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高一物理力学原理英语阅读理解25题1<背景文章>Newton's three laws of motion are fundamental principles in physics that have had a profound impact on our understanding of the physical world.The first law, also known as the law of inertia, states that an object at rest will stay at rest, and an object in motion will stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force. For example, a book lying on a table will remain there until someone pushes or pulls it. This law was revolutionary as it challenged the then - existing ideas about motion. Newton discovered this law through his careful observations and experiments.The second law of motion is expressed as F = ma, where F is the net force acting on an object, m is the mass of the object, and a is the acceleration. This law explains how the force applied to an object is related to its mass and acceleration. In real - life applications, when you push a shopping cart, the harder you push (greater force), the faster it will accelerate, given that the mass of the cart remains the same.The third law states that for every action, there is an equal and opposite reaction. A classic example is when a rocket launches. The rocket expels gas downward (action), and in return, the gas exerts an equal andopposite force on the rocket, propelling it upward (reaction). Newton's discovery of these laws was a milestone in the history of science and has been used in various fields such as engineering, astronomy, and transportation.1. <问题1>A. According to Newton's first law, if an object is moving in a straight line at a constant speed, what will happen if no unbalanced force acts on it?A. It will gradually slow down.B. It will keep moving at the same speed and in the same direction.C. It will suddenly change direction.D. It will stop immediately.答案：B。
free-form deformation of solid
geometric models
“Free-Form Deformation of Solid Geometric Models”是一种编辑几何模型的重要手段。
它于80年代由Sederberg等人提出，目前许多三维建模软件中都有这种变形算法。
自由变形方法在变形过程中不是直接操作几何模型，而是把几何模型嵌入到变形空间，然后通过操作变形空间来使嵌入其中的几何模型发生变形。
其主要过程如下：
1. 创建一个平行六面体的变形空间框架，将待变形几何模型嵌入这个框架中，同时建立局部坐标系，计算几何模型的顶点在局部坐标系下的坐标。
其中，S、T、U可以认为是这个变形框架的3个边长向量，并且0<s<1、0<t<1、0<u<1。
需要注意的是，在变形过程中，几何模型顶点的局部坐标（s，t，u）都是固定不变的。
2. 移动变形框架控制点，利用几何模型顶点的局部坐标（s，t，u）、控制点世界坐标和Bernstein多项式重新计算几何模型每个顶点的世界坐标。
其中，P（i，j，k）为框架控制点的新坐标，l、m、n分别为在S、T、U坐标轴上划分的格子数目。
这种方法可以用于各种实体建模系统，如CSG或B-rep，并且可以对任何类型或程度的曲面基元进行变形，例如平面、二次曲面、参数化曲面片或隐式定义的曲面。
此外，这种变形可以是全局的也可以是局部的，并且可以实现任何期望的连续导数的局部变形，同时还可以保持实体模型的体积不变。
A Facial Aging Simulation Method Using flaccidity deformation criteriaAlexandre Cruz Berg Lutheran University of Brazil.Dept Computer ScienceRua Miguel Tostes, 101. 92420-280 Canoas, RS, Brazil berg@ulbra.tche.br Francisco José Perales LopezUniversitat les Illes Balears.Dept Mathmatics InformaticsCtra Valldemossa, km 7,5E-07071 Palma MallorcaSpainpaco.perales@uib.esManuel GonzálezUniversitat les Illes Balears.Dept Mathmatics InformaticsCtra Valldemossa, km 7,5E-07071 Palma MallorcaSpainmanuel.gonzales@uib.esAbstractDue to the fact that the aging human face encompasses skull bones, facial muscles, and tissues, we render it using the effects of flaccidity through the observation of family groups categorized by sex, race and age. Considering that patterns of aging are consistent, facial ptosis becomes manifest toward the end of the fourth decade. In order to simulate facial aging according to these patterns, we used surfaces with control points so that it was possible to represent the effect of aging through flaccidity. The main use of these surfaces is to simulate flaccidity and aging consequently.1.IntroductionThe synthesis of realistic virtual views remains one of the central research topics in computer graphics. The range of applications encompasses many fields, including: visual interfaces for communications, integrated environments of virtual reality, as well as visual effects commonly used in film production.The ultimate goal of the research on realistic rendering is to display a scene on a screen so that it appears as if the object exists behind the screen. This description, however, is somewhat ambiguous and doesn't provide a quality measure for synthesized images. Certain areas, such as plastic surgery, need this quality evaluation on synthesized faces to make sure how the patient look like and more often how the patient will look like in the future. Instead, in computer graphics and computer vision communities, considerable effort has been put forthto synthesize the virtual view of real or imaginary scenes so that they look like the real scenes.Much work that plastic surgeons put in this fieldis to retard aging process but aging is an inevitable process. Age changes cause major variations in the appearance of human faces [1]. Some aspects of aging are uncontrollable and are based on hereditary factors; others are somewhat controllable, resulting from many social factors including lifestyle, among others [2].1.1.Related WorkMany works about aging human faces have been done. We can list some related work in the simulation of facial skin deformation [3].One approach is based on geometric models, physically based models and biomechanical models using either a particle system or a continuous system.Many geometrical models have been developed, such as parametric model [4] and geometric operators [5]. The finite element method is also employed for more accurate calculation of skin deformation, especially for potential medical applications such as plastic surgery [6]. Overall, those works simulate wrinkles but none of them have used flaccidity as causing creases and aging consequently.In this work is presented this effort in aging virtual human faces, by addressing the synthesis of new facial images of subjects for a given target age.We present a scheme that uses aging function to perform this synthesis thru flaccidity. This scheme enforces perceptually realistic images by preserving the identity of the subject. The main difference between our model and the previous ones is that we simulate increase of fat and muscular mass diminish causing flaccidity as one responsible element for the sprouting of lines and aging human face.In the next section will plan to present the methodology. Also in section 3, we introduce the measurements procedure, defining structural alterations of the face. In section 4, we present a visual facial model. We describe age simulation thrua deformation approach in section 5. In the last section we conclude the main results and future work.2.MethodologyA methodology to model the aging of human face allows us to recover the face aging process. This methodology consists of: 1) defining the variations of certain face regions, where the aging process is perceptible; 2) measuring the variations of those regions for a period of time in a group of people and finally 3) making up a model through the measurements based on personal features.That could be used as a standard to a whole group in order to design aging curves to the facial regions defined.¦njjjpVM2.1Mathematical Background and AnalysisHuman society values beauty and youth. It is well known that the aging process is influenced by several parameters such: feeding, weight, stress level, race, religious factors, genetics, etc. Finding a standard set of characteristics that could possibly emulate and represent the aging process is a difficult proposition.This standard set was obtained through a mathematical analysis of some face measurements in a specific group of people, whose photographs in different ages were available [7]. To each person in the group, there were, at least, four digitized photographs. The oldest of them was taken as a standard to the most recent one. Hence, some face alterations were attained through the passing of time for the same person.The diversity of the generated data has led to the designing of a mathematical model, which enabled the acquiring of a behavior pattern to all persons of the same group, as the form of a curve defined over the domain [0,1] in general, in order to define over any interval [0,Į] for an individual face. The unknown points Įi are found using the blossoming principle [8] to form the control polygon of that face.The first step consisted in the selection of the group to be studied. Proposing the assessment of the face aging characteristics it will be necessary to have a photographic follow-up along time for a group of people, in which their face alterations were measurable.The database used in this work consisted of files of patients who were submitted to plastic surgery at Medical Center Praia do Guaíba, located in Porto Alegre, Brazil.3.MeasurementsAccording to anatomic principles [9] the vectors of aging can be described aswhich alter the position and appearance of key anatomic structures of the face as can be shown in figure 1 which compares a Caucasian mother age 