Robust uniform triangulation algorithm for computer aided design

This paper presents a new robust uniform triangulation algorithm that can be used in CAD/CAM systems to generate and visualize geometry of 3D models. Typically, in CAD/CAM systems 3D geometry consists of 3D surfaces presented by the parametric equations (e.g. surface of revolution, NURBS surfaces) which are defined on a two dimensional domain. Conventional triangulation algorithms (e.g. ear clipping, Voronoi-Delaunay triangulation) do not provide desired quality and high level of accuracy (challenging tasks) for 3D geometry. The approach developed in this paper combines lattice tessellation and conventional triangulation techniques and allows CAD/CAM systems to obtain the required surface quality and accuracy. The algorithm uses a Cartesian lattice to divide the parametric domain into adjacent rectangular cells. These cells are used to generate polygons that are further triangulated to obtain accurate surface representation. The algorithm allows users to control the triangle distribution intensity by adjusting the lattice density. Once triangulated, the 3D model can be used not only for rendering but also in various manufacturing and design applications. The approach presented in this paper can be used to triangulate any parametric surface given in S(u,v) form, e.g. NURBS surfaces, surfaces of revolution, and produces good quality triangulation which can be used in CAD/CAM and computer graphics applications.     

CM,RE和CAD/CAM系统集成环境的研究

对三坐标测量系统、联系实际向工程、CAD/CAM系统信息集成中存在的问题进行分析，提出了面向快速逆向设计和制造集成环境的功能模型、关键技术和处理方法。通过建立CM，RE，CAD/CAM系统的集成平台，对样件、模型进行快速测量，并对测量数据进行数据处理、特征重建、几何造型和数控加工处理，以实现对产品样件或模型的快速逆向设计与制造。     

Theoretically-based algorithms for robustly tracking intersection curves of deforming surfaces

This paper applies singularity theory of mappings of surfaces to 3-space and the generic transitions occurring in their deformations to develop algorithms for continuously and robustly tracking the intersection curves of two deforming parametric spline surfaces, when the deformation is represented as a family of generalized offset surfaces. The set of intersection curves of two deforming surfaces over all time is formulated as an implicit 2-manifold I in an augmented (by time domain) parametric space R⁵. Hyperplanes corresponding to some fixed time instants may touchI at some isolated transition points, which delineate transition events, i.e. the topological changes to the intersection curves. These transition points are the 0-dimensional solution to a rational system of five constraints in five variables, and can be computed efficiently and robustly with a rational constraint solver using subdivision and hyper-tangent bounding cones. The actual transition events are computed by contouring the local osculating paraboloids. Away from any transition points, the intersection curves do not change topology and evolve according to a simple evolution vector field that is constructed in the Euclidean space in which the surfaces are embedded.     

A New Local Control Spline with Shape Parameters for CAD/CAM

Anew local control spline based on shape parameterw with G^3 continuity,called BLC-spline,is pro* posed.Not only is BLC-spline very smoot,but also the spline curve‘s characteristic polygon has only three control vertices,and the characteristic polyhedron has only nine control vertices.The behavior of Iocal control of BLC-spline is better than that of the other splines such as cubic Bezier,B and Beta-spline.The three shape parameters β0，β1and β2 of BLC-spline,which are independent of the control vertices,may be altered to change the shape of the curve or surface.It is shown that BLC-spline may be used to construcet a space are spline for DNC machining directly.That is a powerful tool for the design and manufacture of curves and surfaces in integrated CAD/CAM systems.     

Function Representation of Solids Reconstructed from Scattered Surface Points and Contours

This paper presents a novel approach to the reconstruction of geometric models and surfaces from given sets of points using volume splines. It results in the representation of a solid by the inequality f(x,y,z) ≥ 0. The volume spline is based on use of the Green's function for interpolation of scalar function values of a chosen “carrier” solid. Our algorithm is capable of generating highly concave and branching objects automatically. The particular case where the surface is reconstructed from cross-sections is discussed too. Potential applications of this algorithm are in tomography, image processing, animation and CAD for bodies with complex surfaces.     

