• Title/Summary/Keyword: and symmetry

Search Result 1,962, Processing Time 0.029 seconds

Intelligence Robot control for real-time Measurement of three-dimension object using information (지능로봇트제어를 위한 영상정보의 실시간 3차원 위치측정)

  • Oh, Weon-Geun;Lee, Han-Sik
    • Proceedings of the KIEE Conference
    • /
    • 1987.07b
    • /
    • pp.1090-1093
    • /
    • 1987
  • In this paper, we describe the principle, the procedure and calculation of the measurement. Finally the experimental results are shown and discussions are given. Interpreting of a skewed symmetry in the image as a real symmetry in the 3-D space provides strong constraints on 3-D sharp analysis. In order to apply the idea to the real scene, a method is presented which can find the skewed symmetry in the image of the skewed symmetrical object, even if it is occluded partly. there parameters of the skewed symmetry are estimated by examining peaks in two 2-D hough spaces, onto which the parameters of all candidates of boundary line segments for skewed symmetries are voted. The method is characterized with a small amount of computation, finding of multiple symmetry axes and inference of the occluded parts of the symmetrical object.

  • PDF

On symmetry of figures in elementary geometry (초등기하에서 도형의 대칭에 관한 연구)

  • Han, Gil-Jun;Shin, Bong-Sook
    • Journal for History of Mathematics
    • /
    • v.20 no.2
    • /
    • pp.73-88
    • /
    • 2007
  • In this paper, we study the symmetry of figures in elementary geometry. First, we investigate the historical and mathematical background of symmetry of figures and we explore the suitable teaching and learning methods for symmetry in elementary geometry. Also we study the major problem of geometry education that occurring in elementary school.

  • PDF

Vibration Design of a Rigid Body Supported by Orthogonal Springs (직교스프링들에 의해 지지되는 강체의 진동 설계)

  • Jang, Seon-Jun;Lee, Jun-Ho;Choi, Yong-Je
    • Transactions of the Korean Society of Mechanical Engineers A
    • /
    • v.31 no.1 s.256
    • /
    • pp.97-104
    • /
    • 2007
  • Vibration analysis of a rigid body supported by in-parallel linear springs can be greatly simplified by utilizing the conditions for a plane of symmetry. The vibration modes of an oscillatory system having plane of symmetry are classified into the in-plane and out-of-plane modes. From the viewpoint of screw theory, they represent respectively the vibration axes perpendicular to the plane of symmetry and lying in the plane of symmetry. In this paper, the sets of orthogonal and mutually intersecting three springs are used as resilient support of a rigid body. The geometrical conditions for the system to have a plane of symmetry and diagonalized stiffness matrix are presented. From the orthogonality of the vibration modes with respect to the inertia matrix, the geometrical relation between the reaction wrenches and the vibration modes are derived. This geometrical relation is then used to get the cubic design equation for the design of out-of-plane modes. The numerical design example of engine mounts is presented in order to explain the suggested design technique.

An Investigation on the Undentanding of Spatial Sense of Elementary School Students (초등학생들의 공간감각 이해능력 실태조사)

  • Lee, Sung-Mi;Pang, Jeong-Suk
    • The Mathematical Education
    • /
    • v.46 no.3
    • /
    • pp.273-292
    • /
    • 2007
  • The purpose of this study was to find out how second, fourth and sixth graders understood the main contents related to spatial sense in the Seventh National Mathematics Curriculum. For this purpose, this study examined students' understanding of the main contents of congruence transformation (slide, flip, turn), mirror symmetry, cubes, congruence and symmetry. An investigation was conducted and the subjects included 483 students. The main results are as follows. First, with regards to congruence transformation, whereas students had high percentages of correct answers on questions concerning slide, they had lower percentages on questions concerning turn. Percentages of correct answers on flip questions had significant differences among the three grades. In addition, most students experienced difficulties in describing the changes of shapes. Second, students understood the fact that the right and the left of an image in a mirror are exchanged, but they had poor overall understanding of mirror symmetry. The more complicated the cubes, the lower percentages of correct answers. Third, students had a good understanding of congruences, but they had difficulties in finding out congruent figures. Lastly, they had a poor understanding of symmetry and, in particular, didn't distinguish a symmetric figure of a line from a symmetric figure of a point.

