From curve design algorithms to the design of rigid body motions

We discuss the following problem, which arises in computer animation and robot motion planning: given are N positions or keyframes (t_i) of a moving body ³ at time instances t_i. Compute a smooth rigid body motion (t) that interpolates or approximates the given positions (t_i) such that chosen feature points of the moving system run on smooth paths. We present an algorithm that can be considered as a transfer principle from curve design algorithms to motion design. The algorithm relies on known curve design algorithms and on registration techniques from computer vision. We prove that the motion generated in this way is of the same smoothness as the curve design algorithm employed. Supplementary material is available in the online version of this article at http://dx.doi.org/10.1007/s00371-003-0221-3To the memory of Peter Steiner     

Geometric constraint satisfaction using optimization methods

The numerical approach to solving geometric constraint problems is indispensable for building a practical CAD system. The most commonly-used numerical method is the Newton–Raphson method. It is fast, but has the instability problem: the method requires good initial values. To overcome this problem, recently the homotopy method has been proposed and experimented with. According to the report, the homotopy method generally works much better in terms of stability. In this paper we use the numerical optimization method to deal with the geometric constraint solving problem. The experimental results based on our implementation of the method show that this method is also much less sensitive to the initial value. Further, a distinctive advantage of the method is that under- and over-constrained problems can be handled naturally and efficiently. We also give many instructive examples to illustrate the above advantages.     

Analysis of natural finger-press motions for design of trackball buttons

This study analysed natural press motions of the index, middle and ring fingers for ergonomic design of the positions and surface angles of the left, middle and right trackball buttons. Finger motions of 26 male participants for naturally pressing the trackball buttons were recorded after the participants adjusted the trackball buttons to their preferred locations for comfortable pressing. The natural positions of the finger pulps formed a symmetrically rainbow-shaped reach zone for the fingers. The natural press angles of the fingers’ motion trajectories to the vertical reference line ranged from 14.2° to 20.5°, suggesting an 18-degree surface from the horizontal line for the trackball buttons. Regression formulas (adjusted R²?=?0.90?±?0.07 and mean squared error?=?8.55?±?7.52?mm) were established to estimate the natural positions of finger pulps from hand segment lengths and joint angles for a population having different hand sizes from this study.

Relevance to industry     

Analysis of three-dimensional motions in blocks world

This paper describes a computational analysis of three-dimensional motion in the blocks world. Input is a sequence of line drawings of rigid trihedral blocks projected orthogonally on an image plane. The blocks can show complex coincidental motion such that a block rotates around a joint attached to one side of another moving block.At first, a labeling scheme and an object-to-object matching method are applied to the image sequence to segment the images into individual blocks and find correspondences of their vertices between frames. A transition table of junction labels and contextual information between frames are used to analyze structural changes of the line drawings. Next, the shape rigidness property of three vertices on a block is used to evaluate geometrical parameters, such as orientations and edge lengths, then their interframe rotational movements are determined.Thus, the dynamic line images are interpreted as three-dimensional motion of blocks.     

利用几何代数进行线段模型匹配和运动估计

首先探讨了Clifford代数（几何代数）在计算机视觉中的应用,并得到了2D与3D旋转的统一表达公式,进而探讨了该公式在直线模型匹配和运动估计中的应用;在改进2D多角弧匹配算法的基础上,提出了一个同时进行线段模型的匹配和运动估计的算法。该算法通过最小化模型线段与被检测线段间的距离（距离函数定义为对应点间欧氏距离的积分）而求得的最佳运动估计中的旋转,可由一个矩阵的奇异值分解来表示,从而为首次同时解决这两个问题,进行了初步尝,且该算法不受维数限制。最后的模拟实验结果表明,该算法效果良好。     

