Internal architecture design and freeform fabrication of tissue replacement structures

Modeling, design and fabrication of tissue scaffolds with intricate architecture, porosity and pore size for desired tissue properties presents a challenge in tissue engineering. This paper will present the details of our development in the design and fabrication of the interior architecture of scaffolds using a novel design approach. The interior architecture design (IAD) approach seeks to generate layered scaffold freeform fabrication tool path without forming complicated 3D CAD scaffold models. This involves: applying the principle of layered manufacturing to determine the scaffold individual layered process planes and layered contours; defining the 2D characteristic patterns of the scaffold building blocks (unit cells) to form the Interior Scaffold Pattern; and the generating the process tool path for freeform fabrication of these scaffolds with the specified interior architecture. Feasibility studies applying the IAD algorithm to example models with multi-interior architecture and the generation of fabrication planning instructions will also be presented.     

Efficient Hausdorff Distance computation for freeform geometric models in close proximity

We present an interactive-speed algorithm for computing the Hausdorff Distance (HD) between two freeform geometric models represented with NURBS surfaces. The algorithm is based on an effective technique for matching a surface patch from one model to the corresponding nearby surface patch on the other model. To facilitate the matching procedure, we employ a bounding volume hierarchy (BVH) for freeform NURBS surfaces, which provides a hierarchy of Coons patches and bilinear surfaces approximating the NURBS surfaces (Kim et al., 2011 [1]). Comparing the local HD upper bound against a global HD lower bound, we can eliminate the majority of redundant surface patches from further consideration. The resulting algorithm and the associated data structures are considerably simpler than the previous BVH-based HD algorithms. As a result, we can compute the HD of two freeform geometric models efficiently and robustly even when the two models are in close proximity. We demonstrate the effectiveness of our approach using several experimental results.     

Adaptive tool-path generation of rapid prototyping for complex product models

Rapid prototyping (RP) provides an effective method for model verification and product development collaboration. A challenging research issue in RP is how to shorten the build time and improve the surface accuracy especially for complex product models. In this paper, systematic adaptive algorithms and strategies have been developed to address the challenge. A slicing algorithm has been first developed for directly slicing a Computer-Aided Design (CAD) model as a number of RP layers. Closed Non-Uniform Rational B-Spline (NURBS) curves have been introduced to represent the contours of the layers to maintain the surface accuracy of the CAD model. Based on it, a mixed and adaptive tool-path generation algorithm, which is aimed to optimize both the surface quality and fabrication efficiency in RP, has been then developed. The algorithm can generate contour tool-paths for the boundary of each RP sliced layer to reduce the surface errors of the model, and zigzag tool-paths for the internal area of the layer to speed up fabrication. In addition, based on developed build time analysis mathematical models, adaptive strategies have been devised to generate variable speeds for contour tool-paths to address the geometric characteristics in each layer to reduce build time, and to identify the best slope degree of zigzag tool-paths to further minimize the build time. In the end, case studies of complex product models have been used to validate and showcase the performance of the developed algorithms in terms of processing effectiveness and surface accuracy.     

激光直接制造和再制造中的三维CAD模型直接分层技术

在分析SolidWorks软件平台下CAD模型数据的内部表达方法以及拓扑信息和几何信息提取方法的基础上,研究三维CAD模型直接分层技术.对SolidWorks进行二次开发,调用SolidWorks应用程序接口函数中的曲面一曲面求交函数对CAD模型曲面与分层平面求交,得到的交线首尾相连形成轮廓轨迹;同时研究了光栅填充扫描算法及程序实现.为实现切片数据的通用化,设计了记录切片数据的文件格式,用直线、圆弧或圆描述分层轮廓.对上述的直接分层不仅进行了软件模拟,还用于直接制造.制作的试件与STL间接分层试件比较结果表明,采用直接分层的试件的精度和表面质量优于STL间接分层.     

A surface based approach to recognition of geometric features for quality freeform surface machining

The paper presents a surface-based approach for geometric feature recognition for the purpose of automating the process planning of freeform surface machining. The proposed approach consists of the following four steps for recognition of the geometric features: conversion and preprocessing of the surface geometry data, subdivision of NURBS surface, reconstruction of surface orientation areas, and recognition of geometric features. The proposed scheme assumes that the input geometry data form is based on an IGES CAD model and the surface model can be represented in the form of trimmed NURBS surfaces. The connectivity relations of the product surfaces are analyzed and each surface is subdivided into orientation regions based on the surface normal vector over a certain point density grid, and then all the connected regions with the same orientation type are grouped into surface orientation areas. After that, the geometric feature will be recognized through the analysis of area connectivity and relationship. The paper describes the developed algorithms on surface orientation region subdivision, surface orientation area reconstruction, and geometric feature recognition. The verified feasibility study of the developed method is also presented.     