66 (left side) with her Caucasian daughters, ages 37 (right above) and 33 (right below) respectively.Figure 1 - Observation of family groupsTherefore, basic anatomic and surgical principles must be applied when planning rejuvenative facial surgery and treating specific problems concomitantwith the aging process.4.Visual Facial ModelThe fact that human face has an especially irregular format and interior components (bones, muscles and fabrics) to possess a complex structure and deformations of different face characteristics of person to person, becomes the modeling of the face a difficult task. The modeling carried through in the present work was based on the model, where the mesh of polygons corresponds to an elastic mesh, simulating the dermis of the face. The deformations in this mesh, necessary to simulate the aging curves, are obtained through the displacement of the vertexes, considering x(t) as a planar curve, which is located within the (u,v ) unit square. So, we can cover the square with a regular grid of points b i,j =[i/m,j/n]T ; i=0,...,m; j=0,...,n. leading to every point (u,v ) asfrom the linear precision property of Bernstein polynomials. Using comparisons with parents we can distort the grid of b i,j into a grid b'i,j , the point (u,v )will be mapped to a point (u',v') asIn order to construct our 3D mesh we introduce the patch byAs the displacements of the vertexes conform to the certain measures gotten through curves of aging and no type of movement in the face is carried through, the parameters of this modeling had been based on the conformation parameter.4.1Textures mappingIn most cases the result gotten in the modeling of the face becomes a little artificial. Using textures mapping can solve this problem. This technique allows an extraordinary increase in the realism of the shaped images and consists of applying on the shaped object, existing textures of the real images of the object.In this case, to do the mapping of an extracted texture of a real image, it is necessary that the textureaccurately correspond to the model 3D of that is made use [9].The detected feature points are used for automatic texture mapping. The main idea of texture mapping is that we get an image by combining two orthogonal pictures in a proper way and then give correct texture coordinates of every point on a head.To give a proper coordinate on a combined image for every point on a head, we first project an individualized 3D head onto three planes, the front (x, y), the left (y, z) and the right (y, z) planes. With the information of feature lines, which are used for image merging, we decide on which plane a 3D-head point on is projected.The projected points on one of three planes arethen transferred to one of feature points spaces suchas the front and the side in 2D. Then they are transferred to the image space and finally to the combined image space.The result of the texture mapping (figure 2) is excellent when it is desired to simulate some alteration of the face that does not involve a type of expression, as neutral. The picture pose must be the same that the 3D scanned data.¦¦¦ mi nj lk n j m i lk k j i w B v B u B b w v u 000,,)()()(')',','(¦¦ m i nj n jmij i v B u B b v u 00,)()(),(¦¦ m i nj n j m i j i v B u B b v u 00,)()(')','(¦¦¦ mi nj lk n j m i lk k j i w B v B u B b w v u 000,,)()()(')',','(Figure 2 - Image shaped with texturemapping5.Age SimulationThis method involves the deformation of a face starting with control segments that define the edges of the faces, as¦¦¦ mi nj lk n j m i lk k j i w B v B u B b w v u 000,,)()()(')',','(Those segments are defined in the original face and their positions are changed to a target face. From those new positions the new position of each vertex in the face is determined.The definition of edges in the face is a fundamental step, since in that phase the applied aging curves are selected. Hence, the face is divided in influencing regions according to their principal edges and characteristics.Considering the face morphology and the modeling of the face aging developed [10], the face was divided in six basic regions (figure 3).The frontal region (1) is limited by the eyelids and the forehead control lines. The distance between these limits enlarges with forward aging.The orbitary region (2) is one of the most important aging parameters because a great number of wrinkles appears and the palpebral pouch increases [11]. In nasal region (3) is observed an enlargement of its contour.The orolabial region (4) is defined by 2 horizontal control segments bounding the upper and lower lips and other 2 segments that define the nasogenian fold. Figure 3 - Regions considering the agingparametersThe lips become thinner and the nasogenian fold deeper and larger. The mental region (5) have 8 control segments that define the low limit of the face and descend with aging. In ear curve (6) is observed an enlargement of its size. The choice of feature lines was based in the characteristic age points in figure 6.The target face is obtained from the aging curves applied to the source face, i.e., with the new control segment position, each vertex of the new image has its position defined by the corresponding vertex in the target face. This final face corresponds to the face in the new age, which was obtained through the application of the numerical modeling of the frontal face aging.The definition of the straight-line segment will control the aging process, leading to a series of tests until the visual result was adequate to the results obtained from the aging curves. The extremes of the segments are interpolated according to the previously defined curves, obtained by piecewise bilinear interpolation [12].Horizontal and vertical orienting auxiliary lines were defined to characterize the extreme points of the control segments (figure 4). Some points, that delimit the control segments, are marked from the intersection of the auxiliary lines with the contour of the face, eyebrow, superior part of the head and the eyes. Others are directly defined without the use of auxiliary lines, such as: eyelid hollow, eyebrow edges, subnasion, mouth, nasolabial wrinkle andnose sides.Figure 4 - Points of the control segmentsOnce the control segments characterize the target image, the following step of the aging process can be undertaken, corresponding to the transformations of the original points to the new positions in the target image. The transformations applied to the segments are given by the aging curves, presented in section 4.In the present work the target segments are calculated by polynomial interpolations, based on parametric curves [12].5.1Deformation approachThe common goal of deformation models is to regulate deformations of a geometric model by providing smoothness constraints. In our age simulation approach, a mesh-independent deformation model is proposed. First, connected piece-wise 3D parametric volumes are generated automatically from a given face mesh according to facial feature points.These volumes cover most regions of a face that can be deformed. Then, by moving the control pointsof each volume, face mesh is deformed. By using non-parallel volumes [13], irregular 3D manifolds are formed. As a result, smaller number of deformvolumes are necessary and the number of freedom incontrol points are reduced. Moreover, based on facialfeature points, this model is mesh independent,which means that it can be easily adopted to deformany face model.After this mesh is constructed, for each vertex on the mesh, it needs to be determined which particularparametric volume it belongs to and what valueparameters are. Then, moving control points ofparametric volumes in 3D will cause smooth facialdeformations, generating facial aging throughflaccidity, automatically through the use of the agingparameters. This deformation is written in matricesas , where V is the nodal displacements offace mesh, B is the mapping matrix composed ofBernstein polynomials, and E is the displacementvector of parametric volume control nodes.BE V Given a quadrilateral mesh of points m i,j ,, we define acontinuous aged surface via a parametricinterpolation of the discretely sampled similaritiespoints. The aged position is defined via abicubic polynomial interpolation of the form with d m,n chosen to satisfy the known normal and continuity conditions at the sample points x i,j .