Solid Primitives Research Articles

Numerical Simulation of Welding Distortion in Laser Metal Deposition Additive Manufacturing Process

The article presents the simulation of part distortion during laser metal deposition and a comparison of its results with the deposition performed in experiment. A numerical methodological approach to simulation is viewed which involves dividing the deposited material into primitive solids and further heating and cooling of each primitive solid along the deposition trajectory instead of simulating a moving heat source.

Основы твердотельного проектирования в САПР в обучении

The paper considers the problem of teaching 3D solid modeling in the parametric computer-aided design systems when training students and specialists who need proper occupational study. The author describes the importance of this design method for the production tasks and the problems related to the lack of algorithmization tools of such training. The author proposes using two interrelated techniques: solid geometry modeling and teaching this kind of design. To solve the development task of the first technique, the author proposes to supplement the solid modeling terminology in Russian and formalize the features of solid geometry decomposition. The paper introduces three ways of solid decomposition based on the criteria of the sketch form and specification tree. The author proposes a design technique algorithm consisting of two stages. Each stage is divided into four steps, and the features of some steps are described. Further, the author presents the technique of teaching solid modeling. This technique is based on the frequency of using solid primitives and the necessity to develop tasks for students depending on this frequency. The author identifies the main skill to be mastered by the students. The technique introduces the ways of solving problems faced by students and engineers during solid modeling. The author proposes the distribution of hours for training basic concepts of solid modeling. The paper presents the teaching technique implementation in the existing higher school educational programs and proposes its deployment to the related areas of design.

Topologically robust CAD model generation for structural optimisation

Computer-aided design (CAD) models play a crucial role in the design, manufacturing and maintenance of products. Therefore, the mesh-based finite element descriptions common in structural optimisation must be first translated into CAD models. Currently, this can at best be performed semi-manually. We propose a fully automated and topologically accurate approach to synthesise a structurally-sound parametric CAD model from topology optimised finite element models. Our solution is to first convert the topology optimised structure into a spatial frame structure and then to regenerate it in a CAD system using standard constructive solid geometry (CSG) operations. The obtained parametric CAD models are compact, that is, have as few as possible geometric parameters, which makes them ideal for editing and further processing within a CAD system. The critical task of converting the topology optimised structure into an optimal spatial frame structure is accomplished in several steps. We first generate from the topology optimised voxel model a one-voxel-wide voxel chain model using a topology-preserving skeletonisation algorithm from digital topology. The weighted undirected graph defined by the voxel chain model yields a spatial frame structure after processing it with standard graph algorithms. Subsequently, we optimise the cross-sections and layout of the frame members to recover its optimality, which may have been compromised during the conversion process. At last, we generate the obtained frame structure in a CAD system by repeatedly combining primitive solids, like cylinders and spheres, using boolean operations. The resulting solid model is a boundary representation (B-Rep) consisting of trimmed non-uniform rational B-spline (NURBS) curves and surfaces.

Accelerated robust Boolean operations based on hybrid representations

Constructive Solid Geometry (CSG) is one of the popular techniques that is widely applied in 3D modeling. It combines primitive solids using Boolean operations. However, the trade-off between efficiency and robustness of Boolean evaluation is difficult to balance. Previous methods sacrifice either efficiency or robustness to achieve advantages in one perspective. Recent works attempt to achieve excellent performance in both aspects through replacing the conventional vertex-based representations (V-reps) with plane-based representations (P-reps) of polyhedrons. Different from V-reps, the P-reps use plane coefficients as meta-data and can lead to benign robustness. However, methods using P-reps have disadvantages in efficiency compared to methods using V-reps. In this paper, we proposed a Boolean evaluation approach that absorbs both the efficiency of V-reps based methods and robustness of P-reps based methods. We design a Boolean evaluation method combining P-reps with V-reps. The P-reps information is utilized for exact predicate computation while information in V-reps is collected for fast topology query and coarse tests. Our proposed approach is variadic: it evaluates a Boolean expression regarding multi-input meshes as a whole rather than a tree of decomposed binary operations. We conduct massive experiments and compare our results with those generated by the state-of-the-art methods. Experimental results show that our approach is robust for solid inputs and has advantages in performance compared to some previous non-robust methods.

