Planar Shape Interpolation Based on Local Injective Mapping

在只给出用简单多边形表示的两输入形状的情况下,实现一种简单易用、自然高效的形状插值方法.首先利用基于形状感知的特征匹配算法生成源形状和目标形状之间的匹配;之后在源形状上构造三角剖分,并通过求解映射到目标形状上的尽量刚体的局部单射得到同构三角剖分;最后利用扭曲有界的插值方法得到中间序列.实验结果表明,该方法构造的形变结果能较好地体现源形状和目标形状的特征对应信息,形变过程自然,扭曲较小.This paper presents an efficient and easy-to-use planar shape interpolation method, given two input shapes represented by simple polygons. We firstly used a perception-based feature matching algorithm to match the feature points in the source shape with the target shape, then built compatible triangulations by constructing a locally injective mapping between the source and target shapes. Finally, an interpolation method with bounded distortion was adopted to get intermediate frames. Experimental results show that the interpolation results by our method can well reflect the feature correspondences between the source and the target shapes, and the resultant deformation is visually pleasing with less distortion.国家自然科学基金(61472332);; 中央高校基本科研业务费专项基金(20720140520

改进区域划分的圆Packing变分算法

通过改进基于Power图的区域划分,提出一种收敛速度更快的圆packing算法.首先固定容器面积,将输入圆缩小一定的倍数,随机撒在容器中;之后对圆心点进行三角化,并根据相邻圆的半径比值对容器进行区域划分;再让所有圆在不超出自己区域边界的条件下尽量等比例增长至最大;最后将划分区域-长大的过程迭代下去,得到最大增长倍数.实验结果表明,该算法能够使得圆packing的过程更快地达到收敛.国家自然科学基金(61472332);;福建省自然科学基金(2018J01104

圆组填充算法驱动的平面马赛克模拟

为了生成不规则嵌片排列紧凑的马赛克图案,提出一种基于圆组排列的平面马赛克模拟方法.首先借助嵌片多边形的直骨架得到一组逼近嵌片轮廓的圆;然后以圆半径的平方为权值,在平面上生成关于圆组的Power图,使每组圆各自对应一个Power区域;最后采用松弛法,将圆组在其对应Power区域内尽可能增长到最大.通过不断迭代生成Power图和放大圆组,最后得到嵌片紧凑排列的结果.实验结果表明,该方法得到的马赛克图案有较高的覆盖率,能适应不同嵌片,具有较强的鲁棒性和灵活性.国家自然科学基金(61472332);;福建省自然科学基金(2018J01104);;中央高校基本科研业务费专项基金(20720150002

Knot Placement of B-spline Curves with Equally Spaced Geometric Information

受每个节点区间应该具有相同建模能力的启发,提出一种基于几何信息均分的B样条曲线节点设置算法.首先放置少量节点,以每个节点区间具有相等的几何信息量; 准则来确定节点的位置;为了提高样条的建模能力,根据上一次迭代中的拟合误差确定加细节点区间并使新节点均分该节点区间的几何信息.该算法可以快速有效地; 得到用户指定精度的逼近曲线.通过对一些具有不同几何复杂度的实例进行实验的结果表明,文中算法是有效的;与现有的2种算法相比,; 该算法在相同控制顶点的情况下能够得到更高精度的逼近结果.Motivated by the observation that each knot interval should be of the; same modeling ability, a knot placement algorithm based on equally; spaced geometric information for B-spline curves is proposed. In the; algorithm, a few of knots are determined according to the principle that; each knot interval is of the same amount of geometric information at the; initial iteration. In order to improve the modeling ability of the; B-splines, the knot interval needed to be refined is determined by the; last fitting errors and the new knot inserted is placed to equally space; the accumulated geometric information in the knot interval. Via the; adaptive knot placement algorithm, approximated curve with specified; tolerance can be produced rapidly and efficiently. Several models with; distinct geometric complexities are tested to demonstrate the efficacy; of our algorithm in fitting curves. Comparing to other two available; methods, more accurate results can be obtained by our method with the; same number of control points.国家自然科学基金; 福建省自然科学基金; 中央高校基本科研业务费专项资