>@>M N j i ,...,1,...,1),(u @@>@>1,,1,),,( j j v i i u v u x ¦3,,),(n m n m n m v u d v u x An interactive tool is programmed to manipulate control points E to achieve aged expressions making possible to simulate aging through age ranges. Basic aged expression units are orbicularis oculi, cheek, eyebrow, eyelid, region of chin, and neck [14]. In general, for each segment, there is an associated transformation, whose behavior can be observed by curves. The only segments that do not suffer any transformation are the contour of the eyes and the superior side of the head.5.2Deformation approachThe developed program also performs shape transformations according to the created aging curves, not including any quantification over the alterations made in texture and skin and hair color. Firstly, in the input model the subjects are required to perform different ages, as previouslymentioned, the first frame needs to be approximately frontal view and with no expression.Secondly, in the facial model initialization, from the first frame, facial features points are extracted manually. The 3D fitting algorithm [15] is then applied to warp the generic model for the person whose face is used. The warping process and from facial feature points and their norms, parametric volumes are automatically generated.Finally, aging field works to relieve the drifting problem in template matching algorithm, templates from the previous frame and templates from the initial frame are applied in order to combine the aging sequence. Our experiments show that this approach is very effective. Despite interest has been put in presenting a friendly user interface, we have to keep in mind that the software system is research oriented. In this kind of applications an important point is the flexibility to add and remove test facilities. 6.Results The presented results in the following figuresrefer to the emulations made on the frontalphotographs, principal focus of this paper, with theobjective to apply the developed program to otherpersons outside the analyzed group. The comparisonswith other photographs of the tested persons dependon their quality and on the position in which theywere taken. An assessment was made of the new positions, of the control segments. It consisted in: after aging a face, from the first age to the second one, through the use of polynomial interpolation of the control segments in the models in the young age, the new positions are then compared with the ones in the model of a relative of older age (figure 5). The processed faces were qualitatively compared with theperson’s photograph at the same age. Figure 5 - Synthetic young age model,region-marked model and aged modelAlso the eyelid hollow, very subtle falling of the eyebrow, thinning of the lips with the enlarging of the nasion and the superior part of the lip, enlargingof the front and changing in the nasolabial wrinkle.7.ConclusionsModelling biological phenomena is a great deal of work, especially when the biggest part of the information about the subject involves only qualitative data. Thus, this research developed had has a challenge in the designing of a model to represent the face aging from qualitative data.Due to its multi-disciplinary character, the developed methodology to model and emulate the face aging involved the study of several other related fields, such as medicine, computing, statistics and mathematics.The possibilities opened by the presented method and some further research on this field can lead to new proposals of enhancing the current techniques of plastic face surgery. It is possible to suggest the ideal age to perform face lifting. Once the most affected aging regions are known and how this process occurs over time. Also missing persons can be recognized based on old photographs using this technique. AcknowledgementsThe project TIN2004-07926 of Spanish Government have subsidized this work.8. References[1] Burt, D. M. et al., Perc. age in adult Caucasianmale faces, in Proc. R. Soc., 259, pp 137-143,1995.[2] Berg, A C. Aging of Orbicularis Muscle inVirtual Human Faces. IEEE 7th InternationalConference on Information Visualization, London, UK, 2003a.[3] Beier , T., S. Neely, Feature-based imagemetamorphosis, In Computer Graphics (Proc.SIGGRAPH), pp. 35-42, 1992.[4] Parke, F. I. P arametrized Models for FacialAnimation, IEEE Computer & Graphics Applications, Nov. 1982.[5] Waters, K.; A Muscle Model for Animating ThreeDimensional Facial Expression. Proc SIGGRAPH'87,Computer Graphics, Vol. 21, Nº4, United States, 1987. [6] Koch, R.M. et alia.. Simulation Facial SurgeryUsing Finite Element Models, Proceedings of SIGGRAPH'96, Computer Graphics, 1996.[7] Kurihara, Tsuneya; Kiyoshi Arai, ATransformation Method for Modeling and Animation of the Human Face from Photographs, Computer Animatio n, Springer-Verlag Tokyo, pp.45-58, 1991.[8] Kent, J., W. Carlson , R. Parent, ShapeTransformation for Polygon Objects, In Computer Graphics (Proc. SIGGRAPH), pp. 47-54, 1992. [9] Sorensen, P., Morphing Magic, in ComputerGraphics World, January 1992.[10]Pitanguy, I., Quintaes, G. de A., Cavalcanti, M.A., Leite, L. A. de S., Anatomia doEnvelhecimento da Face, in Revista Brasileira deCirurgia, Vol 67, 1977.[11]Pitanguy, I., F. R. Leta, D. Pamplona, H. I.Weber, Defining and measuring ageing parameters, in Applied Mathematics and Computation , 1996.[12]Fisher, J.; Lowther, J.; Ching-Kuang S. Curveand Surface Interpolation and Approximation: Knowledge Unit and Software Tool. ITiCSE’04,Leeds, UK June 28–30, 2004.[13]Lerios, A. et al., Feature-Based VolumeMetamorphosis, in SIGGRAPH 95 - Proceedings,pp 449-456, ACM Press, N.Y, 1995.[14]Berg, A C. Facial Aging in a VirtualEnvironment. Memória de Investigación, UIB, Spain, 2003b.[15]Hall, V., Morphing in 2-D and 3-D, in Dr.Dobb's Journal, July 1993.。
小学上册英语第一单元全练全测(含答案)英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.Galaxies can collide and merge with ______.2.The scientific study of matter and its changes is called _______.3.What is the name of the famous mountain range in Europe?A. RockiesB. HimalayasC. AlpsD. Andes4.An endothermic reaction requires _____ from its surroundings.5.What do we call a shape with four equal sides?A. RectangleB. SquareC. TriangleD. Pentagon答案:B6.His favorite sport is ________.7.I like to help my dad in the ____.8.The _______ of an object can affect its movement.9.My teacher helps me with ____.10.Which of these colors is made by mixing blue and yellow?A. RedB. GreenC. PurpleD. Orange答案:B11. A _____ (植物网络) can connect enthusiasts globally.12.An ecosystem includes living and non-living ______.13.I enjoy playing with my ______ (玩具车) in the living room. It goes ______ (快).14. A pendulum swings back and ______ (forth).15.Which language is spoken in Brazil?A. SpanishB. PortugueseC. FrenchD. Italian答案:B16.The garden is ________ (美丽).17.中国的________ (legends) 经常包含神话与历史交织的故事。
小学上册英语第四单元真题试卷(有答案)英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.What do we call a young ostrich?A. ChickB. CalfC. KitD. Fawn答案:A.Chick2.We are going to a ________ (音乐会).3.The starfish can regenerate lost ______ (部分).4.The boy plays the ________.5.My _______ (兔子) is curious about everything.6.The __________ is a famous area known for its art.7.My uncle shares his __________ (知识) about fishing.8.The __________ (历史的轮回) reminds us of the cyclical nature of events.9.What is the term for the movement of the Earth around the sun?A. RotationB. RevolutionC. OrbitD. Spin答案: B10.Which planet is known as the Red Planet?A. EarthB. MarsC. JupiterD. Saturn答案:B11.The ______ is the path of the Earth around the sun.12.Asteroids are mostly found in the _______ belt.13.My favorite fruit is ________ (葡萄) in summer.14.The ancient city of Pompeii was buried by the eruption of ______ (维苏威火山).15.What shape has three sides?A. SquareB. TriangleC. CircleD. Rectangle答案: B16.My pet fish swims around its ______ (鱼缸).17.What do you call the process of learning and gaining knowledge?A. EducationB. RecreationC. VacationD. Celebration答案:A18.The country known for its ancient ruins and temples is ________ (以古代遗址和庙宇闻名的国家是________).19.根据图片把下列单词补充完整。
（2条消息）2020CVPR人体姿态估计论文盘点Hey，今天总结盘点一下2020CVPR论文中涉及到人体姿态估计的论文。
人体姿态估计分为2D（6篇）和3D（11篇）两大类。
2D 人体姿态估计[1].UniPose: Unified Human Pose Estimation in Single Images and Videos作者 | Bruno Artacho, Andreas Savakis单位 | 罗切斯特理工学院摘要：我们提出了一个统一的人体姿态估计框架UniPose，它基于我们的“瀑布式”萎缩空间池架构，在多个姿态估计指标上取得了state-of-art结果。
单姿态合并率上下文分割和联合定位在一个阶段内估计人体姿态，精度高，不依赖统计后处理方法UniPose中的瀑布模块利用了级联结构中渐进式过滤的效率，绘制可与空间金字塔结构相媲美的多尺度视野。
此外，我们的方法扩展到单姿态LSTM进行多帧处理，并获得了视频中时间姿态估计的最新结果。
我们在多个数据集上的结果表明，具有ResNet主干网和瀑布模型的UniPose是一个健壮而有效的姿势估计体系结构，可获得单人姿势检测的state-of-the-art.一种不需要后处理的单人姿态估计方法，可扩展到视频[2].The Devil Is in the Details: Delving Into Unbiased Data Processing for Human Pose Estimation作者 | Junjie Huang, Zheng Zhu, Feng Guo, Guan Huang单位 | XForwardAI Technology Co.,Ltd；清华GitHub：https:///HuangJunJie2017/UDP-Pose摘要：近年来，自顶向下的姿态估计方法在人体姿态估计中占据主导地位。
据我们所知，数据处理作为训练和推理中的一个有趣的基本组成部分，并没有在姿态估计领域中得到系统的考虑。
第 63 卷第 2 期2024 年 3 月Vol.63 No.2Mar.2024中山大学学报（自然科学版）（中英文）ACTA SCIENTIARUM NATURALIUM UNIVERSITATIS SUNYATSENI柔性曲拱振动测量的双尺度数字图像相关方法*李婉培1，吕中荣1，谢培悦1，焦柯2，汪利11. 中山大学航空航天学院，广东深圳 5181072. 广东省建筑设计研究院有限公司，广东广州 510010摘要：以柔性曲拱为研究对象，提出一种双尺度数字图像相关方法。
在整数像素尺度，通过傅里叶变换快速找到变形参数的像素级初始估计；在亚像素尺度，结合像素级初始估计和逆合成高斯-牛顿迭代，得到亚像素精度的振动测量。
在获得结构振动响应后，使用频域分解方法识别结构的固有频率、振型。
