Local parameterization of freeform shapes using freeform feature recognition

Form feature modeling is a much used shape modeling technique that offers high-level control over a shape. When a feature-based interpretation of shape data is not available, e.g. when a shape is obtained by a laser range scanner or from a database of shapes, then the features must be reconstructed through feature recognition. Many methods for the recognition of machining features exist, but these methods cannot be used for freeform feature recognition, of which the complexity is much larger. In this paper, a new freeform feature recognition method is presented that is based on a new definition of the freeform feature concept. The method uses a three-step approach to feature recognition, in which first the global shape of a feature is matched to the target shape model. In a second step, this global shape is locally adapted to the target shape by adapting the definition of the feature. Finally, if the desired configuration of the feature has been determined, it can be used to reconstruct the target’s shape. In the first two steps, an evolutionary approach is taken to maximizing the similarity between the feature and the target shape. Finally, the target shape is reconstructed to incorporate the recognized feature. An extensive application example is given and the method is validated by applying it to a large number of artificially created test cases.     

Embedding meshes in Boolean cubes by graph decomposition

This paper explores the embeddings of multidimensional meshes into minimal Boolean cubes by graph decomposition. The dilation and the congestion of the product graph (G₁ × G₂) → (H₁ × H₂) is the maximum of the dilation and congestion for the two embeddings G₁ → H₁ and G₂ → H₂. The graph decomposition technique can be used to improve the average dilation and average congestion. The graph decomposition technique combined with some particular two-dimensional embeddings allows for minimal-expansion, dilation-two, congestion-two embeddings of about 87% of all two-dimensional meshes, with a significantly lower average dilation and congestion than by modified line compression. For three-dimensional meshes we show that the graph decomposition technique, together with two three-dimensional mesh embeddings presented in this paper and modified line compression, yields dilation-two embeddings of more than 96% of all three-dimensional meshes contained in a 512 × 512 × 512 mesh. The graph decomposition technique is also used to generalize the embeddings to meshes with wrap-around. The dilation increases by at most one compared to a mesh without wraparound. The expansion is preserved for the majority of meshes, if a wraparound feature is added to the mesh.     

Motorcycle graph enumeration from quadrilateral meshes for reverse engineering

Recently proposed quad-meshing techniques allow the generation of high-quality semi-regular quadrilateral meshes. This paper outlines the generation of quadrilateral segments using such meshes. Quadrilateral segments are advantageous in reverse engineering because they do not require surface trimming or surface parameterization. The motorcycle graph algorithm of Eppstein et al. produces the motorcycle graph of a given quadrilateral mesh consisting of quadrilateral segments. These graphs are preferable to base complexes, because the mesh can be represented with a smaller number of segments, as T-joints (where the intersection of two neighboring segments does not involve the whole edge or the vertex) are allowed in quadrilateral segmentation.The proposed approach in this study enumerates all motorcycle graphs of a given quadrilateral mesh and optimum graph for reverse engineering is then selected. Due to the high computational cost of enumerating all these graphs, the mesh is cut into several sub-meshes whose motorcycle graphs are enumerated separately. The optimum graph is then selected based on a cost function that produces low values for graphs whose edges trace a large number of highly curved regions in the model. By applying several successive enumeration steps for each sub-mesh, a motorcycle graph for the given mesh is found. We also outline a method for the extraction of feature curves (sets of highly curved edges) and their integration into the proposed algorithm. Quadrilateral segments generated using the proposed techniques are validated by B-spline surfaces.     

On surface meshes induced by level set functions

The zero level set of a continuous piecewise-affine function with respect to a consistent tetrahedral subdivision of a domain in ${\mathbb {R}}^3$ is a piecewise-planar hyper-surface. We prove that if a family of consistent tetrahedral subdivions satisfies the minimum angle condition, then after a simple postprocessing this zero level set becomes a consistent surface triangulation which satisfies the maximum angle condition. We treat an application of this result to the numerical solution of PDEs posed on surfaces, using a $P_1$ finite element space on such a surface triangulation. For this finite element space we derive optimal interpolation error bounds. We prove that the diagonally scaled mass matrix is well-conditioned, uniformly with respect to $h$ . Furthermore, the issue of conditioning of the stiffness matrix is addressed.     

