Identifying the directions of a set of 2D contours for additive manufacturing process planning

Additive Manufacturing (AM) is a process in which material is added layer by layer to build a physical part. In AM process planning, a stack of 2D closed contours is obtained when a 3D stereolithography (STL) model is sliced. Each slice may have a set of closed contours or polygons, each of which needs to be classified (oriented) as internal (clockwise) or external (counterclockwise) to identify where material should be added. This is not a straightforward task as the STL format does not ensure correct surface orientation of the 3D model. This work describes two methods for identifying the direction of each contour in a set, i.e., for sorting them into internal and external contours. Three alternative tests to check whether a point is inside or outside a polygon were evaluated. The tests are based on the ray-tracing principle and the classical point-in-polygon test. The proposed algorithms were devised and implemented in an AM process planning system. The methods were validated using 3D models with a variety of geometries, and the computing time for the alternative tests was compared. The results showed that the method based on the point-in-polygon tests has some advantages.     

A Reverse Engineering Approach to Generating Interference-Free Tool Paths in Three-Axis Machining from Scanned Data of Physical Models

An NC tool path is usually generated by sweeping parametric surfaces of a CAD model. In modern design, freeform or sculptured surfaces are increasingly popular for representing complex geometry for aesthetic or functional purposes. Traditionally, a prototype is realised by machining the workpiece using the NC codes generated from a CAD model. The machined part can then be compared with the CAD model by measurement using a coordinate measuring machine. In this paper, a reverse engineering approach to generating interference-free tool paths in three-axis machining from the scanned data from physical models is presented. There are two steps in this procedure. First, a physical model is scanned by a 3D digitiser, and multiple data sets of the complex model are obtained. A surface registration algorithm is proposed to align and integrate those data to construct a complete 3D data set. A shortest-distance method is used to determine the connecting sequence of the neighbouring points between two adjacent scan lines, such that the scanned data are converted into triangular polygons. Tool paths are then generated from the tessellated surfaces. Using the Z-map method, interference-free cutter-location data are calculated, relative to the vertex, edges, and planes of the triangles. The algorithms for tool-path generation are usually different for cutters of different geometries. Some algorithms found in the literature require complex numerical calculations and are time consuming. In this paper, an efficient algorithm is developed to calculate interference-free cutter-location data by easy geometric reasoning without complex computation. This robust method is suitable for generally used cutters such as ball, flat, and filleted end mills, and the time taken to obtain full tool paths of compound surfaces is short. Some real applications are presented to validate the proposed approach.     

Quadrilateral mesh generation on trimmed NURBS surfaces

An automatic mesh generation scheme with unstructured quadrilateral elements on trimmed NURBS surfaces has been developed. In this paper NURBS surface geometries in the IGES format have been employed to represent geometric models. For unstructured mesh generation with quadrilateral elements, a domain decomposition algorithm employing loop operators has been modified. As for the surface meshing, an indirect 2D approach is proposed in which both quasi-expanded planes and projection planes are employed. Sample meshes for complex models are presented to demonstrate the robustness of the algorithm.     

Mesh smoothing method based on local wave analysis

As the mesh models usually contain noise data,it is necessary to eliminate the noises and smooth the mesh.But existed methods always lose geometric features during the smoothing process.Hence,the noise is considered as a kind of random signal with high frequency,and then the mesh model smoothing is operated with signal processing theory.Local wave analysis is used to deal with geometric signal,and then a novel mesh smoothing method based on the local wave is proposed.The proposed method includes following steps:Firstly,analyze the principle of local wave decomposition for 1D signal,and expand it to 2D signal and 3D spherical surface signal processing;Secondly,map the mesh to the spherical surface with parameterization,resample the spherical mesh and decompose the spherical signals by local wave analysis;Thirdly,propose the coordinate smoothing and radical radius smoothing methods,the former filters the mesh points’ coordinates by local wave,and the latter filters the radical radius from their geometric center to mesh points by local wave;Finally,remove the high-frequency component of spherical signal,and obtain the smooth mesh model with inversely mapping from the spherical signal.Several mesh models with Gaussian noise are processed by local wave based method and other compared methods.The results show that local wave based method can obtain better smoothing performance,and reserve more original geometric features at the same time.     

基于递归分割理论的自由曲面建模技术

为应用递归分割理论增强复杂自由曲面建模能力,通过在递归分割Loop方法中引入节点加权因子,实现了对递归逼近分割曲面形状的有效控制,并可以生成不同的尖锐特征。根据曲面模型各点处的平均曲率,对节点位置进行逐步调整,实现了递归分割曲面模型的光顺处理。论述了通过计算递归分割曲面模型的法向偏置面生成薄壁件表面模型的方法,并给出了所建立的自由曲面模型直接应用于快速原型制造的实例,说明应用该项新技术可以直接建立任意拓扑结构复杂自由曲面模型,为复杂自由曲面的建模提供了新的有效途经。     

Constrained deformation of freeform surfaces using surface features for interactive design

There is an increasing demand in conceptual design for more intuitive methods for creating and modifying freeform curves and surfaces in CAD modeling systems. The methods should be based not only on the change of the mathematical parameters but also on the user's specified constraints and shapes. This paper presents a new surface representation model for freeform surface deformation representation. The model is a combination of two functions: a displacement function and a function for representing an existing NURBS surface called a parent surface. Based on the surface model, the authors develop several novel deformation methods which are named SingleDef (Single-point constraint based deformation method), MultiDef (Multiple-points constraints based deformation method), CurDef (Curve constraints based deformation method) and FeatDef (Feature constraint based deformation method). The techniques for freeform surface deformation allow conceptual designers to modify a parent surface by directly applying point constraints, curve constraint or a surface constraint to the parent surface. The deformation methods are implemented in an experimental CAD system. The results show that designers can easily and intuitively control the surface shape.     