最后，开展柔性曲拱的视觉测量实验，并辅以激光测振仪测量进行对比分析，验证了所提方法在柔性结构振动测量和模态辨识中的有效性。
关键词：数字图像相关方法；双尺度位移恢复；柔性大变形结构；模态辨识中图分类号：O32 文献标志码：A 文章编号：2097 - 0137（2024）02 - 0108 - 07Two-scale digital image correlation methodfor vibration measurement of flexible curved archLI Wanpei1， LÜ Zhongrong1， XIE Peiyue1， JIAO Ke2， WANG Li11. School of Aeronautics and Astronautics， Sun Yat-sen University， Shenzhen 518107， China2. Guangdong Architectural Design & Research Institute Company Limited， Guangzhou 510010， ChinaAbstract：A two-scale digital image correlation method based on flexible curved arch is proposed in this paper. In integer pixel scale， the initial estimation of deformation parameters at pixel level is quickly found by Fourier transform. In sub-pixel scale， combined with pixel level initial estimation and inverse synthesis Gaussian-Newton iteration， the deformation measurement results with sub-pixel precision is obtained. After the vibration response of the structure is obtained， the natural frequency and mode of the structure are identified by frequency domain decomposition method. Finally，the visual measure‐ment experiment was conducted on a flexible curved arch，supplemented by comparative analysis of laser vibration measurement，to verify the effectiveness of the proposed method in vibration measurement and modal identification of flexible structures.Key words：digital image correlation； two-scale displacement recovery； flexible and large deforma‐tion structure； modal identification柔性结构通常由梁、板、杆等组成，广泛应用于航空航天、土木、机械等领域。
第 55 卷第 3 期2024 年 3 月中南大学学报(自然科学版)Journal of Central South University (Science and Technology)V ol.55 No.3Mar. 2024横坡段桥梁双桩双柱式结构受力特征与解析模型王佳佳，陈效坤，肖莉丽，陈星潮，陈浩，李枝强(长安大学 公路学院，陕西 西安，710000)摘要：山区桥梁基础不可避免地建立在陡坡上，不稳定斜坡变形或破坏将会对上覆桥跨结构安全造成严重威胁，亟需研究高效、可靠的力学模型。
首先，对横坡段桥梁双桩双柱式结构划分不同特征段，分析其受力特性；其次，考虑桩土相互作用和桩顶变形协调关系并引入边界条件，建立适用于横坡段桥梁双桩双柱式结构内力及位移的简化模型；第三，综合考虑P −Δ效应及盖/系梁对桩柱受力影响，引入相邻特征段满足的连续条件(即位移、转角、剪力及弯矩连续)，建立挠曲微分方程并以MATLAB 为平台编制相应计算程序，提出横坡段桥梁双桩双柱式结构基础内力及位移的幂级数解；最后，将模型结果与有限元计算结果对比，验证模型的可靠性。
研究结果表明：本文提出的模型将桥墩与桩基础视为整体，对于多道系梁的结构分析该模型同样适用；模型考虑了横向联系对两桩轴向力和弯矩的分配，可获取横向联系中的横向力；模型不需要假设自由段剪力和迭代计算。
随着剩余下滑力增大，结构各特征段前后桩位移和弯矩明显增加；横向联系对桩基位移及内力进行了重新分配，有较强的约束作用，能够较好地改善前后桩受力与变形情况。
关键词：横坡段桥梁；双桩双柱结构；受力特征；幂级数解；有限元分析中图分类号：U441+.5 文献标志码：A 文章编号：1672-7207（2024）03-1092-15Mechanics characteristics and analytical model of double-pile and double-column structure of bridge on steep transverse slopeWANG Jiajia, CHEN Xiaokun, XIAO Lili, CHEN Xingchao, CHEN Hao, LI Zhiqiang(School of Highway, Chang'an University, Xi'an 710000, China)Abstract: The foundation of bridge in mountain area is inevitably built on steep slope, and the deformation or failure of unstable slope will pose a serious threat to the safety of overlying bridge span, so it is urgent to develop an efficient and reliable mechanical model. Firstly, the double pile and double column structure of the bridge was divided into different characteristic sections, and its mechanical characteristics were analyzed. Secondly,considering the coordination relationship between pile-soil interaction and pile top deformation, and introducing收稿日期： 2023 −07 −10； 修回日期： 2023 −09 −23基金项目(Foundation item)：国家自然科学基金资助项目(41907237，41907234)；国家重点研发计划项目(2019YFB1600702，2021YFB1600302) (Projects(41907237, 41907234) supported by the National Natural Science Foundation of China; Projects (2019YFB1600702, 2021YFB1600302) supported by the National Key R&D Program of China)通信作者：肖莉丽，博士，副教授，从事公路岩土工程研究；E-mail ：**************.cnDOI: 10.11817/j.issn.1672-7207.2024.03.022引用格式： 王佳佳, 陈效坤, 肖莉丽, 等. 横坡段桥梁双桩双柱式结构受力特征与解析模型[J]. 中南大学学报(自然科学版), 2024, 55(3): 1092−1106.Citation: WANG Jiajia, CHEN Xiaokun, XIAO Lili, et al. Mechanics characteristics and analytical model of double-pile and double-column structure of bridge on steep transverse slope[J]. Journal of Central South University(Science and Technology), 2024, 55(3): 1092−1106.第 3 期王佳佳，等：横坡段桥梁双桩双柱式结构受力特征与解析模型boundary conditions, a simplified model for the internal force and displacement of double-pile and double-column structure of bridge on cross slope section was established. Thirdly, considering the influence of P−Δ effect and cap/ tie beam on the force of pile, the continuous conditions (i.e., continuity of displacement, rotation angle, shear force and bending moment) satisfied by adjacent feature sections were introduced, the flexure differential equation was established, and the corresponding calculation program was compiled on the MATLAB platform. The power series solution of the internal force and displacement of the foundation of the double-pile and double-column structure of the bridge on the cross slope section was proposed. Finally, the reliability of the model was verified by comparing the model results with the finite element calculation results. The results show that the proposed model regards pier and pile foundation as a whole, and the model is also applicable to the structural analysis of multi-channel beams.The model takes into account the distribution of axial force and bending moment of the two piles in the transverse connection, and obtains the transverse force in the transverse connection. In addition, the model does not need to assume free section shear forces and iterative calculations. With the increase of residual glide force, the displacement and bending moment of piles in front and back of each characteristic section of the structure increase obviously. The lateral connection redistributes the displacement and internal force of pile foundation and has a strong constraint effect, which can better improve the load and deformation of front and rear piles.Key words: bridge on transverse slope; double pile and double column structure; mechanics characteristic; power series solution; finite element analysis山区高速公路通常采用桥梁来跨越地形障碍，以避免“大填大挖”，减少对生态环境的破坏[1−2]。
自动化英语专业英语词汇表文章摘要：本文介绍了自动化英语专业的一些常用的英语词汇，包括自动化技术、控制理论、系统工程、人工智能、模糊逻辑等方面的专业术语。
本文按照字母顺序，将这些词汇分为26个表格，每个表格包含了以相应字母开头的词汇及其中文释义。
本文旨在帮助自动化专业的学习者和从业者掌握和使用这些专业英语词汇，提高他们的英语水平和专业素养。
A英文中文acceleration transducer加速度传感器acceptance testing验收测试accessibility可及性accumulated error累积误差AC-DC-AC frequency converter交-直-交变频器AC (alternating current) electric drive交流电子传动active attitude stabilization主动姿态稳定actuator驱动器，执行机构adaline线性适应元adaptation layer适应层adaptive telemeter system适应遥测系统adjoint operator伴随算子admissible error容许误差aggregation matrix集结矩阵AHP (analytic hierarchy process)层次分析法amplifying element放大环节analog-digital conversion模数转换annunciator信号器antenna pointing control天线指向控制anti-integral windup抗积分饱卷aperiodic decomposition非周期分解a posteriori estimate后验估计approximate reasoning近似推理a priori estimate先验估计articulated robot关节型机器人assignment problem配置问题，分配问题associative memory model联想记忆模型associatron联想机asymptotic stability渐进稳定性attained pose drift实际位姿漂移B英文中文attitude acquisition姿态捕获AOCS (attritude and orbit control system)姿态轨道控制系统attitude angular velocity姿态角速度attitude disturbance姿态扰动attitude maneuver姿态机动attractor吸引子augment ability可扩充性augmented system增广系统automatic manual station自动-手动操作器automaton自动机autonomous system自治系统backlash characteristics间隙特性base coordinate system基座坐标系Bayes classifier贝叶斯分类器bearing alignment方位对准bellows pressure gauge波纹管压力表benefit-cost analysis收益成本分析bilinear system双线性系统biocybernetics生物控制论biological feedback system生物反馈系统C英文中文calibration校准，定标canonical form标准形式canonical realization标准实现capacity coefficient容量系数cascade control级联控制causal system因果系统cell单元，元胞cellular automaton元胞自动机central processing unit (CPU)中央处理器certainty factor确信因子characteristic equation特征方程characteristic function特征函数characteristic polynomial特征多项式characteristic root特征根英文中文charge-coupled device (CCD)电荷耦合器件chaotic system混沌系统check valve单向阀，止回阀chattering phenomenon颤振现象closed-loop control system闭环控制系统closed-loop gain闭环增益cluster analysis聚类分析coefficient of variation变异系数cogging torque齿槽转矩，卡齿转矩cognitive map认知图，认知地图coherency matrix相干矩阵collocation method配点法，配置法combinatorial optimization problem组合优化问题common mode rejection ratio (CMRR)共模抑制比，共模抑制率commutation circuit换相电路，换向电路commutator motor换向电动机D英文中文damping coefficient阻尼系数damping ratio阻尼比data acquisition system (DAS)数据采集系统data fusion数据融合dead zone死区decision analysis决策分析decision feedback equalizer (DFE)决策反馈均衡器decision making决策，决策制定decision support system (DSS)决策支持系统decision table决策表decision tree决策树decentralized control system分散控制系统decoupling control解耦控制defuzzification去模糊化，反模糊化delay element延时环节，滞后环节delta robot德尔塔机器人demodulation解调，检波density function密度函数，概率密度函数derivative action微分作用，微分动作design matrix设计矩阵E英文中文eigenvalue特征值，本征值eigenvector特征向量，本征向量elastic element弹性环节electric drive电子传动electric potential电势electro-hydraulic servo system电液伺服系统electro-mechanical coupling system电机耦合系统electro-pneumatic servo system电气伺服系统electronic governor电子调速器encoder编码器，编码装置end effector末端执行器，末端效应器entropy熵equivalent circuit等效电路error analysis误差分析error bound误差界，误差限error signal误差信号estimation theory估计理论Euclidean distance欧几里得距离，欧氏距离Euler angle欧拉角Euler equation欧拉方程F英文中文factor analysis因子分析factorization method因子法，因式分解法feedback反馈，反馈作用feedback