Impact-induced compaction of primitive solar system solids: The need for mesoscale modelling and experiments

Primitive solar system solids were accreted as highly porous bimodal mixtures of mm-sized chondrules and sub-μm matrix grains. To understand the compaction and lithification of these materials by shock, it is necessary to investigate the process at the mesoscale; i.e., the scale of individual chondrules. Here we document simulations of hypervelocity compaction of primitive materials using the iSALE shock physics model. We compare the numerical methods employed here with shock compaction experiments involving bimodal mixtures of glass beads and silica powder and find good agreement in bulk material response between the experiments and models. The heterogeneous response to shock of bimodal porous mixtures with a composition more appropriate for primitive solids was subsequently investigated: strong temperature dichotomies between the chondrules and matrix were observed (non-porous chondrules remained largely cold, while the porous matrix saw temperature increases of 100’s K). Matrix compaction was heterogeneous, and post-shock porosity was found to be lower on the lee-side of chondrules. The strain in the matrix was shown to be higher near the chondrule rims, in agreement with observations from meteorites. Chondrule flattening in the direction of the shock increases with increasing impact velocity, with flattened chondrules oriented with their semi-minor axis parallel to the shock direction.

An unstructured immersed finite element method for nonlinear solid mechanics.

We present an immersed finite element technique for boundary-value and interface problems from nonlinear solid mechanics. Its key features are the implicit representation of domain boundaries and interfaces, the use of Nitsche’s method for the incorporation of boundary conditions, accurate numerical integration based on marching tetrahedrons and cut-element stabilisation by means of extrapolation. For discretisation structured and unstructured background meshes with Lagrange basis functions are considered. We show numerically and analytically that the introduced cut-element stabilisation technique provides an effective bound on the size of the Nitsche parameters and, in turn, leads to well-conditioned system matrices. In addition, we introduce a novel approach for representing and analysing geometries with sharp features (edges and corners) using an implicit geometry representation. This allows the computation of typical engineering parts composed of solid primitives without the need of boundary-fitted meshes.

CAD-based Monte Carlo automatic modeling method based on primitive solid

Monte Carlo method has been widely used in nuclear design and analysis, where geometries are described with primitive solids. However, it is time consuming and error prone to describe a primitive solid geometry, especially for a complicated model. To reuse the abundant existed CAD models and conveniently model with CAD modeling tools, an automatic modeling method for accurate prompt modeling between CAD model and primitive solid is needed. An automatic modeling method for Monte Carlo geometry described by primitive solid was developed which could bi-convert between CAD model and Monte Carlo geometry represented by primitive solids. While converting from CAD model to primitive solid model, the CAD model was decomposed into several convex solid sets, and then corresponding primitive solids were generated and exported. While converting from primitive solid model to the CAD model, the basic primitive solids were created and related operation was done. This method was integrated in the SuperMC and was benchmarked with ITER benchmark model. The correctness and efficiency of this method were demonstrated.

Isogeometric analysis for CSG models

The IGA (Isogeometric Analysis) was developed as a bridge between CAD and CAE with its highly precise geometry representation. However, IGA can only do little with the models that CAD systems generated in CSG (Constructive Solid Geometry) manner, because the trimmed domain exists. This paper presents a method named Constructive Solid Isogeometric Analysis (CSIGA) to work for CSG models that are composed of primitive solids with union, subtraction and intersection operators. First, this work decomposes the CSG models into several primitive solids represented by NURBS separately, then cuts the primitives with their adjacent ones to produce a set of trimmed tri-variable NURBS primitives, and finally uses Boolean operators to compose them. As to the single trimmed solid, an integration scheme is presented. Meanwhile, a combination scheme has been developed to deal with the union of multiple trimmed solids by using a mortar method. The formulation is verified by applying the isogeometric analysis on several solids which have theoretical solutions such as elliptic cylinder and combined brick, and some tests on multiple trimmed solids are done, too. It is shown that the CSIGA method can deal with CSG models efficiently.