基于重心Delaunay三角剖分的蓝噪声点采样算法

为了生成带有高质量蓝噪声性质的采样分布,提出一种基于重心Delaunay三角剖分的点采样算法.该算法将Delaunay三角剖分与1-邻域三角片重心相结合,迭代地将每个采样点移至其1-邻域三角片的重心处并更新采样点之间的拓扑连接关系;重心通过给定的密度函数计算得出.实验结果表明,本文算法在运行效率与鲁棒性方面均有一定优势.国家自然科学基金(61472332);;福建省自然科学基金(2018J01104

Variational blue noise sampling

Blue noise point sampling is one of the core algorithms in computer graphics. In this paper, we present a new and versatile variational framework for generating point distributions with high-quality blue noise characteristics while precisely adapting to given density functions. Different from previous approaches based on discrete settings of capacity-constrained Voronoi tessellation, we cast the blue noise sampling generation as a variational problem with continuous settings. Based on an accurate evaluation of the gradient of an energy function, an efficient optimization is developed which delivers significantly faster performance than the previous optimization-based methods. Our framework can easily be extended to generating blue noise point samples on manifold surfaces and for multi-class sampling. The optimization formulation also allows us to naturally deal with dynamic domains, such as deformable surfaces, and to yield blue noise samplings with temporal coherence. We present experimental results to validate the efficacy of our variational framework. Finally, we show a variety of applications of the proposed methods, including nonphotorealistic image stippling, color stippling, and blue noise sampling on deformable surfaces. © 1995-2012 IEEE.published_or_final_versio

Approximation by Piecewise Function Based on Generalized Barycentric Coordinates and Voronoi Tessellation

结合广义重心坐标理论,提出了一个新方法,以解决在平面区域上的函数逼近问题。该方法通过构建基于广义重心坐标的最优分片函数来逼近目标函数。采用VOrOnOI图来划分区域,并提出一个度量逼近误差的能量函数。推导出该函数的导数后,采用一种高效的VOrOnOI节点更新方法来获得区域的最优剖分,并通过最优剖分构建最优分片函数。由于该方法对不连续函数具有良好地逼近能力,因此将其应用在图像逼近问题中。分别在解析函数和彩色图像上对该方法进行实验,均获得了很好的逼近效果。Under the generalized barycentric coordinates theory, we propose a new method to solve the problem of approximating a given function on the planar domain.To accomplishing this, an optimal piecewise function which based on the generalized barycentric coordinates is constructed.We use the Voronoi tessellation to create a partition of the domain, then an energy function that measures the approximation error is built.After deriving the gradient of the energy function, an efficient optimization method is adopted to update the tessellation.The optimal piecewise function will be constructed from the optimal tessellation.Due to its good ability of approximating discontinuous functions, our method can be applied to image approximation field.In order to demonstrate its efficacy, some experiments on analytic functions and color images are designed, which have produced good results.国家自然科学基金资助项目(61100107;61472332); 中央高校基本科研业务费专项基金(厦门大学基础创新科研基金)资助项目(20720140520

Adaptive Knot Placement in Non-uniform B-spline Surface Fitting

针对非均匀b样条的节点设置问题,提出一种利用非均匀b样条曲面拟合离散数据的迭代算法,通过优化节点分布来改进拟合曲面的质量.该算法以带参数化的三角网格曲面为输入,在首次迭代中根据输入曲面的几何特征将其对应的参数域划分成若干个子区域,并使得每个子区域上累积的几何特征信息量近似相等,子区域的重心坐标将取为首次迭代的节点;在随后的迭代中,保证前次迭代生成的重心位置固定不变,并根据前次迭代得到的曲面拟合误差再次将区域划分成累积误差接近相等的子区域,新增加的子区域重心的坐标选为拟加入的节点.文中算法自适应地在曲面形状复杂或拟合误差大的区域引入更多的控制顶点,使得拟合曲面的质量得以逐步改进.实验结果表明,该算法快速有效,在拟合具有明显几何特征的输入数据时具有优势.Knot placement of non-uniform B-spline is studied, and an iterative surface fitting scheme is proposed by exploring the degrees of freedom of knots to improve the fitting surface's quality.Our algorithm takes as input triangular meshes with parameterization.In the first iteration, the parametric domain is partitioned into several sub-regions with equally accumulated surface geometric information, and the coordinates of the centroids are chosen as the candidates of knots; in the following iteration steps, we partition the regions according to the fitting errors analogously while the centroids generated by previous steps remain unchanged.The fitting surface's quality is progressively improved as more control points are adaptively introduced into the region of the surface with more features or larger fitting error.Several experiments demonstrate the efficacy of our method in fitting surface with distinct geometric features.国家自然科学基金(61100105;61100107;61170324;61272300); 福建省自然科学基金(2011J05007;2012J01291