control反馈控制feedback linearization反馈线性化feedforward前馈，前馈作用feedforward control前馈控制field effect transistor (FET)场效应晶体管filter滤波器，滤波环节finite automaton有限自动机finite difference method有限差分法finite element method (FEM)有限元法finite impulse response (FIR) filter有限冲激响应滤波器first-order system一阶系统fixed-point iteration method不动点迭代法flag register标志寄存器flip-flop circuit触发器电路floating-point number浮点数flow chart流程图，流程表fluid power system流体动力系统G英文中文gain增益gain margin增益裕度Galerkin method伽辽金法game theory博弈论Gauss elimination method高斯消元法Gauss-Jordan method高斯-约当法Gauss-Markov process高斯-马尔可夫过程Gauss-Seidel iteration method高斯-赛德尔迭代法genetic algorithm (GA)遗传算法gradient method梯度法，梯度下降法graph theory图论gravity gradient stabilization重力梯度稳定gray code格雷码，反向码gray level灰度，灰阶grid search method网格搜索法ground station地面站，地面控制站guidance system制导系统，导航系统gyroscope陀螺仪，陀螺仪器H英文中文H∞ control H无穷控制Hamiltonian function哈密顿函数harmonic analysis谐波分析harmonic oscillator谐振子，谐振环节Hartley transform哈特利变换Hebb learning rule赫布学习规则Heisenberg uncertainty principle海森堡不确定性原理hidden layer隐层，隐含层hidden Markov model (HMM)隐马尔可夫模型hierarchical control system分层控制系统high-pass filter高通滤波器Hilbert transform希尔伯特变换Hopfield network霍普菲尔德网络hysteresis滞后，迟滞，磁滞I英文中文identification识别，辨识identity matrix单位矩阵，恒等矩阵image processing图像处理impulse response冲激响应impulse response function冲激响应函数inadmissible control不可接受控制incremental encoder增量式编码器indefinite integral不定积分index of controllability可控性指标index of observability可观测性指标induction motor感应电动机inertial navigation system (INS)惯性导航系统inference engine推理引擎，推理机inference rule推理规则infinite impulse response (IIR) filter无限冲激响应滤波器information entropy信息熵information theory信息论input-output linearization输入输出线性化input-output model输入输出模型input-output stability输入输出稳定性J英文中文Jacobian matrix雅可比矩阵jerk加加速度，冲击joint coordinate system关节坐标系joint space关节空间Joule's law焦耳定律jump resonance跳跃共振K英文中文Kalman filter卡尔曼滤波器Karhunen-Loeve transform卡尔胡南-洛维变换kernel function核函数，核心函数kinematic chain运动链，运动链条kinematic equation运动方程，运动学方程kinematic pair运动副，运动对kinematics运动学kinetic energy动能L英文中文Lagrange equation拉格朗日方程Lagrange multiplier拉格朗日乘子Laplace transform拉普拉斯变换Laplacian operator拉普拉斯算子laser激光，激光器latent root潜根，隐根latent vector潜向量，隐向量learning rate学习率，学习速度least squares method最小二乘法Lebesgue integral勒贝格积分Legendre polynomial勒让德多项式Lennard-Jones potential莱纳德-琼斯势level set method水平集方法Liapunov equation李雅普诺夫方程Liapunov function李雅普诺夫函数Liapunov stability李雅普诺夫稳定性limit cycle极限环，极限圈linear programming线性规划linear quadratic regulator (LQR)线性二次型调节器linear system线性系统M英文中文machine learning机器学习machine vision机器视觉magnetic circuit磁路，磁电路英文中文magnetic flux磁通量magnetic levitation磁悬浮magnetization curve磁化曲线magnetoresistance磁阻，磁阻效应manipulability可操作性，可操纵性manipulator操纵器，机械手Markov chain马尔可夫链Markov decision process (MDP)马尔可夫决策过程Markov property马尔可夫性质mass matrix质量矩阵master-slave control system主从控制系统matrix inversion lemma矩阵求逆引理maximum likelihood estimation (MLE)最大似然估计mean square error (MSE)均方误差measurement noise测量噪声，观测噪声mechanical impedance机械阻抗membership function隶属函数N英文中文natural frequency固有频率，自然频率natural language processing (NLP)自然语言处理navigation导航，航行negative feedback负反馈，负反馈作用neural network神经网络neuron神经元，神经细胞Newton method牛顿法，牛顿迭代法Newton-Raphson method牛顿-拉夫逊法noise噪声，噪音nonlinear programming非线性规划nonlinear system非线性系统norm范数，模，标准normal distribution正态分布，高斯分布notch filter凹槽滤波器，陷波滤波器null space零空间，核空间O英文中文observability可观测性英文中文observer观测器，观察器optimal control最优控制optimal estimation最优估计optimal filter最优滤波器optimization优化，最优化orthogonal matrix正交矩阵oscillation振荡，振动output feedback输出反馈output regulation输出调节P英文中文parallel connection并联，并联连接parameter estimation参数估计parity bit奇偶校验位partial differential equation (PDE)偏微分方程passive attitude stabilization被动姿态稳定pattern recognition模式识别PD (proportional-derivative) control比例-微分控制peak value峰值，峰值幅度perceptron感知器，感知机performance index性能指标，性能函数period周期，周期时间periodic signal周期信号phase angle相角，相位角phase margin相位裕度phase plane analysis相平面分析phase portrait相轨迹，相图像PID (proportional-integral-derivative) control比例-积分-微分控制piezoelectric effect压电效应pitch angle俯仰角pixel像素，像元Q英文中文quadratic programming二次规划quantization量化，量子化quantum computer量子计算机quantum control量子控制英文中文queueing theory排队论quiescent point静态工作点，静止点R英文中文radial basis function (RBF) network径向基函数网络radiation pressure辐射压random variable随机变量random walk随机游走range范围，区间，距离rank秩，等级rate of change变化率，变化速率rational function有理函数Rayleigh quotient瑞利商real-time control system实时控制系统recursive algorithm递归算法recursive estimation递归估计reference input参考输入，期望输入reference model参考模型，期望模型reinforcement learning强化学习relay control system继电器控制系统reliability可靠性，可信度remote control system遥控系统，远程控制系统residual error残差误差，残余误差resonance frequency共振频率S英文中文sampling采样，取样sampling frequency采样频率sampling theorem采样定理saturation饱和，饱和度scalar product标量积，点积scaling factor缩放因子，比例系数Schmitt trigger施密特触发器Schur complement舒尔补second-order system二阶系统self-learning自学习，自我学习self-organizing map (SOM)自组织映射sensitivity灵敏度，敏感性sensitivity analysis灵敏度分析，敏感性分析sensor传感器，感应器sensor fusion传感器融合servo amplifier伺服放大器servo motor伺服电机，伺服马达servo valve伺服阀，伺服阀门set point设定值，给定值settling time定常时间，稳定时间T英文中文tabu search禁忌搜索，禁忌表搜索Taylor series泰勒级数，泰勒展开式teleoperation遥操作，远程操作temperature sensor温度传感器terminal终端，端子testability可测试性，可检测性thermal noise热噪声，热噪音thermocouple热电偶，热偶threshold阈值，门槛time constant时间常数time delay时延，延时time domain时域time-invariant system时不变系统time-optimal control时间最优控制time series analysis时间序列分析toggle switch拨动开关，切换开关tolerance analysis公差分析torque sensor扭矩传感器transfer function传递函数，迁移函数transient response瞬态响应U英文中文uncertainty不确定性，不确定度underdamped system欠阻尼系统undershoot低于量，低于值unit impulse function单位冲激函数unit step function单位阶跃函数unstable equilibrium point不稳定平衡点unsupervised learning无监督学习upper bound上界，上限utility function效用函数，效益函数V英文中文variable structure control变结构控制variance方差，变异vector product向量积，叉积velocity sensor速度传感器verification验证，校验virtual reality虚拟现实viscosity粘度，黏度vision sensor视觉传感器voltage电压，电位差voltage-controlled oscillator (VCO)电压控制振荡器W英文中文wavelet transform小波变换weighting function加权函数Wiener filter维纳滤波器Wiener process维纳过程work envelope工作空间，工作范围worst-case analysis最坏情况分析X英文中文XOR (exclusive OR) gate异或门，异或逻辑门Y英文中文yaw angle偏航角Z英文中文Z transform Z变换zero-order hold (ZOH)零阶保持器zero-order system零阶系统zero-pole cancellation零极点抵消。
Pose Space Deformation:A Unified Approach to Shape Interpolation andSkeleton-Driven DeformationJ.P.Lewis∗,Matt Cordner,Nickson FongCentropolisAbstractPose space deformation generalizes and improves upon both shape interpolation and common skeleton-driven deformation techniques. This deformation approach proceeds from the observation that sev-eral types of deformation can be uniformly represented as mappings from a pose space,defined by either an underlying skeleton or a more abstract system of parameters,to displacements in the ob-ject local coordinate frames.Once this uniform representation is identified,previously disparate deformation types can be accom-plished within a single unified approach.The advantages of this algorithm include improved expressive power and direct manipula-tion of the desired shapes yet the performance associated with tradi-tional shape interpolation is achievable.Appropriate applications include animation of facial and body deformation for entertainment, telepresence,computer gaming,and other applications where direct sculpting of deformations is desired or where real-time synthesis of a deforming model is required.CR Categories:I.3.5[Computer Graphics]:Computational Geometry and Object Modeling—Curve,surface,solid and ob-ject modeling I.3.6[Computer Graphics]:Methodology and Techniques—Interaction techniques I.3.7[Computer Graphics]: Three-Dimensional Graphics and Realism—Animation Keywords:Animation,Deformation,Facial Animation,Morph-ing,Applications.1IntroductionFree form deformation has been approached from several distinct perspectives.As an abstract and general problem,good methods have been obtained both using the well known technique that bears this name[32,12,17]and other kinematic surface deformation techniques,and with physical models that simulate the time evo-lution of a membrane or solid.The animation of human and creature skin deformation is ar-guably the most common and important application of free form de-formation in computer graphics.While such creature animation can be considered a special case of general free form deformation,its importance and difficulty have lead researchers to propose a number of domain-specific algorithms that will be reviewed in Section2.The problem of realistic facial animation is being actively and successfully addressed by image-based and hybrid techniques. These techniques are not yet suitable for all applications,however:∗zilla@ while a purely image-based approach can achieve very realistic im-ages,this advantage may be lost if one needs to introduce geome-try and surface reflectance in order to re-light characters to match preexisting or dynamically computed environments.Film and en-tertainment applications require fanciful creatures that fall outside the scope of image-based approaches.Some of the most impressive examples of geometry-based(as opposed to image-based)human and creature animation have been obtained in the entertainment industry.These efforts traditionally use shape interpolation for facial animation and a standard but variously-named algorithm that we will term skeleton subspace de-formation(SSD)for basic body deformation[25,9].While shape interpolation is well-liked by production animators,it is not suitable for skeleton-driven deformation.On the other hand SSD produces characteristic defects and is notoriously difficult to control.These issues,which will be detailed in the next section,lead us to look for a more general approach to surface deformation.We consider the following to be desirable characteristics of a skeleton-based surface deformation algorithm:•The algorithm should handle the general problem of skeleton-influenced deformation rather than treating each area of anatomy as a special case.New creature topologies should be accommodated without programming or considerable setup efforts.