A deep learning approach to the classification of 3D CAD models

Model classification is essential to the management and reuse of 3D CAD models.Manual model classification is laborious and error prone.At the same time,the automatic classification methods are scarce due to the intrinsic complexity of 3D CAD models.In this paper,we propose an automatic 3D CAD model classification approach based on deep neural networks.According to prior knowledge of the CAD domain,features are selected and extracted from 3D CAD models first,and then preprocessed as high dimensional input vectors for category recognition.By analogy with the thinking process of engineers,a deep neural network classifier for 3D CAD models is constructed with the aid of deep learning techniques.To obtain an optimal solution,multiple strategies are appropriately chosen and applied in the training phase,which makes our classifier achieve better performance.We demonstrate the efficiency and effectiveness of our approach through experiments on 3D CAD model datasets.

Deterministic and randomized scheduling problems under the lp norm on two identical machines

Parallel machine scheduling problems, which are important discrete optimization problems, may occur in many applications. For example, load balancing in network communication channel assignment, parallel processing in large-size computing, task arrangement in flexible manufacturing systems, etc., are multiprocessor scheduling problem. In the traditional parallel machine scheduling problems, it is assumed that the problems are considered in offline or online environment. But in practice, problems are often not really offline or online but somehow in-between. This means that, with respect to the online problem, some further information about the tasks is available, which allows the improvement of the performance of the best possible algorithms. Problems of this class are called semi-online ones. In this paper, the semi-online problem P2|decr|lp (p>1) is considered where jobs come in non-increasing order of their processing times and the objective is to minimize the sum of the lp norm of every machine’s load. It is shown that LS algorithm is optimal for any lp norm, which extends the results known in the literature. Furthermore, randomized lower bounds for the problems P2|online|lp and P2|decr|lp are presented.

Technical illustration based on 3D CSG models

This paper presents an automatic non-photorealistic rendering approach to generating technical illustration from 3D models. It first decomposes the 3D object into a set of CSG primitives, and then performs the hidden surface removal based on the prioritized list, in which the rendition order of CSG primitives is sorted out by depth. Then, each primitive is illustrated by the pre-defined empirical lighting model, and the system mimics the stroke-drawing by user-specified style. In order to artistically and flexibly modulate the illumination, the empirical lighting model is defined by three major components: parameters of multi-level lighting intensities, parametric spatial occupations for each lighting level, and an interpolation method to calculate the lighting distribution over primitives. The stylized illustration is simulated by a grid-based method, in which we ‘fill’ the desirable pictorial units into the spatial occupation of CSG primitives, instead of “pixel-by-pixel” painting. This region-by-region shading facilitates the simulation of illustration styles.

Direction monotonicity for a rational Bézier curve

The monotonicity of a rational Bezier curve, usually related to an explicit function, is determined by the used coordinate system. However, the shape of the curve is independent of the coordinate system. To meet the affine invariant property, a kind of generalized mono- tonicity, called direction monotonicity, is introduced for rational Bezier curves. The direction monotonicity is applied to both planar and space curves and to both Cartesian and affine co- ordinate systems, and it includes the traditional monotonicity as a subcase. By means of it, proper affine coordinate systems may be chosen to make some rational Bezier curves monotonic. Direction monotonic interpolation may be realized for some of the traditionally nonmonotonic data as well.

Analytical solutions for a uniformly loaded circular plate with clamped edges

A bi-harmonic potential function was constructed in this study. Love solution was employed to obtain analytical solutions of uniformly loaded plates with two different types of clamped edges. The treatment of clamped boundary conditions was the same as that adopted by Timoshenko and Goodier (1970). The analytical solution for the first type of clamped boundary condition is identical with that obtained by Luo et al.(2004), and the solutions for both types were compared with the FEM results and the calculations of thin plate theory.

Degree elevation from Bzier curve to C-Bzier curve with corner cutting form

The existing results of curve degree elevation mainly focus on the degree of algebraic polynomials. The paper considers the elevation of degree of the trigonometric polynomial, from a Bezier curve on the algebraic polynomial space, to a C-Bezier curve on the algebraic and trigonometric polynomial space. The matrix of degree elevation is obtained by an operator presentation and a derivation pyramid. It possesses not a recursive presentation but a direct expression. The degree elevation process can also be represented as a corner cutting form.

Optimal constrained multi-degree reduction of Bézier curves with explicit expressions based on divide and conquer

We decompose the problem of the optimal multi-degree reduction of Bézier curves with corners constraint into two simpler subproblems, namely making high order interpolations at the two endpoints without degree reduction, and doing optimal degree reduction without making high order interpolations at the two endpoints. Further, we convert the second subproblem into multi-degree reduction of Jacobi polynomials. Then, we can easily derive the optimal solution using orthonormality of Jacobi polynomials and the least square method of unequally accurate measurement. This method of 'divide and conquer' has several advantages including maintaining high continuity at the two endpoints of the curve, doing multi-degree reduction only once, using explicit approximation expressions, estimating error in advance, low time cost, and high precision. More importantly, it is not only deduced simply and directly, but also can be easily extended to the degree reduction of surfaces. Finally, we present two examples to demonstrate the effectiveness of our algorithm.