Automesh for trimmed surface entity of IGES/PDES

IGES/PDES is an internationally accepted standard protocol for transferring the information of a two-dimensional or three-dimensional model between different CAD/CAM software. Any solid model can be constituted by a number of surfaces. Trimmed surface is one of the most important entities used to design a two-dimensional or three-dimensional model in IGES/PDES. The main idea in this article is to extract trimmed surface entity information from an IGES protocol created in a CAD/CAM software. Then, from the extracted information of trimmed surface entity in the model space and in the u–v space, a new u–v space is developed for meshing. After meshing the geometric region in the new u–v space, the meshed geometric region is transformed back to the model space by using a particular transformation. A Fortran code which can be used for pre-processing in Boundary Element Method has been developed by the present authors. Some meshed surface models are presented in this paper as examples.     

基于约束优化的B样条曲线形状修改

B样条曲线广泛应用于计算机辅助几何设计(CAGD),并且与Bézier曲线等其它著名曲线相比,在形状设计方面有其更独特的性质。对曲线的设计和形状的修改是一个重要的课题,也是计算机图形学、CAD/CAM和数控技术领域最重要的研究主题之一。论文运用约束优化的方法,修改均匀B-样条的控制点,使B样条曲线通过调整的控制点,使修改前后曲线的距离范数达到最小,并给出相应的实例说明算法的有效性。     

Five-axis pencil-cut planning and virtual prototyping with 5-DOF haptic interface

In this paper, techniques of 5-axis pencil-cut machining planning with a 5-DOF (degree of freedom) output haptic interface are presented. Detailed techniques of haptic rendering and tool interference avoidance are discussed for haptic-aided 5-axis pencil-cut tool path generation. Five-axis tool path planning has attracted great attention in CAD/CAM and NC machining. For efficient machining of complex surfaces, pencil-cut uses relatively smaller tools to remove the remaining material at corners or highly curved regions that are inaccessible with larger tools. As a critical problem for 5-axis pencil-cut tool path planning, the tasks of tool orientation determination and tool collision avoidance are achieved with a developed 5-DOF haptic interface. A Two-phase rendering approach is proposed for haptic rendering and force-torque feedback calculation with haptic interface. A Dexel-based volume modeling method is developed for global tool interference avoidance with surrounding components in a 5-axis machining environment. Hardware and software implementation of the haptic pencil-cut system with practical examples are also presented in this paper. The presented technique can be used for CAD/CAM, 5-axis machining planning and virtual prototyping.     

Uniform offsetting of polygonal model based on Layered Depth-Normal Images

Uniform offsetting is an important geometric operation for computer-aided design and manufacturing (CAD/CAM) applications such as rapid prototyping, NC machining, coordinate measuring machines, robot collision avoidance, and Hausdorff error calculation. We present a novel method for offsetting (grown and shrunk) a solid model by an arbitrary distance r. First, offset polygons are directly computed for each face, edge, and vertex of an input solid model. The computed polygonal meshes form a continuous boundary; however, such a boundary is invalid since there exist meshes that are closer to the original model than the given distance r as well as self-intersections. Based on the problematic polygonal meshes, we construct a well-structured point-based model, Layered Depth-Normal Image (LDNI), in three orthogonal directions. The accuracy of the generated point-based model can be controlled by setting the tessellation and sampling rates during the construction process. We then process all the sampling points in the model by using a set of point filters to delete all the invalid points. Based on the remaining points, we construct a two-manifold polygonal contour as the resulting offset boundary. Our method is general, simple and efficient. We report experimental results on a variety of CAD models and discuss various applications of the developed uniform offsetting method.     

A Visibility Sphere Marching algorithm of constructing polyhedral models for haptic sculpting and product prototyping

This paper presents a Visibility Sphere Marching algorithm of constructing polyhedral models from Dexel volume models for haptic virtual sculpting. Dexel volume models are used as the in-process models representation during interactive modification in a haptic virtual sculpting system. The stock material represented in a Dexel volume model is sculpted into a designed model using a developed haptic sculpting system. The sculpted Dexel volume models are converted to polyhedral surface models in STL format by the proposed visibility sphere marching algorithm. The conversion turns out to be an interesting and challenging problem. The proposed visibility sphere marching algorithm consists of three sub-algorithms: (i) roof and floor covering, (ii) wall-building, and (iii) hole-filling algorithms. The polyhedral surface models converted from the Dexel volume models can then be input to and processed by available computer-aided manufacturing (CAM) or rapid prototyping systems. The presented technique can be used in virtual sculpting, CAD/CAM, numerically controlled machining verification and rapid prototyping.     