Process planning strategies for solid freeform fabrication of metal parts

Process planning of additive manufacturing of metals is a research interest because of the applications of solid freeform fabrication of metal parts in industry. The strategy is to transform the model of the part into the combinations of 2D layers that will be deposited using different fabrication methods. Process planning for metal deposition in this paper consists of three major modules: spatial decomposition, slicing of the part, and toolpath generation for every slicing layer. Algorithmic improvements are proposed and implemented for these major modules. For spatial decomposition, 3D part decomposition based on modular boundary models and centroidal axis extraction methods are combined to decompose parts more robustly and reliably. For generating slicing layers, a planning process for building non-uniform layers is investigated to greatly increase the variety of the parts that can be manufactured without the need of support structure. For toolpath generation methods, optimization of the generated toolpath is studied especially for complex thin-wall structures to ensure the deposition quality. Experiments were carried out to evaluate the improvements of the major modules of process planning strategies for rapid manufacturing.     

A new adaptive slicing approach for the fully dense freeform fabrication (FDFF) process

Fully dense freeform fabrication (FDFF) is a process based on thin line cutting processes, variable thickness layering, slicing in different orientations, and bulk layer attachment. The combination of these capabilities enables the production of good quality complex parts from practically any material at a very fast pace. As for rapid prototypes fabricated by the FDFF process, it is certainly possible to employ adaptive slicing technique due to the possibility of cutting different metal/non-metal sheet at various thicknesses. This paper proposes a new adaptive slicing method whereby the capability of cutting a 3D solid model at the predefined sheets’ thicknesses is achieved and the geometry of all internal and external features of a part is also investigated to ensure the reduction of part geometry deviation through the seamless curvature detection. Despite most previous works which start slicing a tessellated or direct CAD model at the maximum available thickness, this system commences the process with available minimum thickness by applying a new adaptive method to all pairs of contours at the top and bottom slices of the layer. Autodesk Inventor solid modeler, as a design-by-feature solid modeler, is used for 3D solid modeling. The proposed system is implemented by Visual Basic codes inside Inventor using API functions to access both geometry and topology information of the design-by-feature solid model. This system has been successfully tested on a variety of complex parts containing sophisticated internal and external features.     

NURBS体参数化模型的无支撑打印算法

处理大角度悬垂结构的打印问题是无支撑打印的主要挑战。针对NURBS（non-uniform rational Bspline）体参数化模型的多自由度无支撑三维打印技术,提出一种锥形切片算法。通过对模型的三维文件进行几何映射,利用水平切片算法对其进行切片,得到模型变形后的连续打印路径G-code;然后对得到的G-code进行逆映射,生成适用于六轴机械臂的多自由度连续打印路径。利用锥形切片算法规划打印路径,可以在无须支撑的情况下,依靠自支撑结构实现对悬空结构部分的打印。最后,通过仿真实验和对比实验,验证了锥形切片算法的准确性、可行性和有效性。锥形切片算法的引入为NURBS体参数化模型的无支撑三维打印提供了一种更加高效、经济和环保的解决方案。     

NURBS surface fitting using orthogonal coordinate transform for rapid product development

Constructing a CAD model from a physical model plays a key role in some rapid product development processes. Presented in the paper is a method of fitting NURBS surfaces for rotational freeform shapes: (1) cloud-of-points data (COP-data) representing a rotational freeform shape are transformed into an orthogonal coordinate system, (2) a single-valued B-spline surface is fitted to the transformed data, and (3) the resulting B-spline surface is converted to a 3D NURBS surface by applying a symbolic product operation with a quadratic NURBS base-geometry. Compared to the existing ‘direct’ fitting methods, the proposed method has some distinctive advantages: it provides a natural means to parameterization, enables to recover exact NURBS geometry when the COP-data represent a true surface-of-revolution, and allows an easy point-membership classification for NURBS-bounded solid objects.     