Supernova Grains Identified in the Lab

Geochemistry![Figure][1] CREDIT: NASA/JPL-CALTECH/O. KRAUSE/STEWARD OBSERVATORY Primitive meteorites contain grains of materials that predate the formation of the solar system. These materials—which include, among others, diamond, graphite, and various oxides and silicates—were present in the molecular cloud from which the Sun and the solar system formed and were later incorporated into primitive solar system solids. Presolar grains are identified by their unusual isotopic compositions, which can only be explained if they formed outside the solar system, in the outflows or explosions of other stars. Using nano secondary ion mass spectrometry (NanoSIMS) and Auger electron spectroscopy, Haenecour et al. report the identification of two silica (SiO2) grains in the primitive meteorites LaPaz 031117 and Grove Mountains 021710. The oxygen isotopic composition of these two grains is different from those of previously identified presolar SiO2 grains, and it indicates that the two grains originated from core collapse supernovae: the thermonuclear explosions that end the lives of stars heavier than eight times the mass of the Sun. The presence of SiO2 dust in matter ejected by such explosions was predicted by theoretical models; recent observations by NASA's Spitzer Space telescope have also suggested their presence in supernova remnants. Astrophys. J. 768 , L17 (2013). [1]: pending:yes

Morphing Using Polyharmonic Function

In this paper, we discuss morphing using a polyharmonic function. A method for creating implicit surfaces is described using a polyharmonic function (radial basis function) to form complex solid models from scattered surface points. The conventional method of constructing CSG model use simple solid primitives. In the presented method, many quite complex solid primitives can be used, because only surface points are used for boundary representation. The presented methods contain the conventional Boolean operations on solids and new Boolean operations for points. This method uses Poisson's equations and a polyharmonic function, which is a type of thin plate function. Thin-plate solution has several problems. The first problem is that O (n2) computations are required to solve the system of equations. The second problem is that a small change in even one constraint affects the entire resulting interpolated surface, because every known point affects the result. However, thin-plate interpolation is often used in computer vision, because surface patch is not necessary. In order to investigate the efficiency of this method, several examples are given.

オブジェクトデザインシステム開発のための三次元形状モデルの感性評価機構の解析

In order to develop a 3D object-design-system, we intend to construct a Java-based application to serve as Kansei information processing. Designers can customize the system to design the solid primitives, such as ball, cone, cylinder, cube and taper elements, etc., by using their Kansei and then combine the reconfigured solids as an object to reflect the users' desires. In order to mine the Kansei information and construct a Kansei database in the application, Kansei evaluation for ten models of a primitive element cone was measured by the semantic differential method. Fuzzy set theory was applied to investigate the measurement results. The primitive model could be classified among four pairs of adjectives. The amount of the features of classified primitive models was defined as the Kansei evaluation variable. The machine-learning algorithm of an individual adaptation object-design-system was proposed using the Kansei evaluation variable.

Solid reconstruction from orthographic opaque views using incremental extrusion

The reconstruction of 3-D solids from 2-D projections is an important research topic in reverse engineering. The reconstruction can be grouped into two categories: single-view approach and multiple-view approach. Each approach can be classified as wireframe, BRep or CSG. However, not many CSG approaches have been reported in the literature. The methods are also restricted to uniform-thickness objects or require user interaction. The method proposed in this paper employs the CSG approach. A 3-D solid computer model is reconstructed from 2-D line drawings of six orthographic opaque views, viz. top, front, left, right, bottom and rear views. Firstly, the six views are grouped into three pairs. For each pair of views, segmented areas from one of the two views (called g-view) is incrementally extruded according to the information in the neighbouring view (called d-view). Extrusion primitive solids are generated during the incremental extrusion. All primitive solids are then unioned into an extrusion solid. Finally, all extrusion solids are intersected to give a unique 3-D solution object.

Reconstructing a 3-D structure with multiple deformable solid primitives

This paper develops a sophisticated approach to a method for fitting of complex 3-D shapes to unsegmented sets of data. The approach features dynamic models consisting of parametrically defined solid primitives (such as superquadrics), global geometric transformations, global deformations and local finite element deformations. Our technique deals with a deformable model consisting of multiple primitives (parts) that can be used to represent even more complex shapes than are common in the natural world. The deformable model is extended to the case of unsegmented data, incorporating an extended version of a fuzzy clustering technique. The image or range data are transformed into forces acting on the model that deform and conform to the given data set while continually synthesizing nonrigid motion. An adaptive procedure updates a damping factor in accordance with the largest possible step in an implemented iteration process. We demonstrate the fitting process in experiments involving the extraction of the shape of the mouse embryo's organs from microscopic sections.