Interchanging spline curves using IGES

Current CAD/CAM systems employ a variety of spline types, spline representations, and curve design algorithms. The IGES (initial graphic exchange specification) was designed to enable interchange of the more commonly used spline types among CAD/CAM systems, independent of the design algorithms originally used to create them. IGES supports parametric cubic splines through a piecewise polynomial representation. This paper describes the design considerations leading to the interchange common spline curve types. A short introduction to splines and spline representations is included.     

Equidistant Smoothing of Polyhedra with Arbitrary Topologies

Smoothing of polyhedron with arbitrary topology is an important issue in CAGD and CAD/CAM, but so far it is deemed to be difficult to smooth the complex corners of a polyhedron. In this paper, the concept of distance surfaces of a surface and a solid is introduced, and the incisive properties of such surfaces are addressed which provide a theoretical foundation for modifying a general corner. The method is based on making constricted volume and the maximum distance the volume can be constricted is given too. It is shown that by the proposed method in this paper any polyhedron can be G¹ smoothed with quadraic and, sometimes toroidal surfaces. The new approach is suitable for engineering design and NC machining. The associated algorithm based on the classification theorem of corners is simple, fast and robust.     

Uniform trigonometric polynomial B-spline curves

This paper presents a new kind of uniform spline curve, named trigonometric polynomial B-splines, over space Ω = span{sini,cost, tk-3,tk-4, …,t, 1} of which k is an arbitrary integer larger than or equal to 3. We show that trigonometric polynomial B-spline curves have many similar properties to traditional B-splines. Based on the explicit representation of the curve we have also presented the subdivision formulae for this new kind of curve. Since the new spline can include both polynomial curves and trigonometric curves as special cases without rational form, it can be used as an efficient new model for geometric design in the fields of CAD/CAM.     

带双形状参数的C-B样条曲线

利用积分方法构造了带双形状参数的C-B样条曲线基函数,这类曲线具有标准C-B样条曲线主要性质,如连续性、凸包性等;根据形状参数的不同取值可以整体或者局部调控曲线形状,由此生成的曲线与曲面,作为一种新的几何造型方法,可应用于CAD/CAM领域。     

Surface Fairing towards Regular Principal Curvature Line Networks

Freeform surfaces whose principal curvature line network is regularly distributed, are essential to many real applications like CAD modeling, architecture design, and industrial fabrication. However, most designed surfaces do not hold this nice property because it is hard to enforce such constraints in the design process. In this paper, we present a novel method for surface fairing which takes a regular distribution of the principal curvature line network on a surface as an objective. Our method first removes the high‐frequency signals from the curvature tensor field of an input freeform surface by a novel rolling guidance tensor filter, which results in a more regular and smooth curvature tensor field, then deforms the input surface to match the smoothed field as much as possible. As an application, we solve the problem of approximating freeform surfaces with regular principal curvature line networks, discretized by quadrilateral meshes. By introducing the circular or conical conditions on the quadrilateral mesh to guarantee the existence of discrete principal curvature line networks, and minimizing the approximate error to the original surface and improving the fairness of the quad mesh, we obtain a regular discrete principal curvature line network that approximates the original surface. We evaluate the efficacy of our method on various freeform surfaces and demonstrate the superiority of the rolling guidance tensor filter over other tensor smoothing techniques. We also utilize our method to generate high‐quality circular/conical meshes for architecture design and cyclide spline surfaces for CAD modeling.     

Grid_strain and grid_strain3: Software packages for strain field computation in 2D and 3D environments

Two Matlab™ software packages for strain field computation, starting from displacements of experimental points (EPs), are here presented. In particular, grid_strain estimates the strain on the nodes of a regular planar grid, whereas grid_strain3 operates on the points of a digital terrain model (DTM). In both cases, the computations are performed in a modified least-square approach, emphasizing the effects of nearest points. This approach allows users to operate at different scales of analysis by introducing a scale factor to reduce or also exclude points too far from grid nodes. The input data are displacements (or velocities) that can be provided by several techniques (e.g. GPS, total topographical station, terrestrial laser scanner). The analysis can be applied to both regional- and local-scale phenomena, to study tectonic crustal deformations (strain ≈10⁻⁸−10⁻⁶) or rapid landslide collapses (10⁻⁴−10²), and to characterize the kinematics of the studied system. Errors on strains and geometric significance of the results are also provided.     

