Search results for: Horizontal 3D Camera Rig

Authors: Seong-Mo An, Rohit Ramesh, Young-Sook Lee, Wan-Young Chung

Abstract:

The proper assessment of interaxial distance and convergence control are important factors in stereoscopic imaging technology to make an efficient 3D image. To control interaxial distance and convergence for efficient 3D shooting, horizontal 3D camera rig is designed using some hardware components like 'LM Guide', 'Goniometer' and 'Rotation Stage'. The horizontal 3D camera rig system can be properly aligned by moving the two cameras horizontally in same or opposite directions, by adjusting the camera angle and finally considering horizontal swing as well as vertical swing. In this paper, the relationship between interaxial distance and convergence angle control are discussed and intensive experiments are performed in order to demonstrate an easy and effective 3D shooting.

Keywords: Interaxial, Convergence, Stereoscopic, Horizontal 3D Camera Rig

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Authors: Meysam Naeimi, Zili Li, Rolf Dollevoet

Abstract:

A new small–scale test rig developed for rolling contact fatigue (RCF) investigations in wheel–rail material. This paper presents the scaling strategy of the rig based on dimensional analysis and mechanical modelling. The new experimental rig is indeed a spinning frame structure with multiple wheel components over a fixed rail-track ring, capable of simulating continuous wheelrail contact in a laboratory scale. This paper describes the dimensional design of the rig, to derive its overall scaling strategy and to determine the key elements’ specifications. Finite element (FE) modelling is used to simulate the mechanical behavior of the rig with two sample scale factors of 1/5 and 1/7. The results of FE models are compared with the actual railway system to observe the effectiveness of the chosen scales. The mechanical properties of the components and variables of the system are finally determined through the design process.

Keywords: New test rig, rolling contact fatigue, rail, small scale.

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Authors: Peter Podbreznik, Božidar Potocnik

Abstract:

A camera in the building site is exposed to different weather conditions. Differences between images of the same scene captured with the same camera arise also due to temperature variations. The influence of temperature changes on camera parameters were modelled and integrated into existing analytical camera model. Modified camera model enables quantitatively assessing the influence of temperature variations.

Keywords: camera calibration, analytical model, intrinsic parameters, extrinsic parameters, temperature variations.

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Authors: Jin Sun, Hongbin Gu

Abstract:

An important step in three-dimensional reconstruction and computer vision is camera calibration, whose objective is to estimate the intrinsic and extrinsic parameters of each camera. In this paper, two linear methods based on the different planes are given. In both methods, the general plane is used to replace the calibration object with very good precision. In the first method, after controlling the camera to undergo five times- translation movements and taking pictures of the orthogonal planes, a set of linear constraints of the camera intrinsic parameters is then derived by means of homography matrix. The second method is to get all camera parameters by taking only one picture of a given radius circle. experiments on simulated data and real images,indicate that our method is reasonable and is a good supplement to camera calibration.

Keywords: camera calibration, 3D reconstruction, computervision

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Authors: Qidi Lin, Hewei Yu, Jinbin Huang, Weile Liang

Abstract:

This paper introduces a video sharing platform based on WiFi, which consists of camera, mobile phone and PC server. This platform can receive wireless signal from the camera and show the live video on the mobile phone captured by camera. In addition, it is able to send commands to camera and control the camera’s holder to rotate. The platform can be applied to interactive teaching and dangerous area’s monitoring and so on. Testing results show that the platform can share the live video of mobile phone. Furthermore, if the system’s PC server and the camera and many mobile phones are connected together, it can transfer photos concurrently.

Keywords: Wifi Camera, Socket, Mobile platform, Video monitoring, Remote control.

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Authors: Meysam Naeimi, Zili Li, Roumen Petrov, Rolf Dollevoet, Jilt Sietsma, Jun Wu

Abstract:

The substantial similarity of fatigue mechanism in a new test rig for rolling contact fatigue (RCF) has been investigated. A new reduced-scale test rig is designed to perform controlled RCF tests in wheel-rail materials. The fatigue mechanism of the rig is evaluated in this study using a combined finite element-fatigue prediction approach. The influences of loading conditions on fatigue crack initiation have been studied. Furthermore, the effects of some artificial defects (squat-shape) on fatigue lives are examined. To simulate the vehicle-track interaction by means of the test rig, a threedimensional finite element (FE) model is built up. The nonlinear material behaviour of the rail steel is modelled in the contact interface. The results of FE simulations are combined with the critical plane concept to determine the material points with the greatest possibility of fatigue failure. Based on the stress-strain responses, by employing of previously postulated criteria for fatigue crack initiation (plastic shakedown and ratchetting), fatigue life analysis is carried out. The results are reported for various loading conditions and different defect sizes. Afterward, the cyclic mechanism of the test rig is evaluated from the operational viewpoint. The results of fatigue life predictions are compared with the expected number of cycles of the test rig by its cyclic nature. Finally, the estimative duration of the experiments until fatigue crack initiation is roughly determined.