•It should be possible to specify arbitrary desired deformations at arbitrary points in the parameter space,with smooth inter-polation of the deformation between these points.•The system should allow direct manipulation of the desired deformations[33].•The locality of deformation should be controllable,both spa-tially and in the skeleton’s configuration space(pose space).•In addition,we target a conventional animator-controlled work process rather than an approach based on automatic sim-ulation.As such we require that animators be able to visual-ize the interaction of a reasonably high-resolution model with an environment in real time(with‘high resolution’defined in accord with current expectations).Real time synthesis is also required for applications such as avatars and computer games.Our solution,termed pose space deformation,provides a uni-form and expressive approach to both facial skin deformation and skeleton-driven deformation.It addresses the previously mentioned drawbacks of shape interpolation and SSD while retaining the sim-plicity and performance associated with these techniques.The next section reviews various approaches to free form de-formation and describes shape interpolation and skeleton subspace deformation algorithms.The pose space deformation algorithm re-quires well behaved and efficient scattered data interpolation in high dimensional spaces;Section3considers this issue.The pose-space deformation algorithm itself is described in Section4;examples and applications are shown in the last section.2BackgroundRecent research has delivered significant improvements in many ar-eas of character animation,including surface representation,model capture,performance capture,and hybrid(partially image-based) rendering approaches.In this literature review we focus specifically on milestones in the surface deformation models and necessarily omit other important contributions.2.1Surface Deformation ModelsContinuous deformation of a character skin wasfirst addressed in Parke’s pioneering facial animation work[26].In this work,control vertices were deformed by custom algorithmic implementation of carefully selected high-level parameters(‘raise-upper-lip’,etc.).Komatsu[13]and Magnenat-Thalmann et.al.[23]demonstrated human body deformation driven by an underlying skeleton.The region and shape of deformation is algorithmically defined in each of these approaches.Magnenat-Thalmann et.al.developed algo-rithms for each of the various joints in the hand.The discussion in Komatsu focuses on the elbow and shows how the skin crease on the acute side can be obtained by a suitable algorithmic manipula-tion of the surface control vertices.The algorithms in this early work do not suffer the‘collapsing elbow’characteristic of the SSD algorithm(below).On the other hand,the algorithms are specific to particular types of joints and are perhaps too simple to portray the complexity and individual variability of real anatomy.The shortfilm Tony de Peltrie[3]popularized the use of shape in-terpolation for facial animation.Forsey[11]describes a character-oriented deformation scheme in which the bending of a smooth surface can be controlled by anchoring levels of a multi-resolution spline surface to the underlying skeleton.These efforts are distin-guished from the previous purely algorithmic approaches in giving the modeler control of and responsibility for the deformation.The specification and animation of surface deformation remains an active area of investigation[17,10].The Wires technique[22] is one interesting recent contribution;this approach is notable in providing a direct manipulation interface in a form immediately fa-miliar to sculptors(armatures).2.2Multi-Layered and Physically Inspired Models Chadwick,Haumann,and Parent[7]introduced a multi-layered and physically inspired approach to skin deformation.In their model a free-form deformation abstractly represents underlying body tis-sues and mediates skin movement.Chadwick et.al.demonstrated expressive three-dimensional cartoon characters but deformation of a realistic character was not shown.Other researchers have investigated modeling the underlying body tissues in greater depth[27,24,8,35].Most recently,sev-eral groups have undertaken ambitious efforts to produce anatom-ically inspired multi-layered models of animals and humans with considerable verisimilitude.Nedel and Thalmann[19]simulate the surface deformation of muscles using spring mesh dynamics;a modeled skin cross section is reshaped by a ray-casting procedure thatfinds the maximum displacement of the underlying tissue.Sev-eral papers by Wilhelms and coworkers have shown anatomically representative human and animal models.In Wilhelms and Van Gelder[36]several classes of muscles are algorithmically modeled with attention to volume conservation;skin is a spring mesh an-chored to underlying tissue or bone in appropriate areas.Scheepers et.al.[31]produced convincing representations of muscles as well as preliminary but promising skin deformation.2.3Common PracticeIn recent years character animation has moved beyond being a re-search topic and sophisticated deforming characters routinely ap-pear infilms and on television.Various techniques are employed,pp’qq’p"q"Figure1:The skeleton subspace deformation algorithm.The deformed position of a point p lies on the line p p defined by the images of that point rigidly transformed by the neighboring skeletal coordinate frames,resulting in the characteristic‘collapsing elbow’problem(solid line).including manually animated FFDs and custom procedural ap-proaches in the spirit of[26,23,13].Arguably the most com-mon practice in character animation(as reflected in commercial software,animation books and courses,and some custom software) is founded on the twin techniques of shape interpolation and SSD [18,9].2.3.1Shape InterpolationShape interpolation(also called shape blending and multi-target morphing)is probably the most widely used approach to skin de-formation for facial animation[3,18,9].Surface control vertices are simply an animated linear combination(not necessarily con-vex,i.e.,individual weights can be greater than one or less than zero)of the corresponding vertices on a number of key shapes S k:k=0w k S k.A variation of this technique uses a single base shape S0and a number of delta shapes,S0+k=1w k(S k−S0).By writing the delta shape form as(1−1w k)S0+1w k S k it is clear that the space of achievable shapes is identical in both varia-tions.1An attractive feature of shape interpolation is that the desired expressions can be directly specified by sculpting.The limitations of shape interpolation.Given the popularity and effectiveness of this simple approach,it would be desirable to em-ploy it on regions of the body other than the face.The blending of rigid shapes is inconsistent with regions of the body that are bend-ing under the action of an underlying skeleton,however.Of course the key shapes could be deformed to the moving articulatedfigure using some other algorithm,but this defeats the purpose of propos-ing shape interpolation as the means of obtaining the deformation in question.Shape interpolation also has some drawbacks for its intended role of facial animation.For one,the interpolation is not always smooth.Consider interpolating from a smile(shape A)to a neutral pose(B)and then to a frown(C).An individual vertex travels in a straight line between A and B and again in a line between B and C.Selecting smoothly changing weights with dw/dt=0at the key shapes merely causes the deformation to“ease in”and stop at each key pose before continuing on–the time derivative of control point motion is smooth,but the motion path itself is only piecewise linear(parametric versus geometric continuity).In practice ani-mators object to the linear nature of the interpolation[34]and have sometimes