Matrix computations on systolic-type meshes: an introduction to themultimesh graph method

Systolic-type arrays use both the fine-grain parallelism and the regularity of matrix computations effectively. The multimesh graph method for deriving these arrays is systematic, flexible, and easy to use     

融合图卷积和差异性池化函数的点云数据分类分割模型

目的 深度网络用于3维点云数据的分类分割任务时,精度与模型在全局和局部特征上的描述能力密切相关。现有的特征提取网络,往往将全局特征和不同尺度下的局部特征相结合,忽略了点与点之间的结构信息和位置关系。为此,通过在分类分割模型中引入图卷积神经网络（graph convolution neural network,GCN）和改进池化层函数,增强局部特征表征能力和获取更丰富的全局特征,改善模型对点云数据的分类分割性能。方法 GCN模块通过K近邻算法构造图结构,利用相邻点对的边缘卷积获取局部特征,在深度网络模型中动态扩展GCN使模型获得完备的局部特征。在池化层,通过选择差异性的池化函数,联合提取多个全局特征并进行综合,保证模型在数据抖动时的鲁棒性。结果 在ModelNet40、ShapeNet和S3DIS（stanford large-scale 3D indoor semantics）数据集上进行分类、部分分割以及语义场景分割实验,验证模型的分类分割性能。与PointNet相比,在ModelNet40分类实验中,整体精度和平均分类精度分别提升4%和3.7%;在ShapeNet部分分割数据集和S3DIS室内场景数据集中,平均交并比（mean intersection-over-union, mIoU）分别高1.4%和9.8%。采用不同的池化函数测试结果表明,本文提出的差异性池化函数与PointNet提出的池化函数相比,平均分类精度提升了0.9%,有效改善了模型性能。结论 本文改进的网络模型可以有效获取点云数据中的全局和局部特征,实现更优的分类和分割效果。     

Efficient spectral watermarking of large meshes with orthogonal basis functions

Allowing for copyright protection and ownership assertion, digital watermarking techniques, which have been successfully applied to classical media types like audio, images, and video, have recently been adapted for the newly emerged multimedia data type of 3D geometry models. In particular, the widely used spread-spectrum methods can be generalized for 3D datasets by transforming the original model to a frequency domain and perturbing the coefficients of the most dominant basis functions. Previous approaches employing this kind of spectral watermarking are mainly based on multiresolution mesh analysis, wavelet domain transformation, or spectral mesh analysis. Though they already exhibit good resistance to many types of real-world attacks, they are often far too slow to cope with very large meshes due to their complicated numerical computations. In this paper, we present a novel spectral watermarking scheme using new orthogonal basis functions based on radial basis functions. With our proposed fast basis function orthogonalization, while observing a persistence with respect to various attacks that is similar to that of other related approaches, our scheme runs faster by two orders of magnitude and thus can efficiently watermark very large models.     

Prediction of laser solid freeform fabrication using neuro-fuzzy method

In this paper, a new application of a neuro-fuzzy method (ANFIS) to laser solid freeform fabrication (LSFF) is presented. The laser solid freeform fabrication process is a complex manufacturing technique that cannot be modeled analytically due to non-linear behaviours of the physical phenomena involved in the process. A neuro-fuzzy model is proposed to predict the clad height (coating thickness) as a function of laser pulse energy, laser pulse frequency, and traverse speed in a dynamic fashion. Four membership functions are assigned to be associated with each input of the model architecture. Experiments are performed to collect data for the training of the proposed network, and a set of unseen experimental data are also considered for the verification of the identified model. The effects of the assigned inputs on the clad height are discussed. The comparison between the experimental data and the model output shows promising results. The model can predict the process with an absolute error as low as 0.07%.     

The rotation graph of k-ary trees is Hamiltonian

In this paper we show that the graph of k-ary trees, connected by rotations, contains a Hamilton cycle. Our proof is constructive and thus provides a cyclic Gray code for k-ary trees. Furthermore, we identify a basic building block of this graph as the 1-skeleton of the polytopal complex dual to the lower faces of a certain cyclic polytope.     

Composite freeform surface reconstruction using recursive interpolating subdivision scheme

Composite freeform surface reconstruction from 3D scanned data of a physical model has become a more and more important topic in the field of CAD/CAE/CAM. By repeated application of a fixed set of recursive interpolation subdivision schemes on the initial mesh of the 3D sparse scanned data of a physical model, a polygonal model of composite freeform surface can be constructed. In the paper, the algorithm for constructing the initial triangular mesh from 3D sparse scanned data is presented. The unified recursive interpolating subdivision scheme for triangular mesh is proposed. A special quad-tree data structure is suggested to store all the necessary information of the vertices and elements of the polygonal model. Examples of composite surface reconstruction are provided to explain the distinguished superiority of subdivision scheme for reconstructing the arbitrary topological complex surface.     

A constructive count of rotation symmetric functions

In this paper we present a constructive detection of minimal monomials in the algebraic normal form of rotation symmetric Boolean functions (immune to circular translation of indices). This helps in constructing rotation symmetric Boolean functions by respecting the rules we present here.     