表面细分的最优方法的分析与设计

基于模型上采集的非组织的样本点数据,给出了一个非线性至少平方的表面细分的完整框架。通过研究和分析三个几何上最优的表面细分的方法：点距离最小、切线距离最小、平方距离最小,来揭示它们的相交性与稳定性,以及非线性约束最优化的内部联系。对于点距离最小方法的分析,它是切线下降的变体,因此,只有线性相交。对于切线距离最小方法,它是接近二次相交零余留的问题,也有可能没有相交。平方距离最小方法,可以通过牛顿公式得到,并且是三种方法中相对最优的。通过对这三种方法的研究,来保证表面细分稳定地相交,且解决了对最优方法的争议。     

Geometric algorithms for automated design of multi-piece permanent molds

Multi-piece molds, which consist of more than two mold pieces, are capable of producing very complex parts—parts that cannot be produced by the traditional molds. The tooling cost is also low for multi-piece molds, which makes it a candidate for pre-production prototyping and bridge tooling. However, designing multi-piece molds is a time-consuming task. This article describes geometric algorithms for automated design of multi-piece molds. A multi-piece mold design algorithm has been developed to automate several important mold-design steps: finding parting directions, locating parting lines, creating parting surfaces, and constructing mold pieces. This algorithm constructs mold pieces based on global accessibility analysis results of the part and therefore guarantees the disassembly of the mold pieces. A software system has been developed, which has been successfully tested on several complex industrial parts.     

Geometric algorithms for automated design of rotary-platen multi-shot molds

This paper describes algorithms for automated design of rotary-platen type of multi-shot molds for manufacturing multi-material objects. The approach behind our algorithms works in the following manner. First, we classify the given multi-material object into several basic types based on the relationships among different components in the object. For every basic type, we find a molding sequence based on the precedence constraints resulting due to accessibility and disassembly requirements. Then, starting from the last mold stage, we generate the mold pieces for every mold stage. We expect that algorithms described in this paper will provide the necessary foundations for automating the design of rotary-platen molds.     

The application of fractal geometry to the design of grid or reticulated shell structures

The paper proposes an approach where structural systems can be developed according to the mathematical theory of fractals. Architecture can take advantage of the complexity sciences, by the use of present day computer technology, where algorithms of mathematical and geometric functions can produce new motifs of design. In order to demonstrate this, examples of the use of the elliptic and hyperbolic paraboloid, and the design of a tree on the surface of an elliptic paraboloid, are given. Further, the way to compose relevant algorithms is described.     

Retrieval of logically relevant 3D human motions by Adaptive Feature Selection with Graded Relevance Feedback

A system that can retrieve logically relevant 3D captured motions is useful in game and animation production. We presented a robust logical relevance metric based on the relative distances among the joints. Existing methods select a universal subset of features for all kinds of queries which may not well characterize the variations in different queries. To break through this limitation we proposed an Adaptive Feature Selection (AFS) method that abstracts the characteristics of the query by a Linear Regression Model, and different feature subsets can be selected according to the properties of the specific query. With a Graded Relevance Feedback (GRF) algorithm, we refined the feature subset that enhances the retrieval performance according to the graded relevance of the feedback samples. With an ontology that predefines the logical relevance between motion classes in terms of graded relevance, the performance of the proposed AFS-GRF algorithm is evaluated and shown to outperform other class-specific feature selection and motion retrieval methods.     

Evaluation of liquid‐crystal‐display motion blur with moving‐picture response time and human perception

Abstract— The moving‐picture response time (MPRT) for measuring liquid‐crystal‐display (LCD) motion blur was studied by several organizations in 2001. To determine the LCD motion blur that humans perceive, subjective evaluation experiments using the method of adjustment was conducted to find a strong correlation between perceived motion blur and extended blurred edge time (EBET) of the MPRT measurements. MPRT thus clearly indicates the degree of which humans perceive motion blur.     

