Surfaces In Computer-aided Design Research Articles

Advancing Front Mesh Generation on Dirty Composite Surfaces

Computer-aided design (CAD) models usually contain many errors between neighboring surfaces, such as slivers, gaps, and overlaps. To clean up such models, virtual operations have been suggested to merge multiple neighboring CAD surfaces into a single composite surface. However, it remains a challenge to generate a quality mesh on thereby formed dirty composite surfaces. In this paper, we propose a novel advancing front technique (AFT) that can treat such composite surfaces by developing two new schemes to enhance the traditional AFT. Firstly, for each composite surface, we define a parametric plane by using a combined set of the tessellation on this composite surface. Simplicial complex augmentation framework reparameterization approach is suggested since it can treat tessellations containing gap and overlap after introducing a pre-processing step. Meanwhile, this approach can ensure a bijective mapping between the parametric and physical space. The front intersection check can thus be performed on the parametric plane robustly. Secondly, the indirect and direct approaches are alternatively employed to calculate ideal points in different circumstances. In the circumstance that the possible new element is completely contained in one single CAD surface, the ideal point is calculated on the intrinsic parametric plane of the surface; otherwise, the ideal point is directly calculated on the physical space. We avoid using the geometry defined on the tessellation since we prefer to getting a mesh respecting the original CAD model rather than its tessellation counterpart. Presently, the developed new schemes have been incorporated into our in-house surface mesher, and their efficiency and effectiveness have been demonstrated through a comparison with state-of-the-art commercial tools (e.g., COMSOL Multiphysics) and AFT algorithm, using CAD models of industry-level complexity.

A Reverse Modeling Method Based on CAD Model Prior and Surface Modeling

Reverse engineering is an important process of real model digitization. However, the existing methods are limited by the characteristics of the modeling object; the modeling is low efficient, has poor versatility, and unstable accuracy. To complete the reverse engineering of a real workpiece with irregular deformation based on the ideal computer-aided design (CAD) model, a high-precision reverse engineering method of the workpiece based on the CAD model prior was presented. Through the registration of the ideal CAD model and the point cloud model of the real workpiece, the geometric feature position information and feature constraint information contained in the CAD model are transmitted to the modeling process, which helps to improve the accuracy and efficiency of reverse engineering. This method is applied to the reverse engineering process of the engine compartment with slight irregular deformation, the modeling accuracy reaches 0.04 mm, and the high-precision reverse engineering of the engine compartment is successfully realized.

Automated Lofting-Based Reconstruction of CAD Models from 3D Topology Optimization Results

Topology optimization (TO) has become an integral part of the structural design process in recent years. However, automatically deriving parametrized Computer-Aided Design (CAD) models from TO results still represents a great challenge. In this paper, we present a new fully automatic process aimed at converting 3D TO results that tend towards beam-like structures into solid CAD models. Our reconstruction process starts with curve-skeletonization of the optimized shape. The curve-skeleton obtained is used alongside with a boundary triangulation of the optimized shape to compute closed cross-sections along the skeleton branches and junctions at the intersection between branches. These cross-sections are interpolated with cubic B-spline fitting curves, which are used as a basis for lofting operations to generate CAD surface representations of branches and junctions of the optimized shape. Remaining openings in the optimized shape boundary are closed with filling surfaces. A solid CAD model can be built by sewing together all created surfaces and filling, by the way, the closed boundary that comes out of this process. Finite Element Analysis (FEA) is carried out on both the 3D optimal shape and the CAD solid model derived in order to validate this CAD model. Several case studies are presented to demonstrate effectiveness and usefulness of this new approach.

A new single-view 3D pantograph reconstruction aided by prior CAD model

This paper proposes a novel 3D pantograph reconstruction method for the visualization and inspection based on the single-view scanned data and prior Computer-Aided Design (CAD) model. The proposed method uses the point cloud to reconstruct a scanned surface by the fusion of the point cloud and prior CAD surface. Then, a 3D model is reconstructed by integrating the scanned surface and the CAD model through an edge reconstruction process. Finally, the pantograph is inspected by the deviation analysis. The proposed method is validated by the pantograph data collected in a locomotive workshop with line structured light scanning measurement technology. Compared with the state-of-the-art methods, the proposed method can reconstruct the complete 3D model with high accuracy. Furthermore, the reconstructed 3D model has been successfully applied to the anomaly detection and visualization in the pantograph inspection, which is of great significance for improving the pantograph inspection efficiency and reducing traffic accidents.

Quasi-conforming analysis method for trimmed CAD surfaces

In this paper, the quasi-conforming method is introduced for the analysis of trimmed computer aided design (CAD) surfaces. The main benefit of the proposed method is that the boundary curves of elements are adopted for the numerical integration directly. In the quasi-conforming technique, the strains are approximated by using polynomials, and the weighted test functions are used to weaken the strain-displacement equations. The interpolation functions are introduced for strain integration. An appropriate choice of initial strain approximation and weighted test function ensures that inner-field functions are not required for strain integration, and this is used for the analysis of trimmed CAD surfaces. For example, the assumed stress quasi-conforming method is applied for the two-dimensional linear elastic problem. All the element edges are approximated by using quadratic Bézier curves for the conciseness, and this is easily incorporated into existing finite element codes and applied to Dirichlet boundary conditions. Numerical examples indicate the effectiveness and accuracy of the method.

