Freeform texture representation and characterisation based on triangular mesh projection techniques

Texture characterisation for freeform non-Euclidean surfaces is becoming increasingly important due to the widespread of the use of such surfaces in different applications, e.g. the additive manufacturing. Four main steps are required to analyse and characterise those surfaces which include new surface representation, surface filtration and decomposition, texture representation methods and finally the calculation of the surface parameters. Recently, the representation, as well as the filtration and decomposition, of freeform surfaces have been investigated and some algorithms have been proposed. This paper, however, shed the light on how to represent the texture of freeform non-Euclidean surfaces before calculating the parameters. A novel model for freeform surface parameterisation is introduced; this new model proposes the use of a projection algorithm before the actual calculation of the parameters. Different projection algorithms have been adopted from the mesh projection techniques found in the field of computer graphics. The results of applying those algorithms to represent the texture of both simulated and bio-engineering surfaces are shown, also a comparison between those algorithms has been carried out. Furthermore, examples of calculating some of the surface parameters for freeform surfaces are given.     

A robust surface fitting and reconstruction algorithm for form characterization of ultra-precision freeform surfaces

Ultra-precision freeform surfaces are non-rotational symmetric surfaces possessing sub-micrometer form accuracy and nanometric surface finish. Although they can be fabricated accurately by ultra-precision machining technology, their surface quality is difficult to be characterized. Surface reconstruction is a vital task in the form characterization of ultra-precision freeform surfaces. This paper presents a robust surface fitting algorithm to reconstruct a high fidelity surface from measured discrete points while the surface smoothness can be ensured as well. A fitting threshold named confidence interval of fitting error is proposed to strike the balance between fitting accuracy and surface smoothness in the fitting process. The fitting algorithm is in two steps. In the first step, bidirectional sampling method is developed to extract a curve network from measured points cloud to construct an initial surface. In the second step, the fitting error of the initial surface is minimized to meet the prescribed fitting error threshold. A series of experimental work has been conducted and the results show that the proposed algorithm is able to provide effective means for increasing the accuracy in the form characterization of ultra-precision freeform surfaces.     

Fabrication of 3D submicron to micro textured surfaces using backside patterned texturing (BPT)

This work presents a novel fabrication method for submicron to micro size textures on flat surfaces using the backside patterned texturing (BPT). The proposed method utilizes the pre-fabricated macro-features on the backside of work material, and thereafter the front side is face turned with a single point diamond tool to generate textured surfaces. Different from existing texturing methods, BPT produces textured surfaces from submicron to micro scale without any external gadgets such as vibration assisted machining or synchronized tool-spindle motion. The miniature feature arises on the diamond turned surface due to the induced residual stresses when the specimen is unleashed from the machine. To demonstrate the efficacy of the method, a series of machining experiments were conducted to fabricate various types of freeform surface textures like water-drop freeform, cylindrical freeform surfaces, etc. The fabrication methodology of different sizes of bumps with precisely controlled surface quality is illustrated. The texture profiles comprising the deformation height from hundreds of nanometer to few micrometers with mirror surface quality were successfully fabricated on the diamond machined surface. The experimental results suggest that the pre-fabricated pattern, workpiece thickness and machining condition play a critical role to determine the final shape and geometry of generated textures.     

Fast freeform hybrid reconstruction with manual mesh segmentation

In this paper, we presented a method for fitting large B-spline topological surfaces on freeform polygon mesh generated from cloud data of objects. The mesh has been manually segmented and large surfaces are fitted on segments in a hybrid approach, i.e., combination of geometric subdivision and non-uniform rational B-spline (NURBS) interpolation which is an emerging research space. An interpolation method has been proposed to parameterize dense cloud data of any complexity level with capability of handling occluded regions. All junctions are treated with trimming of NURBS surfaces with C ⁰ and C ¹ continuities between adjacent patches. This scheme amalgamated process knowledge of reconstruction on segmented and subdivided point cloud data, various NURBS geometry options and junction treatment resulting in faster high-quality reconstruction. Apart from manual segmentation, almost the entire process is automatic which generated superior quality surface models. Pawn, Stanford Bunny, and human head clouds with occluded surface zones are used for tryout and resulting shapes are recorded in initial graphics exchange specification (IGES) files.     