Greedy Geometric Algorithms for Collection of Balls,with Applications to Geometric Approximation and Molecular Coarse‐Graining

Choosing balls that best approximate a 3D object is a non‐trivial problem. To answer it, we first address the inner approximation problem, which consists of approximating an object defined by a union of n balls with balls defining a region . This solution is further used to construct an outer approximation enclosing the initial shape, and an interpolated approximation sandwiched between the inner and outer approximations. The inner approximation problem is reduced to a geometric generalization of weighted max k‐cover, solved with the greedy strategy which achieves the classical lower bound. The outer approximation is reduced to exploiting the partition of the boundary of by the Apollonius Voronoi diagram of the balls defining the inner approximation. Implementation‐wise, we present robust software incorporating the calculation of the exact Delaunay triangulation of points with degree two algebraic coordinates, of the exact medial axis of a union of balls, and of a certified estimate of the volume of a union of balls. Application‐wise, we exhibit accurate coarse‐grain molecular models using a number of balls 20 times smaller than the number of atoms, a key requirement to simulate crowded cellular environments.     

Algorithms and implementation of a set partitioning approach for modular machining line design

A transfer line design problem is considered. Transfer lines are sequences of workstations equipped with processing modules called blocks each of which performs specific operations. These lines are used for mass production of one type of product and thus execute repetitively a given set of operations. The machine parts move along the stations in the same direction. An identical cost is associated with each station and differing costs are associated with the blocks. The problem is to determine the number of stations, select a set of blocks and assign selected blocks to the stations so that operations of the selected blocks constitute the original set of operations and the total cost is minimized. A distinct feature of the problem is that operations at the same station are performed in parallel. Plus, there are inclusion, exclusion and precedence relations that restrict the assignment of the blocks and operations to the same station as well as the processing order of the operations on the transfer line. We implement a novel set partitioning formulation of this design problem with pre-processing procedures and heuristics. The presented approach has the best performance among the existing methods in terms of solution time and quality.     

Motion/force tracking control of nonholonomic mechanical systems via combining cascaded design and backstepping

This paper considers motion/force tracking control of a class of Lagrange mechanical systems with classical nonholonomic constraints. A tracking control method is proposed by combining cascaded methods and backstepping techniques. The main results of this paper include three parts: (1) error dynamics between the kinematic system and the desired paths are transformed into a cascaded system consisting of two subsystems and an interconnection function; (2) under the framework of cascaded methods, virtual controllers for the subsystems are designed to stabilize the error dynamics; (3) the tracking controller is designed for the overall mechanical systems using backstepping techniques.     

Evaluation of motion performance on scanning‐backlight LCDs

Abstract— The scanning‐backlight technique to improve the motion performance of LCDs is introduced. This technique, however, has some drawbacks such as double edges and color aberration, which may become visible in moving patterns. A method combining accurate measurements of temporal luminance transitions with the simulation of human‐eye tracking and spatiotemporal integration is used to model the motion‐induced profile of an edge moving on a scanning‐backlight LCD‐TV panel that exhibits the two drawbacks mentioned above. The model results are validated with a perception experiment including different refresh rates, and a high correspondence is found between the simulated apparent edge and the one that is perceived during actual motion. Apart from the motion‐induced edge blur, the perception of a moving line or square‐wave grating can also be predicted by the same method starting from the temporal impulse and frame‐sequential response curves, respectively. Motion‐induced image degradation is evaluated for both a scanning‐ and continuous‐backlight mode based on three different characteristics: edge blur, line spreading, and modulation depth of square‐wave grating. The results indicate that the scanning‐backlight mode results in better motion performance.     