Optimal approximate merging of a pair of Bézier curves with G^2-continuity

We present a novel approach for dealing with optimal approximate merging of two adjacent Bézier curves with G2-continuity. Instead of moving the control points, we minimize the distance between the original curves and the merged curve by taking advantage of matrix representation of Bézier curve's discrete structure, where the approximation error is measured by L2-norm. We use geometric information about the curves to generate the merged curve, and the approximation error is smaller. We can obtain control points of the merged curve regardless of the degrees of the two original curves. We also discuss the merged curve with point constraints. Numerical examples are provided to demonstrate the effectiveness of our algorithms.

Sketch based garment modeling on an arbitrary view of a 3D virtual human model

This paper presents a new approach for modeling a virtual garment intuitively and simply by sketching garment style lines.The user sketches directly onto the surface of 3D virtual human from arbitrary viewing directions,and the 3D garment suited to the virtual human can be created automatically.First,a distance field based allocation algorithm is proposed to find the 3D point which has the shortest given distance to the virtual human along the view direction.Then,the 3D style lines are generated by transforming from the 2D strokes on the human model and all the garment pieces are recognized from the 3D style lines.Finally,the 3D garment model is constructed by using the angle and offset based interpolation and Delaunay triangulation.In addition,we propose a body feature based template reusing method to fit the 3D garment to different virtual human models.The method can be adapted to designer habits and improve the usefulness of garment design.Examples show that the method is useful and efficient.

Robustly Tuning Bandgaps in Two-Dimensional Soft Phononic Crystals with Criss-Crossed Elliptical Holes

Tuning band gaps in soft materials by post-buckling deformation is becoming an appealing means to manipulate elastic waves. As one of the most favorable topologies, two- dimensional soft structures with circular holes have been extensively studied. Based on the contrarian thinking, this paper starts from the two-dimensional soft structures with criss-crossed elliptical holes, which is close to the post-buckling configuration of soft structures with circular holes, and then proposes to tune the band gaps through elongating or stretching rather than compressing. Influences of the loading magnitude and loading pattern （i.e., uniaxial and biaxial elongations） on the band gaps are studied via the nonlinear finite element simulations. Effects of the geometric parameters （the major-to-minor half-axis ratio and the porosity of the structure） are also discussed. It is shown that, compared with the traditional circular hole case, the band gaps of the unloaded structure with criss-crossed elliptical holes are much richer, and they could be reversely and continuously tuned by tensile loadings. In particular, the deformation is very robust and is insensitive to small geometric imperfections, which is always necessary for triggering the post-buckling deformations. The present work provides a useful reference to the manipula- tion of elastic waves in periodic structures as well as the design of soft phononic crystals/acoustic devices.

Conditions of G^n Continuity Between Surfaces

Geometric continuity between parametric surfaces is an important issue in CAGD.So far rest-arches have been concentrated on it for N-dimensional surfaces whose common boundary is of N-1 dimensions.No results have ever been obtained for the case where the common boundary of the two surfaces is of L dimensions,0≤L≤N,or the two adjacent surfaces are of unequal dimensions.In this paper,the conditions of high-order geometric continuity between parametric surfaces are studied for these general cases By analysing the structure of Gn transformations,general solutions as well as an iterative method for determining adjustable functions are proposed.Some equivalent conditions of Gn continuity (nth order geometric continuity) are derived with an emphasis on conditions for triangular and rectangular Bezier surfaces.Since the Gn conditions for polynomial parametric surfaces are expressed in the form of explicit relationship of control points of Bezier surfaces,they are very useful both in theory and application

Procedural generation and real-time rendering of a marine ecosystem

Underwater scene is one of the most marvelous environments in the world. In this study, we present an efficient procedural modeling and rendering system to generate marine ecosystems for swim-through graphic applications. To produce realistic and natural underwater scenes, several techniques and algorithms have been presented and introduced. First, to distribute sealife naturally on a seabed, we employ an ecosystem simulation that considers the influence of the underwater environment. Second, we propose a two-level procedural modeling system to generate sealife with unique biological features. At the base level, a series of grammars are designed to roughly represent underwater sealife on a central processing unit(CPU). Then at the fine level, additional details of the sealife are created and rendered using graphic processing units(GPUs). Such a hybrid CPU-GPU framework best adopts sequential and parallel computation in modeling a marine ecosystem, and achieves a high level of performance.Third, the proposed system integrates dynamic simulations in the proposed procedural modeling process to support dynamic interactions between sealife and the underwater environment, where interactions and physical factors of the environment are formulated into parameters and control the geometric generation at the fine level. Results demonstrate that this system is capable of generating and rendering scenes with massive corals and sealife in real time.

Estimates for Eigenvalues of Stochastic Matrices

It is well-known that the eigenvalues of stochastic matrices lie in the unit circle and at least one of them has the value one. Let {1, r 2 , ··· , r N } be the eigenvalues of stochastic matrix X of size N × N . We will present in this paper a simple necessary and sufficient condition for X such that ｜r j ｜ 〈 1, j = 2, ··· , N . Moreover, such condition can be very quickly examined by using some search algorithms from graph theory.

