Most previous methods of bas-relief generation run slow, or require tuning several important parameters. These issues seriously reduce the efficiency of bas-relief modeling. We introduce a fast generation method for high-quality bas-reliefs from 3D objects based on a deep learning technique. Unlike neural networks for image tasks, the proposed network for reliefs (ReliefNet) is elaborately designed

This paper introduces a flexible and easy to use method for designing complex composite heterogeneous materials. These materials feature two distinct phases called core and matrix that remain separate and distinct. Moreover, composite materials have an internal microarchitecture that have to be precisely modeled. All the microarchitecture examples that are shown in this paper have been modeled in the

Additive manufacturing processes enable the fabrication of the material with multiscale complexities. However, to efficiently model the material compositions and microstructures on multiple design scales is an issue for most existing heterogeneous object modeling methods. To solve this problem, a universal material template and its associated heterogeneous object model are developed in this paper.

The present research develops a direct multiscale topology optimization method for additive manufacturing (AM) of coated structures with nonperiodic infill by employing an adaptive mapping technique of adaptive geometric components (AGCs). The AGCs consist of a framework of macro-sandwich bars that represent the macrostructure with the solid coating and a network of micro-solid bars that represent

2.5D processes are ubiquitous in pocket machining of structural parts as well as layer based additive manufacturing. Modern manufacturing systems are mostly integrated with high-speed motion capacity, which conventionally generated tool path cannot fully exploit due to large path stepover variation and sharp turnings at degenerated corners. Advanced geometric approaches strived to increase the local

In this paper, we propose a normal estimation method for unstructured 3D point clouds. In this method, a feature constraint mechanism called Local Plane Features Constraint (LPFC) is used and then a multi-scale selection strategy is introduced. The LPFC can be used in a single-scale point network architecture for a more stable normal estimation of the unstructured 3D point clouds. In particular, it

A field (2-parameter family of similarities) S(x,y) is Tran-Similar (TS) if there exist similarities U and V such that S(x,y)=Ux⋅Vy and U⋅V=V⋅U. The recently proposed COTS map, M, is defined in terms of a planar TS field, S, as M(x,y)=S(x,y)⋅A and is Corner-Operated (CO), i.e., controlled by the images A, B, C, and D of the four corners of the unit-square in parameter space. The CO property enables

In pattern design of a 3D plush toy model, the key task is to draw seam lines on the 3D surface to divide it into surface patches to obtain 2D patterns. However, how to draw seam lines requires a lot of professional knowledge and skills of pattern design. In this paper, we present a new method that can guide and assist users to create 2D patterns of a 3D toy model efficiently. Based on a component-based

Describing data, obtained by various instruments, with an analytic function is one of the tasks that people often face in a wide variety of applications such as virtual reality, CAD design, reverse engineering, data visualization, medical imaging, and cultural relic restoration and so on. Moreover, non-uniform B-spline is an extensively-used tool for interpolation which is an effective means of describing

Functionally graded conformal lattice structures (FGCLSs) are a particular type of lattice structure in which lattice unit cells are populated following structural boundaries and the density of the lattice unit cells is optimally distributed. Additionally, additively manufactured parts are reported to have anisotropic mechanical properties that highly depend on the part build orientations. This is