基于深度剥离的三维打印模型朝向优化算法

为了提高三维打印产品表面质量且有效节省材料,提出一种面向熔融挤压式三维打印机的模型朝向优化算法.该算法基于深度剥离技术,以打印朝向为自变量构建模型悬空面积及其支撑结构体积的双目标优化函数;利用模式搜索方法设计一个两步走的优化方案来确定最优的打印朝向.实验结果表明,利用深度剥离技术能够较为准确、高效地检测出打印模型悬空区域,并计算出相应的悬空面积和支撑体积;设计的优化方案也能够根据双目标的权重比确定一个较优的打印朝向,不但减少了支撑结构与模型表面的接触范围,还能降低支撑结构的体积.文中算法在提高模型表面质量以及减少支撑结构的材料消耗两方面具有优势.     

三维形状的自支撑晶体结构的逼近与填充EI北大核心CSCD

针对三维打印无法制造具有悬空杆和悬空节点的晶体结构的问题,提出自支撑晶体结构针对三维形状的逼近与填充算法.首先以菱形六面体为晶体单元,构造晶体单元的几何形状与其自支撑性的函数关系,进一步生成包围三维形状的最小自支撑晶体单元;然后在最短边长与细分次数的约束下,通过晶体单元的迭代细分对三维形状进行逼近;最后,对悬空节点添加支撑杆以保证整体结构的可打印性.另外,通过晶体结构的细分生成三维形状的自支撑填充结构.实验对选自3D ShapeNet数据库的三维模型进行逼近与填充,在VS 2010和MATLAB R2017a平台上进行算法的实现和结果的可视化,结果表明了所提算法对三维形状的逼近与填充的有效性和鲁棒性.     

基于STL文件的柱状支撑结构自动生成算法

熔融挤压三维打印以热塑性材料为原料逐层打印完成,由于熔丝只能沉积在已存在的物体上层,模型悬空部位需要添加支撑结构。为解决该问题,提出一种基于STL(Stereo Lithography)文件的稀疏柱状支撑结构自动生成算法。算法通过对比三角面片倾斜角度与模型临界角的大小,获取独立的待支撑区域,然后基于边长自适应法和射线与面片相交法得到待支撑点集,自动生成支撑结构。此外为了保证模型表面质量和支撑结构的稳定性,支撑结构不在模型表面生成。调整支撑结构形状,进一步提高支撑结构的稳定性。通过实验证明本文算法比Cura软件节约15%的材料消耗,支撑结构更容易剥离,模型表面质量更好。     

面向耗材节省的三维打印路径规划算法研究

为降低三维打印（three-dimensional printing,3D）耗材费用并进一步提高打印效率,给出一种面向熔融沉积制造的三维打印路径规划算法。该方法综合考虑打印耗材、打印效率以及打印表面质量等因素,通过网格模型及其支撑的相邻层片轮廓关系求得可稀疏打印区域;基于多边形扫描线算法以及多边形单调链关系,得到能够连续打印的路径区域;最终通过区域路径稀疏化得到改进的打印路径。通过复杂网格模型的三维打印路径规划实例,验证了算法的有效性。该算法能够降低打印耗材数量,并进一步提高打印效率。     

曲面浮雕的高效表示及3D打印算法

针对3D浮雕网格点数、面数空间占用大,在打印过程中耗费内存等缺点,提出将凹凸贴图表示的浮雕模型直接进行切片完成打印,并提出基于凹凸贴图的浮雕网格的3D打印自适应细分切片算法.在切片过程中,先对输入的粗网格根据凹凸图深度信息进行自适应中点细分,并更新细分后三角网格顶点的几何位置;然后对生成的局部三角网格集合与切片进行求交运算,将所获得的交线段存储后释放此三角形集合的内存;最后将生成的交线段重组成闭合多边形,生成打印路径,交由打印机完成浮雕模型打印.实验结果证明,将凹凸贴图推广到3D打印中,与传统的打印过程进行对比,该方法的空间利用率得到显著性提高.     

