Geometric Representation And Processing For Additive Manufacturing

As a kind of new integrated manufacturing technology,3D printing(Additive Man-ufacturing)is good at fabricating the object that has a complex internal structure.It is an effective supplement to traditional manufacturing technology and is widely used in many fields.The STL format(or its variants),which is currently used as geometry file standard in 3D printing,has encountered a lot of difficulties and challenges in practical applications.The rapid development of 3D printing technology has put forward higher requirements on developing our own Geometry Exchange Specification for Additive Manufacturing.To this end,we propose to study some key theory and algorithms for geometric representation,processing,and fabrication in 3D printing.The main research contents of this paper include:(1)Implicit geometric model construction method based on signed distance function(SDF)representation for 3D printing;(2)Implicit solid compression method based on 3D B-spline representation;(3)Function representation(F-rep)based 3D printing slicing engine and manufacturing related processing algo-rithms.The signed distance function of a region(set)in a metric space determines the dis-tance of a given point from the boundary of the region,with the sign determined by whether the point is in the region.The function has positive values at points inside the region and negative values at points outside the region,and it takes zero at the boundary of the region.The signed distance function can effectively describe shapes(geometric models),and is widely used in the fields of image processing,computational geometry,curve and surface reconstruction,etc.We establish a sparse optimization model of the signed distance field based on Eikonal equation,and propose a new method to obtain the SDF.Unlike the level set computation on Cartesian grids,we use spline function to approximate a smooth signed distance field,and provide a method to construct SDF-rep implicit geometric model for 3D printing.The experimental results show that the proposed method can still reconstruct SDF from sampling points without normal infor-mation,and the reconstructed SDF can be used to generate approximate offset curves and surfaces,which have great advantages in path planning for 3D printing.Due to advantages in solid modeling with complex geometry and its ideal suitabil-ity for 3D printing,the implicit representation has been widely used in recent years.The demand for free-form shapes makes the implicit tensor-product B-spline represen-tation attract more and more attention.However,it is an important challenge to deal with the storage and transmission requirements of enormous coefficient tensor.We propose a new compression framework for coefficient tensors of implicit 3D tensor-product B-spline solids.The proposed compression algorithm consists of four steps,i.e.,preprocessing,block splitting,using a lifting-based 3D discrete wavelet transform,and coding with 3D set partitioning in hierarchical trees algorithm.Finally,we manage to lessen the criticism of the implicit tensor-product B-spline representation of surface for its redundancy store of 3D coefficient tensor.Experimental results show that the proposed compression framework not only achieves satisfactory reconstruction quality and considerable compression ratios,but also supports progressive transmissions and random access by employing patch-wise coding strategy.We present a framework for a 3D printing slicer that is specially designed for func-tion representation(F-rep)models.A direct slicing scheme for F-rep models is pro-posed,avoiding the expensive steps of generating intermediate triangle meshes,so the memory cost of our approach is low.Interval arithmetic provides an adaptive sampling mechanism,which is a key strategy to improve efficiency by reducing the sampling points.The marching squares algorithm and the bisection method ensure that the con-tour we extracted is function-faithful,which safeguards the accuracy and the topolog-ical correctness.The strategies of inner shells,sparse infill,internal ceiling supports and creating hollow models are also explored.The experimental results show signif-icant advantages of the proposed directly slicing method over the conventional STL based method both in terms of time and memory consumption.The good performance of direct slicing of F-rep models supports the view that F-rep is more suitable than the traditional B-rep as a specified input geometry of 3D printing.These researches will build solid theoretical foundation for 3D printing technol-ogy and provide reliable tools and key algorithms for high-end manufacture industry in China.