Industrial geometry: recent advances and applications in CAD

Industrial Geometry aims at unifying existing and developing new methods and algorithms for a variety of application areas with a strong geometric component. These include CAD, CAM, Geometric Modelling, Robotics, Computer Vision and Image Processing, Computer Graphics and Scientific Visualization. In this paper, Industrial Geometry is illustrated via the fruitful interplay of the areas indicated above in the context of novel solutions of CAD related, geometric optimization problems involving distance functions: approximation with general B-spline curves and surfaces or with subdivision surfaces, approximation with special surfaces for applications in architecture or manufacturing, approximate conversion from implicit to parametric (NURBS) representation, and registration problems for industrial inspection and 3D model generation from measurement data. Moreover, we describe a ‘feature sensitive’ metric on surfaces, whose definition relies on the concept of an image manifold, introduced into Computer Vision and Image Processing by Kimmel, Malladi and Sochen. This metric is sensitive to features such as smoothed edges, which are characterized by a significant deviation of the two principal curvatures. We illustrate its applications at hand of feature sensitive curve design on surfaces and local neighborhood definition and region growing as an aid in the segmentation process for reverse engineering of geometric objects.     

Applying geometric constraints for perfecting CAD models in reverse engineering

An important area of reverse engineering is to produce digital models of mechanical parts from measured data points. In this process inaccuracies may occur due to noise and the numerical nature of the algorithms, such as, aligning point clouds, mesh processing, segmentation and surface fitting. As a consequence, faces will not be precisely parallel or orthogonal, smooth connections may be of poor quality, axes of concentric cylinders may be slightly tilted, and so on. In this paper we present algorithms to eliminate these inaccuracies and create “perfected” B-rep models suitable for downstream CAD/CAM applications.Using a segmented and classified set of smooth surface regions we enforce various constraints for automatically selected groups of surfaces. We extend a formerly published technology of Benkő et al. (2002). It is an essential element of our approach, however, that we do not know in advance the set of surfaces that will actually get involved in the final constrained fitting. We propose local methods to select and synchronize “likely” geometric constraints, detected between pairs of entities. We also propose global methods to determine constraints related to the whole object, although the best-fit coordinate systems, reference grids and symmetry planes will be determined only by surface entities qualified as relevant. Lots of examples illustrate how these constrained fitting algorithms improve the quality of reconstructed objects.     

Development of a collaborative CAD/CAM system

This paper presents the development of a collaborative CAD/CAM system (COCADCAM). COCADCAM extends an existing single-location CAD/CAM system to a multi-location CAD/CAM application so that two geographically dispersed CAD/CAM users can work together on a three-dimensional CAD-geometry coediting and CAD-related tasks collaboratively and dynamically. COCADCAM dynamically supports CAD data communication that are not available in traditional single-location CAD/CAM. The dynamic data communication is achieved through the development of networking algorithms and CAD/CAM functions in this paper. The networking algorithms based on UNIX Interprocess Communication (IPC), the Network File System (NFS), and a connection-oriented client and server model under the Transmission Control Protocol/Internet Protocol (TCP/IP) suite. The CAD/CAM functions included surface modelling, simulation of a milling toolpath, and post-processing of an NC program following collaborative CAD-geometry coediting, which are directly or indirectly supported by the Application Programming Interface (API) of the CAD/CAM software. The networking algorithms and CAD/CAM functions together can facilitate an environment for CAD-geometry coediting and related tasks such as design, analysis and manufacture. COCADCAM has been successfully implemented through local area network (LAN) and the Internet; a remote machining cell is also linked so that the generated NC program based on a coedited free-form surface can be used for the physical machining operation. The algorithm proposed by COCADCAM can be referenced for the extension of other single-location CAD/CAM systems to multi-location applications.