Digital watermarking of polygonal meshes with linear operators of scale functions

Digital watermarking is already used to establish the copyright of graphics, audio and text, and is now increasingly important for the protection of geometric data as well. Watermarking polygonal models in the spectral domain gives protection against similarity transformation, mesh smoothing, and additive random noise attacks. However, drawbacks exist in analyzing the eigenspace of Laplacian matrices. In this paper we generalize an existing spectral decomposition and propose a new spatial watermarking technique based on this generalization. While inserting the watermark, we avoid the cost of finding the eigenvalues and eigenvectors of a Laplacian matrix in spectral decomposition; instead we use linear operators derived from scaling functions that are generated from Chebyshev polynomials. Experimental results show how the cost of inserting and detecting watermarks can be traded off against robustness under attacks like additive random noise and affine transformation.     

Feature design on deformation of freeform surfaces using range control

This research is to develop a freeform surface design method which uses a feature-based design approach to process surface deformation. Using this method, called range control, a user modifies or changes the position of a characteristic control point of the control polyhedron for a Bspline surface, and regional surface deformation is then carried out through automatic displacements of a group of control points surrounding the characteristic point. The position changes of the group of control points are the interpolations of the maximum movement of the characteristic point related to a feature dimension and zero movements of some fixed points on the designated boundary. In this range control surface deformation method, three interpolating approaches are proposed to smooth out the changes between the characteristic vertex and fixed vertices. they are based on the linear interpolation under the consideration of index, distance and angle distributions. The ideas are implemented on a feature-based designing system for shoe lasts. Design examples are given to show that the range control method is simple, fast and practically applicable for shape deformation of freeform surfaces.     

Continuous point projection to planar freeform curves using spiral curves

We present an efficient algorithm for projecting a continuously moving query point to a family of planar freeform curves. The algorithm is based on the one-sided Hausdorff distance from the trajectory curve (of the query point) to the planar curves. Using a bounding volume hierarchy (BVH) of the planar curves, we estimate an upper bound [`(h)]\overline{h} of the one-sided Hausdorff distance and eliminate redundant curve segments when they are more than distance [`(h)]\overline{h} away from the trajectory curve. Recursively subdividing the trajectory curve and repeating the same elimination procedure to the BVH of the remaining curves, we can efficiently determine where to project the moving query point. The explicit continuous point projection is then interpreted as a curve reparameterization problem, for which we propose a few simple approximation techniques. Using several experimental results, we demonstrate the effectiveness of the proposed approach.     

Restricting Voronoi diagrams to meshes using corner validation

Restricted Voronoi diagrams are a fundamental geometric structure used in many applications such as surface reconstruction from point sets or optimal transport. Given a set of sites V = { v _k}ⁿ_k=1 ? ?^d and a mesh X with vertices in ?^d connected by triangles, the restricted Voronoi diagram partitions X by computing for each site the portion of X for which the site is the nearest. The restricted Voronoi diagram is the intersection between the regular Voronoi diagram and the mesh. Depending on the site distribution or the ambient space dimension computing the regular Voronoi diagram may not be feasible using classical algorithms. In this paper, we extend Lévy and Bonneel's approach [ LB12 ] based on nearest neighbor queries. We show that their method is limited when the sites are not located on X . We propose a new algorithm for computing restricted Voronoi which reduces the number of sites considered for each triangle of the mesh and scales smoothly when the sites are far from the surface.     

Remeshing into normal meshes with boundaries using subdivision

In this paper, we present a remeshing algorithm using the recursive subdivision of irregular meshes with boundaries. A mesh remeshed by subdivision has several advantages. It has a topological regularity, which enables it to be used as a multiresolution model and to represent an original model with less data. Topological regularity is essential for the multiresolutional analysis of the given meshes and makes additional topological information unnecessary. Moreover, we use a normal mesh to reduce the geometric data size requirements at each resolution level of the regularized meshes. The normal mesh uses one scalar value, i.e. normal offset as wavelet, to represent a vertex position, while the other remeshing schemes use one three-dimensional vector at each vertex. The normal offset is a normal distance from a base face, which is the simplified original mesh. Since the normal offset cannot be properly used for the boundaries of a mesh, we use a combined subdivision scheme that resolves the problem of the proposed normal offset method at the boundaries. Finally, we show examples that demonstrate the effectiveness of the proposed scheme in terms of reducing the data requirements of mesh models.     

On the number of rotation symmetric Boolean functions

Rotation symmetric Boolean functions (RSBFs) have been used as components of different cryptosystems. This class of functions are invariant under circular translation of indices. In this paper, we investigated balanced RSBFs and 1st order correlation immune RSBFs. Based on constructive techniques, we give an accurate enumeration formula for n-variable balanced RSBFs when n is a power of a prime. Furthermore, an original and efficient method to enumerate all n-variable (n prime) 1st order correlationimmune f...