Keywords: Fatigue, test rig, crack initiation, life, rail, squats.

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Authors: Ravindra Mallya, B. Satish Shenoy, B. Raghuvir Pai

Abstract:

The study deals with the challenges in developing a test rig to test the performance of water lubricated journal bearing. The test rig is designed to simulate the working conditions of the bearing in order to understand their performance before they are put in operation. The bearing that is studied is the commercially available water lubricated bearing which has a rubber liner bonded with a rigid metal shell. The lubricant enters the bearing axially through a pressurized inlet tank and exits to an outlet tank which is at sufficiently low pressure. The load on the bearing is applied through the dead weight system which acts both in upward and downward direction so that net load acts on the bearing. The issues in feeding the lubricant into the bearing from the inlet side and preventing the leakage of the lubricant is discussed. The application of the load on the test bearing while maintaining the bearing afloat is also discussed.

Keywords: Axial groove, hydrodynamic pressure, journal bearing, test rig, water lubrication.

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Authors: Marine Segui, Matthieu Mantilla, Ruxandra Mihaela Botez

Abstract:

This research is the part of a major project at the Research Laboratory in Active Controls, Avionics and Aeroservoelasticity (LARCASE) aiming to improve a Cessna Citation X aircraft cruise performance with an application of the morphing wing technology on its horizontal tail. However, the horizontal stabilizer of the Cessna Citation X turns around its span axis with an angle between -8 and 2 degrees. Within this range, the horizontal stabilizer generates certainly some unwanted drag. To cancel this drag, the LARCASE proposes to trim the aircraft with a horizontal stabilizer equipped by a morphing wing technology. This technology aims to optimize aerodynamic performances by changing the conventional horizontal tail shape during the flight. As a consequence, this technology will be able to generate enough lift on the horizontal tail to balance the aircraft without an unwanted drag generation. To conduct this project, an accurate aerodynamic model of the horizontal tail is firstly required. This aerodynamic model will finally allow precise comparison between a conventional horizontal tail and a morphed horizontal tail results. This paper presents how this aerodynamic model was designed. In this way, it shows how the 2D geometry of the horizontal tail was collected and how the unknown airfoil’s shape of the horizontal tail has been recovered. Finally, the complete horizontal tail airfoil shape was found and a comparison between aerodynamic polar of the real horizontal tail and the horizontal tail found in this paper shows a maximum difference of 0.04 on the lift or the drag coefficient which is very good. Aerodynamic polar data of the aircraft horizontal tail are obtained from the CAE Inc. level D research aircraft flight simulator of the Cessna Citation X.

Keywords: Aerodynamic, Cessna, Citation X, coefficient, Datcom, drag, lift, longitudinal, model, OpenVSP.

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Authors: Yue Zhao, Chao Li

Abstract:

Camera calibration is an important step in 3D reconstruction. Camera calibration may be classified into two major types: traditional calibration and self-calibration. However, a calibration method in using a checkerboard is intermediate between traditional calibration and self-calibration. A self is proposed based on a square in this paper. Only a square in the planar template, the camera self-calibration can be completed through the single view. The proposed algorithm is that the virtual circle and straight line are established by a square on planar template, and circular points, vanishing points in straight lines and the relation between them are be used, in order to obtain the image of the absolute conic (IAC) and establish the camera intrinsic parameters. To make the calibration template is simpler, as compared with the Zhang Zhengyou-s method. Through real experiments and experiments, the experimental results show that this algorithm is feasible and available, and has a certain precision and robustness.

Keywords: Absolute conic, camera calibration, circle point, vanishing point.

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Authors: Qihe Li, Yupin Luo

Abstract:

Camera calibration plays an important role in the domain of the analysis of sports video. Considering soccer video, in most cases, the cross-points can be used for calibration at the center of the soccer field are not sufficient, so this paper introduces a new automatic camera calibration algorithm focus on solving this problem by using the properties of images of the center circle, halfway line and a touch line. After the theoretical analysis, a practicable automatic algorithm is proposed. Very little information used though, results of experiments with both synthetic data and real data show that the algorithm is applicable.

Keywords: Absolute conic, camera calibration, circular points, line at infinity.