基于分层切片原理的三维雕刻算法

分析了多种基于STL模型的快速分层算法。在综合多种算法优点的基础上,首先提出了对三角面片的顶点按其切片方向进行从小到大排序,以快速滤除冗余顶点;并在此基础上建立三角面片的顶点链表及面向量,以实现STL模型的拓扑信息重构;最后基于所重构的拓扑信息,结合几何连续性分层算法实现高效的自适应分层算法。并通过C+〖KG-*3〗+实现了这一算法,证明了快速成型技术的分层制造思想可应用于三维雕刻的CAD/CAM,在技术上是可行的。     

A simple technique for NURBS shape modification

Non-uniform rational B-splines (NURBS) have become a de-facto industry standard primarily because they offer a unified mathematical form for representing both freeform shapes and analytical curves or surfaces. Despite these advantages, designers need software that lets them work with NURBS in a natural way. The paper presents a unified approach to NURBS shape modification that builds on a perspective functional transformation of arbitrary origin and provides a homogeneous interface based on simple, easily understood geometric concepts     

带平台伸缩函数的参数曲线变形

目的 随着科学技术的快速发展,曲线的几何造型技术开始成为近来的热点研究方向.为了获得更多的变形效果,面向2维、3维参数曲线和自由曲线变形,提出一种带平台伸缩函数的变形方法。方法 有别于现有的大多数自由变形算法,首先构造了一种形式简洁的多项式形式伸缩函数;其次借助于伸缩函数,构造了含有伸缩参数与光滑参数的新型伸缩因子,算法表明,这种新型伸缩因子具有单点峰值性、区间峰值性、对称性等优良性质;最后将伸缩因子所构造变形矩阵作用于待变形的曲线,通过控制变形区间、伸缩参数、光滑参数以及变形方向,可以获得整体的、局部的、周期的、伸缩的等各类丰富的图形效果。结果 此变形操作对造型系统中的主流参数曲线(Bézier和NURBS)具有封闭性;通过大量数值实例表明了该方法计算量小,可控性强,重复使用可以得到形状多样、具有艺术效果的轮廓线等效果。结论 与其他方法相比,本文算法不仅可以用于一般的平面与空间参数曲线,也可以用于自由型曲线,扩大了多数自由变形算法的适用范围;由于伸缩函数具备单点峰值性、区间峰值性、对称性等性质,从而能够产生以前变形方法无法产生各类角点、尖点的特殊曲线,在一定程度上极大丰富了曲线的变形效果。     

A New Approach for Direct Manipulation of Free-Form Curve

There is an increasing demand for more intuitive methods for creating and modifying free-form curves and surfaces in CAD modeling systems. The methods should be based not only on the change of the mathematical parameters, such as control points, knots, and weights, but also on the user's specified constraints and shapes. This paper presents a new approach for directly manipulating the shape of a free-form curve, leading to a better control of the curve deformation and a more intuitive CAD modeling interface. The user's intended deformation of a curve is automatically converted into the modification of the corresponding NURBS control points and knot sequence of the curve. The algorithm for this approach includes curve elevation, knot refinement, control point repositioning, and knot removal. Several examples shown in this paper demonstrate that the proposed method can be used to deform a NURBS curve into the desired shape. Currently, the algorithm concentrates on the purely geometric consideration. Further work will include the effect of material properties.     

One-sided offset approximation of freeform curves for interference-free NURBS machining

Generating valid tool path curves in NURBS form is important in realizing an efficient NURBS machining. In this paper, a method for computing one-sided offset approximations of freeform curves with NURBS format as tool paths is presented. The approach first uses line segments to approximate the progenitor curve with one-sided deviations. Based on the obtained line approximating curve and its offsets, a unilateral tolerance zone (UTZ) is constructed subsequently. Finally, a C¹-continuous and completely interference-free NURBS offset curve is generated within the UTZ to satisfy the required tolerance globally. Since all of the geometric computations involved are linear, the proposed method is efficient and robust. Interference-free tool path generation thus can be achieved in NURBS based NC machining.     

Tool path generation for a surface model with defects

A 3-axis tool path generation algorithm for free-form surface models including defects, such as gaps and overlaps is presented in this paper. To avoid the difficulty of computing a complete cutter location (CL)-surface, the proposed approach generates a tool path by slicing CL-elements instead of a complete CL-surface. A key feature of the proposed approach is that it reduces the number of CL-elements to be sliced by utilizing the correspondence information between CL-elements and cutter contact (CC)-elements. This feature significantly improves the computational efficiency of the proposed algorithm. Empirical tests show that the proposed approach is robust to geometric defects of CAD models, gaps and overlaps, with a near O(n) time complexity, where n is the number of slicing planes.     