Discrete CAD Model for Visualization and Meshing

During the design of an object using a CAD (computer aided design) platform, the user can visualize the ongoing model at every moment. Visualization is based on a discrete representation of the model that coexists with the exact analytical representation of the object. Most CAD systems have this discrete representation available, and each of them applies its own construction methodology. This paper presents a new method to build a discrete (“triangulated” with quadrilaterals and triangles) model for CAD surfaces. It presents two major particularities: most elements are aligned with iso-parametric curves and the accuracy of the surface approximation is controlled. In addition, we present a new technique of surface mesh generation that is based on this discrete model. Several examples are presented to confirm the efficacy of this approach.

A distortion measure to validate and generate curved high‐order meshes on CAD surfaces with independence of parameterization

SummaryA framework to validate and generate curved nodal high‐order meshes on Computer‐Aided Design (CAD) surfaces is presented. The proposed framework is of major interest to generate meshes suitable for thin‐shell and 3D finite element analysis with unstructured high‐order methods. First, we define a distortion (quality) measure for high‐order meshes on parameterized surfaces that we prove to be independent of the surface parameterization. Second, we derive a smoothing and untangling procedure based on the minimization of a regularization of the proposed distortion measure. The minimization is performed in terms of the parametric coordinates of the nodes to enforce that the nodes slide on the surfaces. Moreover, the proposed algorithm repairs invalid curved meshes (untangling), deals with arbitrary polynomial degrees (high‐order), and handles with low‐quality CAD parameterizations (independence of parameterization). Third, we use the optimization procedure to generate curved nodal high‐order surface meshes by means of an a posteriori approach. Given a linear mesh, we increase the polynomial degree of the elements, curve them to match the geometry, and optimize the location of the nodes to ensure mesh validity. Finally, we present several examples to demonstrate the features of the optimization procedure, and to illustrate the surface mesh generation process. Copyright © 2015 John Wiley & Sons, Ltd.

QMCF: QMorph Cross Field-driven Quad-dominant Meshing Algorithm

We propose a new method for generation of quadrilateral meshes. Our algorithm takes a triangle mesh generated on a computer-aided design surface together with a size field as input. A novel cross field, defined on vertices of the triangle mesh, is derived from both curvature directions and constraints on the boundary. Our algorithm uses a modified QMorph algorithm for quad dominant meshing, to follow size field and to align edges with the cross field previously computed.

Subdivision surfaces integrated in a CAD system

The main roadblock that has limited the usage of subdivision surfaces in computer-aided design (CAD) systems is the lack of quality and precision that a model must achieve for being suitable in the engineering and manufacturing phases of design. The second roadblock concerns the integration into the modeling workflows, that, for engineering purposes, means providing a precise and controlled way of defining and editing models possibly composed of different geometric representations. This paper documents the experience in the context of a European project whose goal was the integration of subdivision surfaces in a CAD system. To this aim, a new CAD system paradigm with an extensible geometric kernel is introduced, where any new shape description can be integrated through the two successive steps of parameterization and evaluation, and a hybrid boundary representation is used to easily model different kinds of shapes. In this way, the newly introduced geometric description automatically inherits any pre-existing CAD tools, and it can interact in a natural way with the other geometric representations supported by the CAD system.To overcome the irregular behavior of subdivision surfaces in the neighborhood of extraordinary points, we locally modify the limit surface of the subdivision scheme so as to tune the analytic properties without affecting its geometric shape. Such a correction is inspired by the polynomial blending approach in Levin (2006) [1] and Zorin (2006) [2], which we extend in some aspects and generalize to multipatch surfaces evaluable at arbitrary parameter values. Some modeling examples will demonstrate the benefits of the proposed integration, and some tests will confirm the effectiveness of the proposed local correction patching method.

Designing and Manufacturing Spiral Bevel Gears Using 5-Axis Computer Numerical Control (CNC) Milling Machines

The design of spiral bevel gears remains complex since tooth geometry and the resulting kinematic performance stem directly from the manufacturing process. Spiral bevel gear cutting up to now has relied on the works of several manufacturers. Recent advances in milling machine technology and computer aided manufacturing (CAM) now make it possible to manufacture good quality spiral bevel gears on a standard 5-axis milling machine. This paper describes the computer aided design (CAD) definition and manufacturing of spiral bevel gear tooth surfaces. Process performance is assessed by comparing the resulting surfaces after machining with the predefined CAD surfaces. This manufacturing process makes it possible to obtain geometry analytically, making design easier than with standard spiral bevel gears.