高性能非结构化四面体网格解耦并行生成算法

针对大规模科学计算领域非结构化网格生成问题,提出一种基于AFT-Delaunay方法的三维复杂域解耦并行四面体网格生成算法.该算法以待剖分三维域的闭合的表面三角形网格为输入,采用边界一致约束Delaunay剖分方法串行地生成较小规模的初始四面体网格;采用界面优先策略扩展三维AFT-Delaunay方法,以几何分界面为参考指引前沿推进方向,在分界面处生成一层由四面体单元构成的有厚度的"墙",递归、并行地将初始四面体网格分割成完全解耦的子区域;此时,各子区域均为不含内部节点的四面体网格,继续利用AFT-Delaunay方法解耦并行地生成各子区域内部四面体网格.算例结果表明,文中算法很好地解决了分界面处网格质量差的难题以及收敛性问题,具有较好的并行效率及几何适应性,可在PC平台全自动地完成108量级的非结构四面体网格生成.     

医学体数据中基于局部特征尺寸的Delaunay四面体化算法*

为了从医学体数据构建面向虚拟手术仿真系统的器官实体模型,提出一种基于局部特征尺寸的Delaunay四面体化算法。首先采用Marching Cubes算法和外存模型简化技术从体数据中得到器官等值面简化模型,提出重心射线法去除内部冗余网格,获得器官多面体表面;然后基于局部特征尺寸构建表面顶点保护球,结合Delaunay细分算法生成边界一致的初始四面体网格;最后提出基于随机扰动的空间分解法快速生成内部节点,并逐点插入到四面体网格中优化单元质量。该算法克服了Delaunay细分算法无法处理锐角输入的缺点,并从理论     

三维有限元网格尺寸场光滑化的优化模型和算法

针对单元尺寸值过渡剧烈会导致有限元网格包含低质量单元的问题,提出基于优化原理的单元尺寸场光滑化理论及对应的几何自适应四面体网格生成算法.首先输入CAD模型,生成一套覆盖模型内部的非结构背景网格;然后结合用户参数计算背景网格点上的曲率和邻近特征,以获得自适应CAD模型几何特征的初始单元尺寸场;再以最小化初始单元尺寸场的改变为目标,以单元尺寸值过渡受控为约束,通过求解一类凸优化问题光滑初始尺寸场;最后以光滑后的尺寸场为输入,先后在CAD模型表面与内部生成曲面网格和实体网格.实验结果表明,文中算法仅需5个用户参数,即可在给定CAD模型内部全自动生成高质量的四面体网格.     

熔丝沉积制造中稳固低耗支撑结构生成

熔丝沉积制造(Fused deposition modeling, FDM)是利用熔融塑料丝的一种3D打印技术,热塑料由喷嘴喷出逐层堆积完成打印.由于熔丝只能沉积在已存在物体的上层,因此需要构造支撑结构以支撑悬空部分.针对现有支撑结构生成算法中存在的或结构不稳固或耗材多的缺陷,提出一种以熔丝为支撑单位的树形稀疏支撑结构.与传统算法计算模型表面支撑区域不同,本算法计算每段熔丝需要支撑的区域,使支撑结构更契合熔丝沉积特点.算法还将支撑结构分为三类,将多约束优化问题分解,降低算法复杂度.实验结果表明,本文算法生成的支撑结构算法耗材少、支撑稳定.     

表驱动的细分曲面GPU绘制

为了充分利用GPU的并行计算能力高效地绘制递归定义的细分曲面,提出一种基于GPU的面分裂细分曲面的实时绘制算法.该算法通过离线预计算生成可以复用的细分查找表,它由细分矩阵组成,其大小仅与奇异点度数和最大细分深度线性相关,与输入网格无关;对于细分曲面控制网格的每个曲面片,如果包含2个或2个以上奇异点,则进行一次局部预细分;之后对于不规则曲面片,利用细分查找表由初始控制网格直接计算得到各细分层次上的控制顶点,无需逐层计算,从而最大限度地发挥GPU的并行处理能力;最后对各层次上的规则曲面片使用硬件细分着色器绘制,大大提高绘制效率.实验结果表明,文中算法可以高效地绘制细分曲面的极限曲面.     