  • PDF

The Symmetry of Cart-Pole System and A Table Look-Up Control Technique (운반차-막대 시스템의 대칭성과 Table Look-Up 제어 기법)

  • Kwon, Sunggyu
    • Journal of the Korean Institute of Intelligent Systems
    • /
    • v.14 no.3
    • /
    • pp.290-297
    • /
    • 2004
  • The control laws for cart-pole system are studied to see the schemes on which the control laws are made. Also, the odd symmetry of the relation between the output of the control laws and the system state vector is observed. Utilizing the symmetry in quantizing the system state variables and implementing the control laws into look-up table is discussed. Then, a CMAC is trained for a nonlinear control law for a cart-pole system such that the symmetry is conserved and its learning performance is evaluated. It is found that utilizing the symmetry is to reduce the memory requirement as well as the training period while improving the learning quality in terms of preserving the symmetry.

A Test for Spherical Symmetry (구형 대칭성 검정에 대한 연구)

  • Park Cheolyong
    • The Korean Journal of Applied Statistics
    • /
    • v.18 no.1
    • /
    • pp.99-113
    • /
    • 2005
  • In this article, we propose a chi-squared test of spherical symmetry. The advantage of this test is that the test statistic and its asymptotic p-value are easy to compute. The limiting distribution of the test statistic is derived under spherical symmetry and its accuracy, in finite samples, is studied via simulation. Also, a simulation study is conducted in which the power of our test is compared with those of other tests for spherical symmetry in various alternative distributions. Finally, an illustrative example of application to a real data is provided.

Software development for the visualization of brain fiber tract by using 24-bit color coding in diffusion tensor image

  • Oh, Jung-Su;Song, In-Chan;Ik hwan Cho;Kim, Jong-Hyo;Chang, Kee-Hyun;Park, Kwang-Suk
    • Proceedings of the KSMRM Conference
    • /
    • 2002.11a
    • /
    • pp.133-133
    • /
    • 2002
  • Purpose: The purpose of paper is to implement software to visualize brain fiber tract using a 24-bit color coding scheme and to test its feasibility. Materials and Methods: MR imaging was performed on GE 1.5 T Signa scanner. For diffusion tensor image, we used a single shot spin-echo EPI sequence with 7 non-colinear pulsed-field gradient directions: (x, y, z):(1,1,0),(-1,1,0),(1,0,1),(-1,0,1),(0,1,1),(0,1,-1) and without diffusion gradient. B-factor was 500 sec/$\textrm{mm}^2$. Acquisition parameters are as follows: TUTE=10000ms/99ms, FOV=240mm, matrix=128${\times}$128, slice thickness/gap=6mm/0mm, total slice number=30. Subjects consisted of 10 normal young volunteers (age:21∼26 yrs, 5 men, 5 women). All DTI images were smoothed with Gaussian kernel with the FWHM of 2 pixels. Color coding schemes for visualization of directional information was as follows. HSV(Hue, Saturation, Value) color system is appropriate for assigning RGB(Red, Green, and Blue) value for every different directions because of its volumetric directional expression. Each of HSV are assigned due to (r,$\theta$,${\Phi}$) in spherical coordinate. HSV calculated by this way can be transformed into RGB color system by general HSV to RGB conversion formula. Symmetry schemes: It is natural to code the antipodal direction to be same color(antipodal symmetry). So even with no symmetry scheme, the antipodal symmetry must be included. With no symmetry scheme, we can assign every different colors for every different orientation.(H =${\Phi}$, S=2$\theta$/$\pi$, V=λw, where λw is anisotropy). But that may assign very discontinuous color even between adjacent yokels. On the other hand, Full symmetry or absolute value scheme includes symmetry for 180$^{\circ}$ rotation about xy-plane of color coordinate (rotational symmetry) and for both hemisphere (mirror symmetry). In absolute value scheme, each of RGB value can be expressed as follows. R=λw|Vx|, G=λw|Vy|, B=λw|Vz|, where (Vx, Vy, Vz) is eigenvector corresponding to the largest eigenvalue of diffusion tensor. With applying full symmetry or absolute value scheme, we can get more continuous color coding at the expense of coding same color for symmetric direction. For better visualization of fiber tract directions, Gamma and brightness correction had done. All of these implementations were done on the IDL 5.4 platform.