A New Algorithm for The Rendering of CSG Scenes

The generation of 3-D solid objects, and more generally solid geometric modelling, is very important in Computer Aided Design (CAD). An important role is played by the Constructive Solid Geometry (CSG) representation scheme. In CSG, objects are described by trees of Boolean operations on half-spaces or boundaries of primitive solids. The study of techniques to speed up the rendering of scenes modelled with the CSG scheme is an attractive field of research; in this paper we propose a new algorithm which reduces the computational complexity for ray casting approaches. Our strategy identifies a set of areas on the plane of view where the rays starting from the observer have to be traced; for each zone, only a portion of the entire CSG tree has to be considered for intersection tests, instead of the whole database of the primitive objects. A comparison of our algorithm with a ray caster that adopts bounding volume hierarchies and with a freeware ray tracer called POV-Ray shows that, for the examples considered, we may reduce the intersection tests to one third of those performed when standard optimizations are adopted.

Similarity measure for superquadrics

Superquadrics with parametric deformations are suitable models for use as solid primitives for describing a complicated 3-D object. Some different methods for the recovery of superquadric primitives from range data have been proposed, but there is still no effective similarity measure for the matching task between two superquadrics in a 3-D object recognition system. The authors propose a similarity measure to evaluate the degree of shape similarity between two superquadric-based objects. This similarity measure is defined as the volume of regions bounded by the surfaces of two 3-D objects. The proposed measure has been proved to be a metric. The metric value is computed by the Monte Carlo integration method. The experimental results illustrate that the proposed similarity measure is effective in matching a recovered superquadric with a set of superquadrics in the model database.

A prototype solid-modeling-based automated process planning system

This paper presents a prototype solid modeling-based automated process planning system. In this system a three dimensional (3D) finished part is built by using a solid modeling package. The solid primitives (cylinder, cone, block, wedge, sphere, and torus) are used to define the removal volume. The process plan is then generated based on the recognized solid primitives and production rules. This research was implemented on a PC platform. The CAD interfaces for this system were developed by using the AutoCAD Advanced Modeling Extension (AME) software. The solid primitives recognition program was written in the C language and embedded in an expert system program developed by using the CLIPS software.

Volume-preserving free-form solids

Some important trends in geometric modeling are the reliance on solid models rather than surface-based models and the enhancement of the expressive power of models, by using free-form objects in addition to the usual geometric primitives and by incorporating physical principles. An additional trend is the emphasis on interactive performance. In this paper, we integrate all of these requirements into a single geometric primitive by endowing the tri-variate tensor-product free-form solid with several important physical properties, including volume and internal deformation energy. Volume preservation is of benefit in several application areas of geometric modeling, including computer animation, industrial design and mechanical engineering. However, previous physics-based methods, which have usually used some form of "energy", have neglected the issue of volume (or area) preservation. We present a novel method for modeling an object composed of several tensor-product solids while preserving the desired volume of each primitive and ensuring high-order continuity constraints between the primitives. The method utilizes the Uzawa algorithm for non-linear optimization, with objective functions based on deformation energy or least squares. We show how the algorithm can be used in an interactive environment by relaxing exactness requirements while the user interactively manipulates free-form solid primitives. On current workstations, the algorithm runs in real-time for tri-quadratic volumes and close to real-time for tri-cubic volumes.

Rational tensor product Bézier volumes

Free form volumes in rational Bézier representation are derived via homogeneous coordinates. Some properties and constructions are presented and two applications of free form volumes are discussed: definition of solid primitives and curve and surface modelling by the way of volume deformation.

NURBS-based free-form deformations

Since the advent of computer-based geometric modeling, designers have tried to develop modeling and deformation tools that allow users to emulate the ease with which sculptors work with clay. T.W. Sederberg and S.R. Parry (1986) demonstrated the application of free-form deformations. FFDs let the user conceptually embed an object in a clear pliable solid and apply deformations to the solid, which then carry through to the encased object. We describe a technique that logically extends current FFDs by basing them on nonuniform rational B-splines. The resulting NURBS-based FFDs (NFFDs) offer flexibility and control not achieved in prior implementations. We conclude by describing a straightforward combination of this technique with global and local deformations of solid primitives used to animate a lifelike surface model of the human leg.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Rational tensor product Bézier volumes

Free form volumes in rational Bézier representation are derived via homogeneous coordinates. Some properties and constructions are presented and two applications of free form volumes are discussed: definition of solid primitives and curve and surface modelling by the way of volume deformation.