compensated by sculpting new key shapes as often as every three tofive frames[38].These comments will be revisited in the discussion of the pose space approach later in the paper.1Provided that the weights sum to one.This is enforced in the delta shape formulation.It is not enforced in the(non-delta)shape interpolation formulation as written,but weights that do not sum to one are a separate effect–they cause the face to change overall scale.Figure 2:The ‘collapsing elbow’in action,c.f.Figure 1.2.3.2Skeleton-Subspace DeformationThis simple algorithm has been repeatedly conceived and appears in commercial software packages under several rather uninformative names such as skinning,enveloping,etc.The algorithm is unpub-lished but is subsumed by more general published schemes such as [23].The position of a control vertex p on the deforming sur-face of an articulated object lies in the subspace defined by the rigid transformations of that point by some number of relevant skeletal coordinate frames (Figure 1).This may be notated¯p=w k L k (p )p(in more detail)¯p=w k L δk L 0k−1L 0p pwhere L 0p is the transform from the surface containing p to theworld coordinate system,L 0k is the transform from the stationaryskeletal frame k to the world system (L 0k−1L 0p together represent p in the coordinate system of skeletal frame k ),and L δk expresses the moving skeletal frame k in the world system.The deformation is controlled by the user through the weights w k .SSD is fairly versatile.For example,secondary animation effects such as muscle bulging and swelling of the chest can be achieved by variably weighting the surface to an abstract “bone”whose transla-tion or scale is manually animated.The limitations of SSD.The first major shortcoming of SSD re-sults directly from the fact that the deformation is restricted to the indicated subspace.In common situations such as shoulders and elbows the desired deformation does not lie in this subspace,hence no amount of adjusting the algorithm weights will produce good re-sults.This fact leads to considerable frustration by users of the algo-rithm –the character of the deformation changes as the weights are changed,sometimes sustaining the incorrect assumption that some combination of weights will produce good results.In fact,the SSD algorithm can be easily identified in animations by its characteristic ‘collapsing joint’defect (Figures 1,2).This problem is extreme in the case of simulating the twist of a human forearm (the pose taken in turning a door handle,Fig-ure 3).In this case the subspace basis consists of surface points rigidly transformed by the forearm frame (no axis rotation)and the wrist frame (axis rotation).With a rotation of 180degrees this line crosses the axis of the arm,i.e.,the forearm collapses entirely as the SSD weights transition at some point from the forearm to wristframes.Figure 3:The forearm in the ‘twist’pose,as in turning a door handle,computed by SSD.As the twist approaches 180◦the arm collapses.A second difficulty with SSD is that,unlike shape interpolation,it does not permit direct manipulation;artists instead directly or indirectly edit the meshes of weights w k (for each control vertex on a surface there is one weight per skeletal frame that affects the vertex).SSD algorithms consequently have the reputation for being tedious and difficult to control.Artists with a poor understanding of the underlying algorithm have difficulty distinguishing between results that can be further improved by adjusting weights and results that cannot be improved since the desired result lies outside the achievable subspace,resulting in the impression of unpredictability (“sometimes adjusting the weights helps,sometimes it doesn’t”).In some cases the SSD defects can be manually corrected us-ing FFDs and other techniques,and one could consider a scheme whereby these fixes are procedurally invoked as the skeleton articu-lates.But although FFDs work well (and have a direct manipulation algorithm [12])the layered FFDs do not reduce the difficulty in ad-justing the underlying SSD.The algorithm introduced in the subse-quent sections removes the need for such layered fix-it approaches and permits direct specification of the desired deformations.2.3.3Unified ApproachesSeveral published algorithms and commercial packages combine aspects of skeleton-driven deformation and shape interpolation in ways that anticipate our approach.In the pioneering work of Burt-nyk and Wein,two dimensional characters were animated using a polygonal rubber sheet that afforded both skeletal and local defor-mation control [6].Van Overveld described a two-dimensional an-imation system in which animation is controlled by a skeleton and character deformation is driven from this skeleton through a scat-tered interpolation [20].This work is similar in spirit to ours but dif-fers in that it used the image plane as a global interpolation domain rather than introducing a pose space.Litwinowicz and Williams’s system [16]is also a precedent and introduced sophisticated scat-tered interpolation (again in the image domain).Several papers consider animation (and indeed image synthesis in general)as a special case of neural net learning and interpolation/extrapolation [14,15,21].While this viewpoint is valid,in practice it is per-haps excessively general,for example,a skeleton is merely learned rather than being an intrinsic part of the model.While employed at Industrial Light and Magic the first author of the present paper developed a system that attempted to blend shape interpolation and SSD algorithms;a small portion of it remains in use in their well known Caricature animation system.Drawbacks of this work in-cluded both a complicated dependence on the details of SSD and its overall conception as a “correction”to SSD.Some commercialFigure4:Shepard’s interpolant operating on a set of colinear points.The derivative is zero at the data points,and the curve extrapolates to the average of the data values. packages allow blending between two sculpted deformations as afunction of a single-joint rotation,thereby combining shape inter-polation and skeleton-driven deformation in a limited but useful set-ting.2.4Kinematic or Physical Simulation?The depth of simulation is a prevalent issue in computer graph-ics,albeit one that is not always consciously considered.Earlyapproaches to animation were purely kinematic;an emphasis onphysically based modeling appeared in the literature later.Recentsophisticated approaches allow a hybrid of animator-controlled andphysically governed animation as needed.In rendering we perhapssee the opposite trend–much of the literature a decade ago focusedon ever deeper simulations of reality,whereas‘shallower’image-based approaches are attracting attention at present.Similarly,in character deformation both deep and shallow ap-proaches have their place.Deep models promise universally accu-rate simulation,and the importance of representing humans justifiesthe needed effort.The authors of these approaches acknowledgethat producing anatomically plausible models is a daunting task,however.Pose space deformation is a shallow,purely kinematic approach to deformation(i.e.without reference to underlying forces,mass,volume),and it has consequent disadvantages.In particular,accu-racy is reliant on the modeler/animator rather than being guaranteedby the simulation.On the other hand,our algorithm has clear ad-vantages with respect to simplicity and generality,direct manipula-tion,real-time synthesis,and other criteria listed in the introduction. 3Deformation as Scattered Interpolation In abstract,we wish to express the deformation of a surface as afunction of either the pose of an underlying skeleton,or equiva-lently as a function of some other set of parameters such as the {smile,raise-eyebrow,...}controls desirable in facial animation.We also wish to directly sculpt the desired deformation at various pointsin the parameter space,rather than working in a more abstract spacesuch as the coefficients on various coordinate frames as required bythe SSD algorithm.A scattered data interpolation method is required because defor-mations will be sculpted at arbitrary(rather than regularly spaced)poses.Since this interpolation is central to our application(the re-sults of the interpolation will be directly visible in the animatingdeformation),we will consider the available scattered interpolationapproaches before settling on a candidate.3.1Shepard’s MethodShepard’s method[1,2]is a frequently employed scattered datainterpolation scheme in computer graphics.In this method the in-terpolated value is a weighted sum of the surrounding datapoints Figure5:Radial basis functionsφ(x)=exp(−x2/2σ2),σ=10interpolating the same set of colinear points as in Figure4.A different y scale is used tofit the curve. The curve extrapolates to zero.normalized by the sum of the weights,ˆd(x)=w k(x)d kw k(x)with weights set to an inverse power of the distance:w k(x)= x−x k −p.