Automatic balancing of 3D models

3D printing technologies allow for more diverse shapes than are possible with molds and the cost of making just one single object is negligible compared to traditional production methods. However, not all shapes are suitable for 3D print. One of the remaining costs is therefore human time spent on analyzing and editing a shape in order to ensure that it is fit for production. In this paper, we seek to automate one of these analysis and editing tasks, namely improving the balance of a model to ensure that it stands. The presented method is based on solving an optimization problem. This problem is solved by creating cavities of air and distributing dense materials inside the model. Consequently, the surface is not deformed. However, printing materials with significantly different densities is often not possible and adding cavities of air is often not enough to make the model balance. Consequently, in these cases, we will apply a rotation of the object which only deforms the shape a little near the base. No user input is required but it is possible to specify manufacturing constraints related to specific 3D print technologies. Several models have successfully been balanced and printed using both polyjet and fused deposition modeling printers.     

六面体插值体细分方法研究与应用

细分方法是一种非常有效的表示曲线、曲面和三维体甚至高维数据的手段，针对细分方法新的研究热点问题——体细分实体造型，提出了一种新的基于六面体拓扑网格结构的插值型体细分方法，使用多元情形下生成函数的性质进行了收敛性证明，给出了计算实例；结合离散动力学方程，对细分方法初始控制网格赋予一定的物理属性和运动约束，建立动态细分体变形算法，并将其应用在三维紧身服装穿着时弹性人体变形的实际问题中．     

A geometric study of parameters for the recursive midpoint subdivision

For producing numerous frames as in computer animation, the direct application of the Mandelbrot theory of fractals is very expensive. The recursive midpoint subdivision is much more efficient although it sacrifices mathematical purity for execution speed. In our implementation, fractal polygons are created using subdivisions of meshes of triangles. But the midpoint is randomly generated inside a revolution volume where the axis is the edge itself. Based on this implementation, we study the impact of three geometric parameters for controlling this algorithm: the edge threshold, the eccentricity of the smallest cylinder surrounding the revolution volume and the displacement of the revolution volume towards the segment center. Several examples are provided. The subdivision algorithm is also applied to generate textures by perturbation of the normal length.     

大型全回转浮式起重机平衡系统优化数学模型

针对大型全回转浮式起重机的结构和工况特点,在满足抗倾覆稳定性要求下,将浮式起重机自重产生的不平衡力矩与起升货物产生的不平衡力矩之和的均方根力矩作为目标函数值,建立以平衡系统主要构件强度、刚度、结构尺寸和回转轮压合理性为约束条件的多目标设计优化数学模型,运用遗传算法优化浮式起重机平衡系统,最终得出优化数据.该数学模型在具体优化过程中取得较为满意的优化结果,为大型全回转浮式起重机的设计优化提供有效方法.     

Clever Support: Efficient Support Structure Generation for Digital Fabrication

We introduce an optimization framework for the reduction of support structures required by 3D printers based on Fused Deposition Modeling (FDM) technology. The printers need to connect overhangs with the lower parts of the object or the ground in order to print them. Since the support material needs to be printed first and discarded later, optimizing its volume can lead to material and printing time savings. We present a novel, geometry‐based approach that minimizes the support material while providing sufficient support. Using our approach, the input 3D model is first oriented into a position with minimal area that requires support. Then the points in this area that require support are detected. For these points the supporting structure is progressively built while attempting to minimize the overall length of the support structure. The resulting structure has a tree‐like shape that effectively supports the overhangs. We have tested our algorithm on the MakerBot® Replicator? 2 printer and we compared our solution to the embedded software solution in this printer and to Autodesk® Meshmixer? software. Our solution reduced printing time by an average of 29.4% (ranging from 13.9% to 49.5%) and the amount of material by 40.5% (ranging from 24.5% to 68.1%).     