Structural visualization of sequential DNA data

To date,comparing and visualizing genome sequences remain challenging due to the large genome size.Existing approaches take advantage of the stable property of oligonucleotides and exhibit the main characteristics of the whole genome,yet they commonly fail to show progression patterns of the genome adjustably.This paper presents a novel visual encoding technique,which not only supports the binning process (phylogenetic analysis),but also allows the sequential analysis of the genome.The key idea is to regard the combination of each k-nucleotide and its reverse complement as a visual word,and to represent a long genome sequence with a list of local statistical feature vectors derived from the local frequency of the visual words.Experimental results on a variety of examples demonstrate that the presented approach has the ability to quickly and intuitively visualize DNA sequences,and to help the user identify regions of differences among multiple datasets.

A Robust and Fast Non-Local Means Algorithm for Image Denoising

In the paper, we propose a robust and fast image denoising method. The approach integrates both Non- Local means algorithm and Laplacian Pyramid. Given an image to be denoised, we first decompose it into Laplacian pyramid. Exploiting the redundancy property of Laplacian pyramid, we then perform non-local means on every level image of Laplacian pyramid. Essentially, we use the similarity of image features in Laplacian pyramid to act as weight to denoise image. Since the features extracted in Laplacian pyramid are localized in spatial position and scale, they are much more able to describe image, and computing the similarity between them is more reasonable and more robust. Also, based on the efficient Summed Square Image （SSI） scheme and Fast Fourier Transform （FFT）, we present an accelerating algorithm to break the bottleneck of non-local means algorithm - similarity computation of compare windows. After speedup, our algorithm is fifty times faster than original non-local means algorithm. Experiments demonstrated the effectiveness of our algorithm.

A new method in highway route design:joining circular arcs by a single C-Bézier curve with shape parameter

We constructed a single C-Bézier curve with a shape parameter for G2 joining two circular arcs. It was shown that an S-shaped transition curve, which is able to manage a broader scope about two circle radii than the Bézier curves, has no curvature extrema, while a C-shaped transition curve has a single curvature extremum. Regarding the two kinds of curves, specific algo- rithms were presented in detail, strict mathematical proofs were given, and the effectiveness of the method was shown by examples. This method has the following three advantages: (1) the pattern is unified; (2) the parameter able to adjust the shape of the tran- sition curve is available; (3) the transition curve is only a single segment, and the algorithm can be formulated as a low order equation to be solved for its positive root. These advantages make the method simple and easy to implement.

Rigidity Constraints for Large Mesh Deformation

It is a challenging problem of surface-based deformation to avoid apparent volumetric distortions around largely deformed areas. In this paper, we propose a new rigidity constraint for gradient domain mesh deformation to address this problem. Intuitively the proposed constraint can be regarded as several small cubes defined by the mesh vertices through mean value coordinates. The user interactively specifies the cubes in the regions which are prone to volumetric distortions, and the rigidity constraints could make the mesh behave like a solid object during deformation. The experimental results demonstrate that our constraint is intuitive, easy to use and very effective.

Topic discovery and evolution in scientific literature based on content and citations

Researchers across the globe have been increasingly interested in the manner in which important research topics evolve over time within the corpus of scientific literature. In a dataset of scientific articles, each document can be considered to comprise both the words of the document itself and its citations of other documents. In this paper, we propose a citationcontent-latent Dirichlet allocation(LDA) topic discovery method that accounts for both document citation relations and the content of the document itself via a probabilistic generative model. The citation-content-LDA topic model exploits a two-level topic model that includes the citation information for ‘father' topics and text information for sub-topics. The model parameters are estimated by a collapsed Gibbs sampling algorithm. We also propose a topic evolution algorithm that runs in two steps: topic segmentation and topic dependency relation calculation. We have tested the proposed citation-content-LDA model and topic evolution algorithm on two online datasets, IEEE Transactions on Pattern Analysis and Machine Intelligence(PAMI) and IEEE Computer Society(CS), to demonstrate that our algorithm effectively discovers important topics and reflects the topic evolution of important research themes. According to our evaluation metrics, citation-content-LDA outperforms both content-LDA and citation-LDA.

基于Bézier曲线的柔性曲面装配变动分析（英文）

在装配过程中,柔性零件表面特征会发生形状变化,相比刚性体,其变动分析复杂许多。现有柔性装配变动分析方法大多未考虑零件表面邻近点的相互关系,或者将零件表面上所有特征点的概率分布情况视为统一。本文将柔性曲面零件装配简化为边侧线匹配问题,提出基于Bézier曲线来表征曲面零件边侧线的方法,解决了柔性零件装配中考虑表面连续性的曲面零件装配变动分析问题。该方法利用控制点变动来获取零件边侧线上特征点的偏差,并将它们作为输入参数进行有限元分析,从而计算出最终产品变形量。通过天线表面装配的两个实例,对所提方法进行了验证。