(This is singular at the data points x k and should computed as(||x−x k + )−p).With p>1the interpolation surface is once differentiable.Unfortunately this simple scheme has some potentially undesirable properties.Far from the data the weights will be approximately the same,ˆd(∞)=w∞d k/w∞1=d k/N,i.e.the interpolated surface converges to the average of the data values.A serious drawback for some applications is that the derivative of the surface is zero at the data points(Figure4). 3.2Radial Basis FunctionsRadial basis functions[28,29]have become a popular choice for scattered interpolation.The interpolant is a linear combination of nonlinear functions of distance from the data points:ˆd(x)=Nkw kφ( x−x k )(1)If N values of d are available then the weights can be easily solved by a linear system;this can be derived either by least squaresfit or by subspace projection.Taking the latter approach,we reconsider the available data points as a single point d in an N dimensional space,and considerφk()=φ( x j−x k )as the k th basis vec-tor.The best approximation to d in the space spanned byφk()oc-curs(in direct analogy with the three-dimensional case)when the weights are such that the error d−Φw(withφk()comprising the columns ofΦ)is orthogonal to each of theφk():ΦT(Φw−d)=0so(the so-called“normal equation”)ΦTΦw=ΦT dcan be solved for the familiarw=(ΦTΦ)−1ΦT dA least squares approach leads to the identical result.Any nonlinear functionφ()will interpolate the data,includ-ing odd choices such asφ(x)=x(which is nonlinear since x= x−x k is the argument),provided that the columns ofΦare independent.On the other hand a smoothφ()will result in asmooth interpolant(a weighted sum of continuous functions is con-tinuous).In fact radial basis functions have a universal convergence property similar to Fourier series,though the convergence definition is different.The preceding description maps a k-dimensional input space(ar-bitrary k)to a one dimensional range,i.e.,it is the k-dimensional version of a heightfield.Surfaces can of course be interpolated by allowing different combinations of the same basis functions in different dimensions,i.e.,vector valued w k.The distance can be generalized to Mahalanobis distance(effectively rotating and stretching the basis function)[4].3.3Energy Functionals and Non-Convex Methods Various visual reconstruction schemes can be adapted for scattered data interpolation.In these schemes the interpolated or approxi-mated surface is found as the minimum of a functional such as|ˆd(x)−d(x)|2d x+λP(ˆd)where thefirst term penalizes deviation of the surfaceˆd from the available data d and the second regularizing term votes for surface smoothness e.g.by integrating the squared second derivative of the surface.With smallλmany of these schemes can serve as scat-tered data interpolants;reference[5]is a good introduction to these approaches.In some of the most powerful formulations of scattered interpo-lation the regularizer is considered to hold everywhere except at an unknown set of edges–this is the piecewise-smooth prior desirable in image reconstruction.Since the unknown edges may exist(or not exist)at any location in the domain,all combinations of possi-ble edge locations must be considered and the interpolation cost is prima facie exponential in the surface resolution.4Pose Space DeformationThe crux of our approach is the identification of an appropriate space for defining deformations.As discussed above,the inter-polation domain is(a subset of)the pose space of an articulated character,or equivalently the space defined by some set of parame-ters such as facial controls.In concept the range of the interpolation function could simply be the desired movement of the surface control vertices.To make the job easier for the interpolation we instead interpolate the desired deviation of a surface vertex(expressed in the local frame)from its initially computed position(the rigidly transformed position in the case of an articulated model).Several reasons for this choice will be mentioned shortly.Thus the deforming surface is defined by p+ δwith p moved rigidly by the skeleton or other underlying system,andδ=finterp(configuration)where configuration is the configuration of the set of joints or pa-rameters controlled by the animator.Our scheme can be bootstrapped on top of an existing software system:the model is posed as desired and the desired surface at that pose is sculpted.Our algorithm computes the difference between the initial and resculpted model at that pose.This‘deformation’is associated with the joints or other parameters that have moved from their default positions to create the particular pose.One or more deformations will then be interpolated in this subspace using a scattered data approach.We now have enough criteria to select a particular interpolation scheme.Although it would be desirable to allow deformations to change both continuously and discontinuously with respect to the pose space,creature deformations that are discontinuous with re-spect to pose seem unlikely.As such the expensive energy func-tional and non-convex schemes are not necessary.In addition we want δto approach zero away from the data,and the width of this falloff should be selectable.Together these comments supportφk(x)=exp(−( x−x k )22σ2) as one possible choice of radial basis(Figure5).Gaussian radial basis functions are reputed to be well behaved and our experience supports this judgement.Gaussian radial basis functions with ad-justable placement andσare discussed in the neural net literature and optimizing over these parameters is possible.This issue does not arise in our application,however,since the animator decides where in the parameter space to sculpt a pose(effectively decid-ing the basis function placement).The falloffσis also specified explicitly by the animator,as described below.4.1Algorithm SummaryThe steps in a pose space deformation(PSD)algorithm will now be described consecutively.Definitions.A pose is defined as the configuration of any pose controls(joints or abstract manipulators)that have changed from their default values.An abstract manipulator is a UI control or ar-bitrary piece of geometry whose movement will control the inter-polation of some deformation,such as a muscle bulge or a desired facial attribute such as“happiness.”A self-relative configuration of the controls is actually considered,for example,an elbow involves two skeletal frames but only one joint angle.The pose space is the space spanned by the variations of these controls.If n=2pose controls are active and each has three degrees of freedom then a3(n−1)pose space is defined,and the particular position of the controls defines a point in that space.Sculpt.The artistfirst positions some set of pose controls and then sculpts a deformation for that pose.The artist also assigns a falloff(Gaussianσ),either as a symmetric radius across all controls or to each control individually(axis stretched falloff).Define δ(pose).Any control vertices that have moved from their rest position are found.This is done in the local coordinate frame, i.e.,rigid body articulated motion results in zero δ.The δvalues for the deformed vertices are computed(again in the local coordi-nate system)and they are saved in a database together with their corresponding location in a pose space.(At the boundary of sev-eral surface patches there may be shared vertices that need to be coincident to maintain surface continuity.Unlike some SSD imple-mentations interpolation in pose space by definition cannot separate such vertices).Solve.When several such deformations have been saved(or when the artist is ready to try animating)it is necessary to solve the interpolation problem.For each control vertex that was moved during sculpting there are now one or more δvalues at points in the pose space.Note that the dimension of the pose space can vary across vertices,for example,a particular vertex might be modified in three sculpted deformations but a neighboring vertex might have been modified in only two deformations.The interpolation is done independently for each control vertex(but see additional details be-low);in our experience using patch surfaces this has not been prob-lematic.SingularΦTΦis interpreted as a user error;in practice this has turned out to be the result of saving new deformations without moving any pose controls rather than a result of actual numerical problems.Synthesis.The model is now moved to an arbitrary pose.The location in pose space is determined from the concatenated relative degrees of freedom of the pose controls(simply interpreted as in-dependent dimensions).For each deforming control vertex a δis interpolated from the delta values at the stored poses using Eq.(1).。