Finite element modelling and simulations for golf impact

The objective of this study was to construct a finite element model of a golf ball and an impact simulation model between the ball and a club, and to devise a method for the construction of simulation models by investigating the factors affecting the behaviour of the ball during and after impact. A ball model with hyperelasticity and viscoelasticity was constructed using solid elements, and the relationship between the material properties and the ball behaviour at impact was revealed by varying several material constants of the ball model. A finite element model of a club with elasticity was created from a computer-aided design surface model of a commercially available driver. The club head and shaft were modelled using solid and shell elements, respectively. The effects of initial conditions at impact on the rebound behaviour of the ball, that is, the velocity, angle and spin rate, were investigated from impact simulations by varying the impact points of the ball and the postures of the club. Then, methods for the construction of simulation models were proposed based on these relationships. Impact experiments were also conducted to obtain the ball behaviour. The results simulated using the models, constructed by the proposed methods, closely matched the experimental results.

Progressive iterative approximation for triangular Bézier surfaces

Recently, for the sake of fitting scattered data points, an important method based on the PIA (progressive iterative approximation) property of the univariate NTP (normalized totally positive) bases has been effectively adopted. We extend this property to the bivariate Bernstein basis over a triangle domain for constructing triangular Bézier surfaces, and prove that this good property is satisfied with the triangular Bernstein basis in the case of uniform parameters. Due to the particular advantages of triangular Bézier surfaces or rational triangular Bézier surfaces in CAD (computer aided design), it has wide application prospects in reverse engineering.

Linéarisation et maillage des surfaces paramétrées

We propose a methodology to simplify the parameterization of a surface composed of parametric patches, typically encountered in CAD (computer aided design) environments. This new parameterization is defined via the construction of an adaptive triangulation, called support, of each patch. The adaptation is governed by the control of the gap between the initial parameterization of the patch and that of the support. This support is used to generate the mesh of the CAD surface using an indirect approach, in which the mesh is generated via the parametric domains. The support makes it possible to disconnect the mesher from the CAD system, and in this sense it constitutes a universal tool for meshing such surfaces. An application example is given to show the pertinency of our methodology.

Trimming of Curved Surfaces in Computer-aided Design

The work examines methods of free-form surfaces limitation by arbitrary contour in CAD/CAM systems. Algorithms of surfaces contour trimming in automatic and automated modes are described. The article represents results of the algorithm realization in CAD/CAM system SPOP-3.

Accuracy analysis of 3D data collection and free-form modelling methods

In industrial applications such as the automotive industry, it is often necessary to design and manufacture surfaces to a desired smoothness. This can be achieved by computer-aided design (CAD) methods, or from the creation of a physical prototype. To gain an adequate feel for the part to be manufactured, physical prototype models are often made by the designer.In the case of free-form surfaces, it can be difficult to judge the overall smoothness of the surface. The optimum smoothness, or continuity, relies on there being no continuity deviations. Without a mathematical model of the surface, it is difficult to confirm that a manufactured surface conforms to the desired specifications. The only method is by way of a designer’s judgement and experience.Thus, to accurately assess a physical surface it is necessary to inspect the part. This is with the aim of collecting accurate 3D data, allowing a 3D CAD surface to be generated. This forms a quality assessment stage. However, this method of verification can also succumb to inaccuracies.This paper offers a method of automating the verification of an acceptable free-form surface, using the co-ordinate measuring machine (CMM) as a means of collecting data from the surface in question. Methods are proposed to analyse the surface for optimum continuity, using computer-aided geometric design (CAGD), as well as assess the CMM data accuracy. This surface can be improved, if desired, using reverse engineering (RE) methods.

An Algorithm for Projecting Points onto a Patched CAD Model

We are interested in building structured overlap-ping grids for geometries defined by Computer-Aided-Design (CAD) packages. Geometric information defining the boundary surfaces of a computation domain is often provided in the form of a collection of possibly hundreds of trimmed patches. The first step in building an overlapping volume grid on such a geometry is to build overlapping surface grids. A surface grid is typically built using hyperbolic grid generation; starting from a curve on the surface, a grid is grown by marching over the surface. A given hyperbolic grid will typically cover many of the underlying CAD surface patches. The fundamental operation needed for building surface grids is that of projecting a point in space onto the closest point on the CAD surface. We describe a fast and robust algorithm for performing this projection which makes use of a fairly coarse global triangulation of the CAD geometry. Before the global triangulation is constructed the connectivity of the model is determined by an edge-matching algorithm which corrects for gaps and overlaps between neighbouring patches.

CADICAM Design of Trunnion Mount (Short Communication)

The computer-aided design (CAD), computer-aided manufacturing (CAM) of a 3-D trunnion mount located on the intercasing housing of a gas turbine engine is described. The mount carries load and thrust, hence stress-concentrating locations, like sharp edges and corners must be avoided. A program involving CAD, CAM and post-processing CAD surfaces for tool paths has been developed. Preliminary machining of a scrap aluminum piece that verified the program is described. This method is applicable to a wide variety of proprietary packages.

Representation and deformation of developable surfaces

The purpose of the paper is to contribute to the study of developable surfaces in computer-aided design by proposing a means of specifying and controlling them. A discrete representation for a developable is derived from the orientation of the tangent plane along a geodesic. The original surface is thus approximated by a smooth developable surface which consists of pieces of circular cones. This representation easily allows deformation of the developable.