EQUIVALENT NORMAL CURVATURE APPROACH MILLING MODEL OF MACHINING FREEFORM SURFACES

A new milling methodology with the equivalent normal curvature milling model machining freeform surfaces is proposed based on the normal curvature theorems on differential geometry. Moreover, a specialized whirlwind milling tool and a 5-axis CNC horizontal milling machine are introduced. This new milling model can efficiently enlarge the material removal volume at the tip of the whirlwind milling tool and improve the producing capacity. The machining strategy of this model is to regulate the orientation of the whirlwind milling tool relatively to the principal directions of the workpiece surface at the point of contact, so as to create a full match with collision avoidance between the workpiece surface and the symmetric rotational surface of the milling tool. The practical results show that this new milling model is an effective method in machining complex three- dimensional surfaces. This model has a good improvement on finishing machining time and scallop height in machining the freeform surfaces over other milling processes. Some actual examples for manufacturing the freeform surfaces with this new model are given.     

基于Freeform的逆向工程数据修复

介绍了基于力反馈技术的Freeform触觉式设计系统在逆向工程测量数据修复方面强大的功能。利用非接触式光栅扫描仪测量飞机模型的表面数据点云,通过Freeform的分割黏土、膨胀、镜像、平滑等功能,成功地恢复了飞机模型完整的表面数据。     

光学自由曲面快速刀具伺服车削误差的补偿

受各种误差因素以及周期性变化的切削力的影响,快速刀具伺服金刚石车削技术往往难以用一次车削获得满足光学性能要求的自由曲面。本文提出了一种利用线性差动传感器(LVDT)实现高精度接触式自由曲面在位测量的方法。该方法结合两自由度快速刀具伺服系统,实现了基于快速刀具伺服(FTS)的自由曲面车削加工的误差补偿。试验结果表明,该技术将自由曲面的加工精度提高了20%,表面粗糙度降低18.1%,解决了FTS系统与机床运动的同步问题,可补偿机床xyz三向运动误差,可用于自由曲面加工误差的修正。该方法还可用于不对称幅度较大的曲面或硬脆性材料的加工等,故促进了高精度光学自由曲面的推广应用。     

自由曲面测量点云数据的建模方法研究

本文提出了一种散乱点云数据的建模新方法。通过对点云数据进行空间三维划分，实现了边界信息的高效提取。采用局部曲面拟合方式得到位于截平面上的有序数据，使得无序的散乱数据形成了有序的阵列数据，实现了NURBS曲面的精确拟合。实验证明，该方法非常适合卷曲类模型的自由曲面重构，在某零件的测量、建模和加工中已经得到了实际应用。     

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.     

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.     

Accessible regions of tool orientations in multi-axis milling of blisks with a ball-end mill

Noninterference tool orientations are hard to be determined in multi-axis milling of blisks, because the integrated structure of blisks introduces more geometrical constraints. To address this problem, an original approach without interference detection is proposed to solve accessible regions of tool orientations in milling of blisks. Based on the visibility of checking surfaces, only critical points on surface profiles are searched and processed to construct the accessible regions. In this approach, the start point of each profile is sought on boundaries of the main surface with a constant step length. From this point, a new critical point is first searched along a specified direction and then adjusted iteratively until it locates on a profile. When all critical points on profiles are searched like this, the searched points on each checking surface are reordered to form one or more than one closed curve to present the accessible region related to this checking surface. These curves are then mapped onto a unit sphere and divided into nonintersecting segments. After that, a concise approach is proposed to combine accessible regions of all checking surfaces into simply connected regions. This algorithm is finally verified with two kinds of blisks and compared with a referenced method. The results show that the proposed method can efficiently solve accessible regions in multi-axis milling of blisks with an expected accuracy.     