Interactive rendering of NURBS surfaces

NURBS (Non-uniform rational B-splines) surfaces are one of the most useful primitives employed for high quality modeling in CAD/CAM tools and graphics software. Since direct evaluation of NURBS surfaces on the GPU is a highly complex task, the usual approach for rendering NURBS is to perform the conversion into Bézier surfaces on the CPU, and then evaluate and tessellate them on the GPU. In this paper we present a new proposal for rendering NURBS surfaces directly on the GPU in order to achieve interactive and real-time rendering. Our proposal, Rendering Pipeline for NURBS Surfaces (RPNS), is based on a new primitive KSQuad that uses a regular and flexible processing of NURBS surfaces, while maintaining their main geometric properties to achieve real-time rendering. RPNS performs an efficient adaptive discretization to fine tune the density of primitives needed to avoid cracks and holes in the final image, applying an efficient non-recursive evaluation of the basis function on the GPU. An implementation of RPNS using current GPUs is presented, achieving real-time rendering rates of complex parametric models. Our experimental tests show a performance several orders of magnitude higher than traditional approximations based on NURBS to Bézier conversion.     

Interactive design exploration for constrained meshes

In architectural design, surface shapes are commonly subject to geometric constraints imposed by material, fabrication or assembly. Rationalization algorithms can convert a freeform design into a form feasible for production, but often require design modifications that might not comply with the design intent. In addition, they only offer limited support for exploring alternative feasible shapes, due to the high complexity of the optimization algorithm.We address these shortcomings and present a computational framework for interactive shape exploration of discrete geometric structures in the context of freeform architectural design. Our method is formulated as a mesh optimization subject to shape constraints. Our formulation can enforce soft constraints and hard constraints at the same time, and handles equality constraints and inequality constraints in a unified way. We propose a novel numerical solver that splits the optimization into a sequence of simple subproblems that can be solved efficiently and accurately.Based on this algorithm, we develop a system that allows the user to explore designs satisfying geometric constraints. Our system offers full control over the exploration process, by providing direct access to the specification of the design space. At the same time, the complexity of the underlying optimization is hidden from the user, who communicates with the system through intuitive interfaces.     

基于区域分割的三维自由曲面相似性评价算法

为了在工程应用中检索已有的三维CAD模型,以便重用相应零件的设计信息,节省设计和加工成本,提出一种基于曲面分割技术的CAD自由曲面相似性评价算法.依据曲面的曲率将自由曲面分割成具有相对固定曲率特征的不同区域;对每个分割得到的区域用一个7维向量表达其形状的几何特征和拓扑特征,一个自由曲面形状特征即可通过各分割区域所对应的7维向量组成的向量组表达;将该向量组作为自由曲面的形状描述子,2个自由曲面的相似性可通过相对应的形状描述子间的相似性表达.在评价2个曲面形状描述子的相似性时,将描述子中的每个向量看成是一个带有属性的节点,2个形状描述子所对应的2组属性节点可看成是一个二分图,2组属性节点间相应节点距离看成是二分图的权值,并利用赋权二分图最优匹配的算法求出2组属性节点的相似性,实现2个自由曲面之间的相似性评价.实验结果表明,该算法是有效、可行的.     

Signed algebraic level sets on NURBS surfaces and implicit Boolean compositions for isogeometric CAD–CAE integration

Boundary-representation (B-rep) geometrical models, often mathematically represented using Non-Uniform Rational B-Spline (NURBS) surfaces, are the starting point for complex downstream product life-cycle evaluations including Computer-Aided Engineering (CAE). Boolean operations during B-rep model generation require surface intersection computations to describe the composed entity. However, for parametric NURBS surfaces, intersection operations are non-trivial and typically carried out numerically. The numerical intersection computations introduce challenges relating to the accuracy of the resulting representation, efficiency with which the computation is carried out, and robustness of the result to small variations in geometry. Often, for downstream CAE evaluations, an implicit, procedural knowledge of the Boolean operations between the composed objects that can resolve point containment queries (exact to the original NURBS bounding surfaces) maybe sufficient during quadrature. However, common point containment queries on B-rep models are numerical, iterative and relatively expensive. Thus, the first goal of the present paper is to describe a purely algebraic, and therefore non-iterative, approach to carrying out point containment queries on complex B-rep models built using low-degree NURBS surfaces. For CAE operations, the boundary representation of B-rep solids is, in general, not convenient and as a result, the B-rep model is converted to a meshed volumetric approximation. The major challenges to such a conversion include capturing the geometric features accurately when constructing the secondary (meshed) representation, apart from the efficiency of carrying out such a mesh generation step repeatedly as the geometric shape evolves. Thus, an ideal analysis procedure would operate directly on B-rep CAD models, without needing a secondary mesh, and would procedurally unify the geometric operations during CAD as well as CAE stages. Therefore, the second and broader goal of the present paper is to demonstrate CAD–CAE integration using signed algebraic level set operations directly on B-rep models by embedding or immersing the bounding surfaces within a discretized domain while preserving the geometric accuracy of the surfaces exact to the original NURBS representation during analysis.