Homogenization of material properties in additively manufactured structures

Additive manufacturing transforms material into three-dimensional parts incrementally, layer by layer or path by path. Subject to the build direction and machine resolution, an additively manufactured part deviates from its design model in terms of both geometry and mechanical performance. In particular, the material inside the fabricated part often exhibits spatially varying material distribution (heterogeneity) and direction dependent behavior (anisotropy), indicating that the design model is no longer a suitable surrogate to consistently estimate the mechanical performance of the printed component.We propose a new two-stage approach to modeling and estimating effective elastic properties of parts fabricated by fused deposition modeling (FDM) process. First, we construct an implicit representation of an effective mesoscale geometry–material model of the printed structure that captures the details of the particular process and published material information. This representation of mesoscale geometry and material of the printed structure is then homogenized at macro scale through a solution of an integral equation formulated using Green’s function. We show that the integral equation can be converted into a system of linear equations that is symmetric and positive definite and can be solved efficiently using conjugate gradient method and Fourier transform. The computed homogenized properties are validated by both finite element method and experiment results. The proposed two-stage approach can be used to estimate other effective material properties in a variety of additive manufacturing processes, whenever a similar effective mesoscale geometry–material model can be constructed.     

Slice coherence in a query-based architecture for 3D heterogeneous printing

We report on 3D printing of artifacts with a structured, inhomogeneous interior. The interior is decomposed into cells defined by a 3D Voronoi diagram and their sites. When printing such objects, most slices the printer deposits are topologically the same and change only locally in the interior. The slicing algorithm capitalizes on this coherence and minimizes print head moves that do not deposit material. This approach has been implemented on a client/server architecture that computes the slices on the geometry side. The slices are printed by fused deposition, and are communicated upon demand.     

PackMerger: A 3D Print Volume Optimizer

We propose an optimization framework for 3D printing that seeks to save printing time and the support material required to print 3D shapes. Three‐dimensional printing technology is rapidly maturing and may revolutionize how we manufacture objects. The total cost of printing, however, is governed by numerous factors which include not only the price of the printer but also the amount of material and time to fabricate the shape. Our PackMerger framework converts the input 3D watertight mesh into a shell by hollowing its inner parts. The shell is then divided into segments. The location of splits is controlled based on several parameters, including the size of the connection areas or volume of each segment. The pieces are then tightly packed using optimization. The optimization attempts to minimize the amount of support material and the bounding box volume of the packed segments while keeping the number of segments minimal. The final packed configuration can be printed with substantial time and material savings, while also allowing printing of objects that would not fit into the printer volume. We have tested our system on three different printers and it shows a reduction of 5–30% of the printing time while simultaneously saving 15–65% of the support material. The optimization time was approximately 1 min. Once the segments are printed, they need to be assembled.     

Efficient biased random bit generation for parallel lattice gas simulations

Lattice gas methods are often used to model the kinetics of a variety of diffusive systems. One of the main advantages of these methods is the ease at which they can be parallelized using simple bit vector operations. However, to describe the kinetics of the lattice gas in a randomly biased fashion, it is necessary to efficiently generate a randomly biased bit vector. If one generates a random floating point number per bit, then this is very costly. In this paper, an efficient algorithm is developed that leads to a fully bit vector implementation of a lattice gas automation while significantly reducing the amount of needed generated random floating point numbers. The bit vector algorithm using the new random biased bit vector algorithm is tested on a lattice gas method whose solution is modeled by the solution of the 1-D Burgers' equation. This new lattice gas method is then implemented on the BBN TC2200 and CRAY 90 parallel processors.     

Three-Dimensional Volume Datafield Reconstruction from Physical Model

This paper focuses on entirety interpretation,representation and reconstruction of three-dimensional volume data sets based on the physical model of the data.The data model is represented by three-dimensional geometric model The surfaces inside the datafield are extracted and matched to the model surfaces in order to reconstruct the new datafield based on the model.A conclusion is drawn that physical modeling provides a good basis and approach to interpret and represent the data sets.This paper also presents a subdivision algorithm to fast trace B-spline curve and the contrary algorithms is adopted to extract the geometry feature of the curve.