  • PDF

Elastic Wave Propagation in Monoclinic System Due to Harmonic Line Load

  • Kim, Yong-Yun
    • The Journal of the Acoustical Society of Korea
    • /
    • v.17 no.2E
    • /
    • pp.47-52
    • /
    • 1998
  • An analysis of dynamic responses is carried out on monoclinic anisotropic system due to a buried harmonic line source. The load is in the form of a normal stress acting along an arbitrary axis on the plane of symmetry within the orthotropic materials: In case that the line load is acting along the symmetry axis normal to the plane of symmetry, plane wave equation is coupled with verital shear wave and longitudinal wave. However, if the line load is acting along an arbitrary axis normal to the plane of symmetry, plane wave equation is coupled with vertical shear wave, longitudinal wave and horizontal shear wave. We first considered the equation of motion in a reference coordinate system, where the line load is coincident with a symmetry axis of the orthotropic material. Then the equation of motion is transformed into one with respect to general coordinate system with azimuthal angle by using transformation tensor. Plane wave solutions of monoclinic systems are derived for infinite media. Finally complete solutions for the plane harmonic wave are obtained by calculating the inverse of the integral transforms, in which bulk wave poles are avoided by deforming the contour of the integration to the complex plane. Numerical results for examples of orthotropic material belonging to monoclinic symmetry are demonstrated.

  • PDF

Textbook analysis on the application of concave polygons in congruence and symmetrical teaching and learning (합동과 대칭의 교수학습에서 오목다각형의 활용에 대한 교과서 분석)

  • Kang, Yunji
    • Communications of Mathematical Education
    • /
    • v.38 no.2
    • /
    • pp.215-230
    • /
    • 2024
  • Congruences and symmetry are familiar concepts that can be encountered in everyday life. In order to effectively understand and acquire these concepts, the role of appropriate visual examples is important. This analysis examined various visual examples used in the process of learning the concepts of congruence and symmetry in elementary mathematics textbooks and focused on the use of convex polygons and concave polygons. As a result of the analysis, various types of polygons were used as visual examples for teaching and learning of congruence and symmetry in textbooks. The frequency of use of concave polygons was higher in the order of congruence, line symmetry, and point symmetry, and it was confirmed that it was used more frequently in the process of exploring properties than in the introduction of the concept. Based on these results, a plan to utilize concave polygons in teaching and learning of congruence and symmetry was sought.

Dynamic Responses in Orthotropic Media Due to Pulsating Line Source

  • Kim, Yong-Yun
    • The Journal of the Acoustical Society of Korea
    • /
    • v.17 no.1E
    • /
    • pp.70-75
    • /
    • 1998
  • The analysis of dynamic responses are carried out on several anisotropic systems due to buried pulsating line sources. These include infinite, semi-infinite spaces. The media possess orthotropic or higher symmetry. The load is in the from of a normal stress acting with parallel to symmetry axis on the plane of symmetry within the materials. The results are first derived for infinite media. Subsequently the results for semi-infinite are derived by using superposition of the solution in the infinite medium together with a scattered solution from the boundaries. The sum of both solutions has to satisfy stress free boundary conditions, thereby leading to the complete solutions. The solutions are simplified to the systems possessing of higher symmetry, such as orthotropic, transversely isotropic, cubic, and isotropic symmetry.

  • PDF