星系中心大质量黑洞及潮汐瓦解恒星事件

黑洞潮汐瓦解恒星事件(Tidal Disruption Events,TDE)是星系中心黑洞瓦解进入其潮汐瓦解半径内的恒星并吸积恒星碎片物质而产生的一种剧烈辐射耀发现象.TDE的能谱和光变特征中蕴含了中心黑洞和被瓦解的恒星的信息,为我们证实和普查宁静星系中的黑洞,研究其参数、吸积过程和喷流产生、以及核区星际介质等提供了可能.TDE还可能提供中等质量黑洞和双黑洞存在的证据.TDE的观测和理论已成为一个新开辟的天体物理研究领域,但目前的进展受制于探测到事件太少(尤其是在X射线波段),且观测数据普遍质量不高.TDE的发生率很低,要探测大样本的事例需要监测足够大的空间体积.爱因斯坦探针卫星(Einstein Probe,EP)覆盖了0.5–4 keV的软X射线波段(接近TDE耀发时的辐射峰值能段),具有大视场以及高灵敏度,非常利于对TDE的探测.预期爱因斯坦探针卫星每年可以发现约几十至上百例TDE,其中有约10例或更多具有相对论性喷流特征.这将使我们可以获得较为完备、具有统计意义的TDE的样本,为进一步研究黑洞的存在和统计性质、增长和演化、发现中等质量黑洞和大质量双黑洞等提供了新的途径.中国科学院空间科学战略性先导科技专项(编号:XDA15052100);;北京大学“985工程”建设项目“星团环境对双黑洞形成演化过程的干扰及其对引力波探测的影响”资

Topology Improvement for Constructing Optimal Delaunay Triangulation

最优dElAunAy三角剖分(OdT)是生成区域网格剖分的一种优化方法.从数值优化的角度来看,现有的OdT优化方法属于局部方法,对于任意给定初值容易陷入较差的局部极小值点,从而不能产生高质量网格.为此提出一种简单的拓扑优化方法,使得OdT方法能有效地从局部极小值点中跳出,进一步提高网格的质量.该方法只涉及到局部的边翻转操作,实现简单;而且具有显式的目标函数,能在理论上保证算法的收敛性.实验结果表明,文中算法运行速度快,不论是在拓扑连接关系还是在三角形的形状上都显著地提高了OdT方法生成的网格质量.Optimal Delaunay triangulation(ODT) is an optimization method for mesh generation.From the point of view of numerical optimization,existing ODT methods are local optimization methods,which can be easily fallen into a local minimum corresponding to a mesh with low quality.In this paper,a topology improvement method is introduced into the ODT optimization procedure,which effectively enables the ODT method to jump out from a poor local minimum and therefore improves the qualities of generated meshes.The proposed topology improvement method consists of only local operations of edge flipping,which is easy to implement.Moreover,our topology improvement method has an explicit objective function,and its convergence is guaranteed theoretically.Experimental results show that our algorithm is fast and can greatly improves the qualities of meshes generated from ODT,with respect to the regularities of the mesh and the aspect ratios of the triangles.国家自然科学基金(61100105;61100107);福建省自然科学基金(2011J05007);中央高校基本科研业务费专项资金(2011121041);国防基础科研计划项目(B1420110155