NURBS output based tool path generation for freeform pockets

A robust method is proposed to generate tool paths for NURBS-based machining of arbitrarily shaped freeform pockets with islands. Although the input and output are all of higher-degree NURBS curves, only one simple category of geometric entities, i.e., line segments, is required for initial offsetting and for detecting and removing self-intersecting loops. Furthermore, using those linear non-self-intersecting offsets as the legs of NURBS control polygons, NURBS-format tool paths can be smoothly reconstructed with G¹-continuity, no overcutting, no cusps, and global error control. Since all operations involved in computing tool path curves are linear geometric calculations, the method is robust and simple. Examples with integrated rough and finish cutting tool paths of pockets demonstrate the usefulness and effectiveness of this method.     

Direct slicing and G-code contour for rapid prototyping machine of UV resin spray using PowerSOLUTION macro commands

Rapid prototyping processes produce parts layer by layer directly from 3D CAD models. An important technique is required to slice the geometric model of a part into layers and to generate a motion code of the cross-sectional contour. Several slicing methods are available, such as slicing from sterolithgraphy (STL) files, tolerate-error slicing, adaptive slicing, direct slicing, and, adaptive and direct slicing. This paper proposes direct slicing from 3D CAD models and generating a G-code contour of each layer using PowerSOLUTION software (Delcam International, Birmingham, UK). PowerSOLUTION includes two main modules: PowerSHAPE is used to build 3D CAD models and PowerMILL is used to produce G-Code tool paths. It provides macro language, picture files and cutting paths for secondary development work.The authors used macro commands to write an interface generating direct slicing from 3D CAD models and G-code contours for all layers. Most well-known controllers in the market accept the G-Code. Therefore, it is easier to apply this scheme in a CNC-machining center to produce rapid prototyping such as laminated object manufacturing (LOM) for complex geometries. The interface was successfully applied the interface to the UV resin spray rapid prototyping (UVRS-RP) machine that was developed to produce RP.     

基于图像频谱分析三维网格模型数字浮雕生成算法

由3维模型生成2.5维数字浮雕曲面是最近国内外数字浮雕研究的热点,通过对三维网格模型频率域的能量进行压缩来得到几何高度被压缩的浮雕模型.算法通过对三维模型进行重新采样,获得视线方向上的规则化深度图,然后利用图像傅里叶变换对深度图进行频谱分析,最后将模型高度的压缩转换为频谱域能量系数的压缩来得到浮雕曲面模型.在压缩过程中,应用高通滤波器工具对低频能量进行压缩、应用对数压缩函数对高频边缘压缩,从而使得生成的浮雕达到较好的效果.实例表明在频率域对三维模型的能量进行压缩来生成浮雕是可行的,算法对细节不太丰富的模型同样具有较好的效果.     

由基于轮廓重建的表面模型构建实体几何模型

基于工业CT(ICT)图象进行反求是逆向工程的重要内容 ,由ICT图象提取轮廓并进行轮廓重建的模型为表面模型 ,只包含表面几何信息 ,而实体几何模型具有完备的几何和拓扑信息。本文论述了由轮廓重建表面模型的方法和步骤 ,提出了一种由表面模型构建实体几何模型的方法。文中还对存在分叉轮廓、内轮廓的情况提出了具体处理方法。用轮廓重建生成表面模型 ,再转成实体模型的方法可作为三维CAD系统的一种造型手段     

复杂曲面特征线自动提取技术研究

复杂曲面零件的几何模型重构是逆向工程的研究重点之一,由零件表面的数字化数据提取特征线是构造几何模型的重要步骤。针对由CMM获取的三维数据“点云”,提出了基于扫描线的三维分层式方法实现特征线的自动提取,提出了基于局部增量网格扩张的三维散乱数据三角剖分算法,实现任意曲面尖锐棱线的自动提取。实践说明,通过该算法得到的复杂曲面的边界线能够满足模型重建的工程需求。     

线激光-立体视觉三维数据获取系统研究

通过将三目立体视觉和线激光扫描传感器两种物体表面三维数据获取设备集成到三坐标测量机(CMM),形成一种新型的反求工程中的数据获取系统,其中由三目立体视觉来获得物体的边界或轮廓信息、线激光扫描传感器获得物体表面的三维数据,利用多传感器的信息融合技术对三维数据进行分割,提取被测物体的几何特征,并在此基础上构建物体模型.采用这种多传感器集成坐标测量系统避免了单一传感器的局限性,从而为非接触测量系统在反求工程中的应用开辟了新的途径.     