Adaptive tool-path generation on point-sampled surfaces

In this paper, we present a new approach to generate tool paths for machining point sampled surfaces using a direct projection algorithm, which is based on generating tool paths along planar intersection curves. In our implementation, a guide surface, with simple geometry like planes or cylinder surfaces, is first created according to the bound volume of the point cloud and initial tool paths are planned on it in terms of the motion pattern of the cutters. For each point of the initial tool paths, then, the corresponding cutter contact point (CC) of the point set surface is located by projecting the point onto the point cloud using the direct projection algorithm. In order to obtain adaptive cutter location points (CL), a least squares-based curve fitting method is applied to approximate the CC points using piecewise cubic Bezier, and a numerical method derived to estimate the length of the curve is used to adjust the position of the points along the curve, and make them evenly spaced on the curve with equal arc lengths. In addition, considering that offset curves or surfaces are necessary for locating CL points in many applications, such as machining using ball end milling cutter, torus ended milling cutters, an offset strategy for cubic Bezier curves is also studied. By testing the proposed method on several point clouds, it has been demonstrated to be promising.     

A method for deforming a surface model using guide surfaces in shoe design

This paper presents a method for deforming a surface model using guide surfaces. Two guide surfaces are given as references on which the surface model lies before and after deformation. The proposed method consists of two steps: surface development and model deformation. The surface development first constructs a one-to-one mapping between two guide surfaces and yields displacement constraints. Displacement constraints are then used to create a smooth 3D vector field, a deformation function for model deformation which maps an arbitrary point on the original model onto the corresponding point on the deformed model. The proposed method, implemented as a module of the shoe design system in C++ and Unigraphics using UG/Open, can also be applied to a variety of design problems (e.g., clothing).     

Prediction of surface reconstruction uncertainties for freeform surface inspection

A method is introduced to predict uncertainties of the B-spline freeform surfaces that are reconstructed from the measurement points for inspection of freeform surfaces. The uncertainties of a reconstructed B-spline surface are modeled by variances of coordinates of points on this freeform surface. Prediction of the uncertainty at any location on the reconstructed B-spline surface is carried out in two steps: (1) estimation of variances of the B-spline surface’s control points introduced by the surface reconstruction process, and (2) propagation of the variances from the control points to the points on the B-spline freeform surface. In this research, the variances of the control points of the reconstructed B-spline surface in all three directions are considered to improve the accuracy of uncertainty prediction in the regions with significant changes of geometric shapes. Both the errors and uncertainties at different locations on the reconstructed surface are considered in freeform surface inspection to compare the manufactured surface against the design surface and its tolerance. The developed method has been applied to two case studies to demonstrate its effectiveness.     

基于参数曲面建模的车身表面逆向设计研究

针对在汽车车身设计逆向工程过程中,由于雕塑模型的精度有限以及三坐标测量的机测误差,所得的散乱点不能真实反映曲面形状而建立了一种曲面拟合方法,能够减小误差较大点的影响,保证据散乱点求得的曲面最接近于"理想"曲面.并简述了车身曲面逆向设计拟合方法的数学模型和CATIA软件创成式曲面设计模块的主要功能.将车身曲面的逆向设计分为2D图纸和3D实物逆向设计2类,给出设计流程和应用开发实例,解决了设计中容易出现的问题.     