Motion extrapolation of auditory–visual targets

Many tasks involve the precise estimation of speed and position of moving objects, for instance to catch or avoid objects that cohabit in our environment. Many of these objects are characterised by signal representations in more than one modality, such as hearing and vision. The aim of this study was to investigate the extent to which the simultaneous presentation of auditory and visual signals enhances the estimation of motion speed and instantaneous position. Observers are asked to estimate the instant when a moving object arrives at a target spatial position by pressing a response button. This task requires observers to estimate the speed of the moving object and to calibrate the timing of their manual response such that it coincides with the true arrival time of the moving object. When both visual and auditory motion signals are available, the variability in estimating the arrival time of the moving object is significantly reduced compared to the variability in the unimodal conditions. This reduction in variability is consistent with optimal integration of the auditory and visual speed signals. The average bias in the estimated arrival times depends on the motion speed: for medium speeds (17 deg/s) observers’ subjective arrival times are earlier than the true arrival times; for high speeds (47 deg/s) observers exhibit a (much smaller) bias in the other direction. This speed-dependency suggests that the bias is due to an error in estimating the motion speeds rather than an error in calibrating the timing of the motor response. Finally, in this temporal localization task, the bias and variability show similar patterns for motion defined by vision, audition or both.     

光纤生物传感器探针锥形设计及参数优化

对免疫型光纤生物传感器的关键部件--光纤探针进行了分析.以模式匹配理论计算出的匹配半径为基础,采用图解法分析激发光在锥型光纤探头中的光线传输轨迹.根据倏逝波透射深度与光线入射角之间的关系,结合不同形状的探针内面对光线反射角的影响,提出抛物线锥形光纤探头,并对抛物线参数进行了比较.计算结果表明,为使入射光在均匀感应部分激发的能量最大,入射角在锥形感应部分必须满足在锥形终端最小且刚好是临界角的条件.通过对抛物线参数的选择,在锥形过渡段入射角在满足全反射的同时更接近于临界角,从而激发出更大的倏逝波,并与实验结果较好地符合.     

概念设计中草图类型笔触的语义理解研究

通过研究设计人员在绘图中的绘制行为及习惯, 提出了一种笔触语义与几何特征相结合的草图理解技术, 目的是建立一个在创意阶段适合概念设计人员的手绘交互界面系统。这种方法按照草绘过程提取笔触类型并分析其中所含的语义特征, 通过定义弯曲度阈值、压力度阈值的概念, 采用阈值检测来判断和理解草绘笔触类型, 将其融入到草绘各个阶段。结果使得不同阶段、不同功能笔触类型得到有效分类和辅助识别, 并且草绘过程中可以通过人机交互方式实现草绘稿和规整线稿的转换。实验表明, 这种手绘方法既在一定程度上达到了手绘效果, 又不妨碍设计者创意思路的延伸, 满足了个性化的绘制习惯。     

CAD系统的二次开发在飞机构型优化中的应用

飞机概念设计优化目前存在的主要问题是分析对象的几何描述过于简单、描述不统一和修改困难,造成分析计算可信度不高而且不同学科分析模块间信息很难转换。从建立一个三维运输机参数模型入手,通过CAD系统的二次开发,将模型集成到设计优化框架中,应用高信度的计算流体方法（CFD）,以飞机起飞重量最小为目标完成构型优化。     

A hierarchy of cameras for 3D photography

The view-independent visualization of 3D scenes is most often based on rendering accurate 3D models or utilizes image-based rendering techniques. To compute the 3D structure of a scene from a moving vision sensor or to use image-based rendering approaches, we need to be able to estimate the motion of the sensor from the recorded image information with high accuracy, a problem that has been well-studied. In this work, we investigate the relationship between camera design and our ability to perform accurate 3D photography, by examining the influence of camera design on the estimation of the motion and structure of a scene from video data. By relating the differential structure of the time varying plenoptic function to different known and new camera designs, we can establish a hierarchy of cameras based upon the stability and complexity of the computations necessary to estimate structure and motion. At the low end of this hierarchy is the standard planar pinhole camera for which the structure from motion problem is non-linear and ill-posed. At the high end is a camera, which we call the full field of view polydioptric camera, for which the motion estimation problem can be solved independently of the depth of the scene which leads to fast and robust algorithms for 3D Photography. In between are multiple view cameras with a large field of view which we have built, as well as omni-directional sensors.