反求工程中产品三维模型重建技术综述

阐述了反求工程的基本概念、研究内容及基本过程 ,总结了反求工程中的两个关键技术问题——形状表面数字化和产品几何模型重建技术的研究现状 ,提出了应该重点解决的理论与技术问题     

散乱模型的四边形网格剖分方法

针对基于CAD几何信息的网格剖分方法无法避免繁琐模型修补,导致网格剖分效率低下的现状,提出一种基于散乱模型的全四边形网格剖分方法.使用散乱点或者STL格式文件作为网格剖分的输入模型,使用改进的基于散乱模型进行网格剖分的铺路算法,在很大程度上减少甚至避免了模型修补问题.提出以散乱模型作为背景网格,作为控制网格单元尺寸调整的依据:使用网格细分和网格粗化的手段实现网格疏密变化的光滑过渡;自动识别几何模型中的特征并在网格模型中保留.提出了一种高效的铺路面相交搜索方法,综合考虑影响相交处理的多种因素,有效地处理了铺路面相交问题.多个复杂的汽车覆盖件网格剖分的算例结果表明,运用所提出方法完成的网格模型质量很高,算法具有较强的工程实用性.     

A Freeform Surface Modelling System Based on Laser Scan Data for Reverse Engineering

Reverse engineering technology starts with a measurement process, inspecting the surface contour of the object, and applies a CAD geometric modelling technique to construct the surface model. The purpose of this study is to develop a freeform surface modelling system involving the functions of data reorganisation and surface construction of reverse engineering. An important task in reverse engineering is the process of reducing the large amount of coordinate data derived by measurement devices. Reduction methods in common use include uniform deviation, division by a factor, spatial sampling, chordal deviation and interpolated sampling. Each of the above modes has its advantages and weaknesses, and suitable application areas. A new data reduction mode, which integrates the space concept and height characteristic, is proposed, called the height decision method. This method can achieve the aim of data simplification while maintaining the curve characteristics of the model. The CAD modelling system is developed by an AutoLISP program with MDT v4.0 software. An egg model is presented in this paper for explanation and verification.     

Any-degrees-of-freedom (anyDOF) registration for the characterization of freeform surfaces

This paper presents an any-degrees-of-freedom (anyDOF) registration method for the characterization of freeform surfaces. The method attempts to fill the research gap regarding traditional surface registration methods which are normally dedicated to solving the global optimization problem with all DOF but they lack flexibility. The proposed anyDOF method is capable of registering surfaces with any specified combination of DOF. This is particularly useful when some of the DOF are known to be unchanged according to the a priori knowledge. The anyDOF surface registration method is regarded as a typical optimization problem of finding the minimum distance from target surface to the reference surface, with constraints of the unwanted DOF. The problem is solved by the Levenberg-Marquardt method. Simulated experiments for a two-dimensional (2D) profile and a three-dimensional (3D) surface were undertaken, together with three measurement experiments including a fluid-jet polished surface, a bonnet polished surface and a diamond machined freeform surface. Experimental results show that the anyDOF registration method is highly flexible in the characterization of freeform surfaces.     

基于优化算法和GVT结果的结构质量模型修正

提出了一种基于优化算法和 GVT结果的结构质量模型修正方法。该方法利用模态正交性条件构造目标函数 ,并考虑结构总质量特性约束 ,利用 GVT结果对给定的粗糙的结构离散质量分布进行修正。数值仿真表明 ,该方法提高了结构质量模型的精度 ,使修正后的离散质量分布与真实的离散质量分布吻合     

A History-Independent Modelling-Oriented Approach to Solve Geometric Constraints Between Features in 3D Space

History-independent modelling systems are more flexible than history-based ones. They let designers manipulate the model in a more associative, rather than prescribed, way. In this paper, an approach based on 2D geometric constraint solving and a topological entity naming mechanism (TENM) is presented to solve the geometric constraints between features in 3D space. Firstly, in order to break the unidirectional dependency between features in a history-based modelling system, a data structure named feature constraint graph(FCG) is adopted to represent the geometric constraints between features in 3D space. Then a solving sequence is obtained using degree-of-freedom (DOF) based graph analysis. And finally, during the evaluation of the solving sequence, the dimensions in 3D space are mapped to 2D space, the dimensions in 3D space are satisfied indirectly by solving the corresponding 2D geometric constraint system. An example is given to illustrate the process of our approach.     

FREE-FORM SURFACE RECON-STRUCTION BASED ON NURBS TO SERIAL CROSS-SECTIONS

A new method for recovering shape from cross-sectional contours with complex branchingstructures is presented. First, each branching problem by providing an intermediate contour using dis-tance function and image processing technology is solved. Then, all contours are divided into severalgroups of simple contours. For each group, a NURBS curve is fitted to contour points in each sectionwithin a given accuracy on a common knot vector.Finally, the NURBS surface skinning of these con-tours is performed for providing a smooth geometric model. The method is suitable to reproduce theobject by NC machining or rapid prototyping. Some results demonstrate its usefulness and feasibility.