Measurement of nonrigid freeform surfaces by coordinate measuring machine

Nonrigid part could be subjected to significant distortion after the removal of manufacturing forces. This condition, known as free-state variation, is principally due to weight and flexibility of the part and the release of internal stresses resulting from fabrication. The present work deals with the inspection of freeform surfaces belonging to nonrigid parts. A manufactured aeronautic component, named Mid Cowling, is considered as case study. The design of an appropriate fixture equipment will be firstly presented: it enables both to simulate the mating part interface and to locate the part in coordinate measuring machines working volume. Then, a method for evaluation of a freeform surface with respect to the nominal one will be presented. This evaluation is based on Euclidean distance between actual and nominal surfaces. Finally, an analysis of the part deformation presented in order to evaluate the measurement process in terms of interaction of the measurement system with the inspected part will be proposed. The adopted method, based on a finite element analysis, was proposed in order to evaluate the interaction, due to the measuring force, between the touch probe and the inspected surface and thus its effect on the measurement result.     

回转曲面及变形在花朵造型中的应用

花朵各部分的形状大多接近于回转曲面;提出了通过回转曲面变形获得所需曲面。对回转曲面的变形,主要是通过对其母线和轴线加变形函数实现;这种方法构造曲面参数方程较为简单,易于实现且执行速度快,是花朵造型的一种实用方法。     

Imageware中光滑拼接曲面的方法

逆向工程软件的曲面反求中,曲率较大的地方往往难以得到较好的曲面反求效果,针对该问题提出了一种基于曲率变化的分块曲面构建拼接方法。该方法根据曲率显示的点的颜色特征进行点云数据的分割,分别获得单片光滑曲面,然后将单片曲面拼接起来以实现完整的自由曲面造型。在曲面拼接过程中,调整两片曲面相邻两列控制点,使其三点共线,以达到拼接处一阶连续。最后通过一个典型的实例证明该方法构造的曲面与原始点云的最大误差为由点阵直接拟合生成的曲面误差的1／3,为由点一线一面构造的整块曲面误差的1／5。     

基于面形斜率的光学自由曲面表征

对光学自由曲面设计的关键问题——光学自由曲面的表征模型进行了研究。在传统高斯径向基模型的基础上,通过改善基函数的分布特性以及基于面形斜率调整基函数的形状因子,建立了基于面形斜率的高斯径向基表征模型。利用建立的模型、传统径向基模型和Zernike多项式模型拟合了不同类型的自由曲面,并进行了分析比较。结果证实了文中提出的模型较传统径向基模型的面形拟合精度提高了1~2个数量级,具有较强的面形表征能力。应用该模型进行了离轴三反系统的设计,结果显示设计的三反系统的全视场平均调制传递函数(MTF)达到80%以上。与传统面形表征模型相比,该模型的应用提高了系统的像差平衡能力,改善了系统的成像质量。综合分析表明,该模型适用于表征具有显著非对称性的、面形矢高带有显著局域性变化的自由曲面,有望应用于具有大离轴量和大视场的光学系统设计中。     

Barrel cutter design and toolpath planning for high-efficiency machining of freeform surface

Improvement of machining efficiency is always one of the most interesting problems in CNC machining. Traditionally, the ball-end cutter is widely used in sculptured surface machining for the highly flexible controllability. But the process efficiency is low especially for freeform surface machining, which generally needs multiple tool-paths. To improve the machining efficiency of multi-axis flank milling of freeform surface, a novel barrel cutter design method is proposed in this paper. There are two principle parameters determining the revolution surface of the barrel cutter: the radius of the generatrix curve and the maximum rotating radius. The main work in this paper is to calculate the two parameters for strip-width-maximization machining without local over-gouging. Firstly, the curvature properties are introduced by the geometry model of the barrel cutter. Then the contact condition between the barrel cutter and the freeform surface is analyzed, relationship between cutter parameters and surface curvature is derived. To avoid the over-gouging, based on the curvature constraint, the designed surface is fitted into the cutter surface by surface approximation theory, so that the cutter surface can approach to the designed surface as close as possible. After that, toolpath planning method for milling of freeform surface with the barrel cutter is presented. Finally, machining implementations are presented to verify the effectiveness of the proposed method.