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Authors: M. Azadbakht, B. Azadbakht, R. Janzade Galogah, A. Kiapei, H. Jafari

Abstract:

In this research, performance of rotavator with horizontal rotary axis and vertical rotary axis has been evaluated and compared. The mean weight diameter (MWD), cross-sectional area disturbed and cone index of soil investigated. Factorial experiments based on a randomized complete block with 18 treatments, three different velocities 2.2, 3.5, 6.1 km/h; three different depth of 5, 10, 15cm and with two rotary plows horizontal axis and vertical axis with three replications were used. Result showed that maximum MWD in 6.1 km/h and 15cm of depth were 55.6 and 52.5mm for horizontal axis rotavator, respectively. The minimum MWD in 2.2 km/h and 5cm of depth for vertical axis rotavator were 34.9 and 35.1mm, respectively. The values of cone index 1861.1 and 2339.5 kPa for vertical axis rotavator and horizontal axis rotavator were obtained, respectively, also the values of cross-sectional area disturbed 687 and 497.2cm² for vertical axis rotavator and horizontal axis rotavator were obtained, respectively.

Keywords: Horizontal rotary axis, vertical rotary axis, rotavator, MWD, cone index, cross-sectional area.

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Authors: Yunyoung Nam, Junghun Ryu, Yoo-Joo Choi, We-Duke Cho

Abstract:

This paper presents a novel approach for representing the spatio-temporal topology of the camera network with overlapping and non-overlapping fields of view (FOVs). The topology is determined by tracking moving objects and establishing object correspondence across multiple cameras. To track people successfully in multiple camera views, we used the Merge-Split (MS) approach for object occlusion in a single camera and the grid-based approach for extracting the accurate object feature. In addition, we considered the appearance of people and the transition time between entry and exit zones for tracking objects across blind regions of multiple cameras with non-overlapping FOVs. The main contribution of this paper is to estimate transition times between various entry and exit zones, and to graphically represent the camera topology as an undirected weighted graph using the transition probabilities.

Keywords: Surveillance, multiple camera, people tracking, topology.

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Authors: Kyoung-Mi Lee, Youn-Mi Lee

Abstract:

This paper proposes a way to track persons by making use of multiple non-overlapping cameras. Tracking persons on multiple non-overlapping cameras enables data communication among cameras through the network connection between a camera and a computer, while at the same time transferring human feature data captured by a camera to another camera that is connected via the network. To track persons with a camera and send the tracking data to another camera, the proposed system uses a hierarchical human model that comprises a head, a torso, and legs. The feature data of the person being modeled are transferred to the server, after which the server sends the feature data of the human model to the cameras connected over the network. This enables a camera that captures a person's movement entering its vision to keep tracking the recognized person with the use of the feature data transferred from the server.

Keywords: Person tracking, human model, networked cameras, vision-based surveillance.

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Authors: Jinseon Song, Yongwan Park

Abstract:

In this paper, propose method that can user’s position that based on database is built from single camera. Previous positioning calculate distance by arrival-time of signal like GPS (Global Positioning System), RF(Radio Frequency). However, these previous method have weakness because these have large error range according to signal interference. Method for solution estimate position by camera sensor. But, signal camera is difficult to obtain relative position data and stereo camera is difficult to provide real-time position data because of a lot of image data, too. First of all, in this research we build image database at space that able to provide positioning service with single camera. Next, we judge similarity through image matching of database image and transmission image from user. Finally, we decide position of user through position of most similar database image. For verification of propose method, we experiment at real-environment like indoor and outdoor. Propose method is wide positioning range and this method can verify not only position of user but also direction.

Keywords: Positioning, Distance, Camera, Features, SURF (Speed-Up Robust Features), Database, Estimation.

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Authors: A. H. W. Goh, Y. S. Yong, C. H. Chan, S. J. Then, L. P. Chu, S. W. Chau, H. W. Hon

Abstract:

This paper proposes an alternative control mechanism for an interactive Pan/Tilt/Zoom (PTZ) camera control system. Instead of using a mouse or a joystick, the proposed mechanism utilizes a Nintendo Wii remote and infrared (IR) sensor bar. The Wii remote has buttons that allows the user to control the movement of a PTZ camera through Bluetooth connectivity. In addition, the Wii remote has a built-in motion sensor that allows the user to give control signals to the PTZ camera through pitch and roll movement. A stationary IR sensor bar, placed at some distance away opposite the Wii remote, enables the detection of yaw movement. In addition, the Wii remote-s built-in IR camera has the ability to detect its spatial position, and thus generates a control signal when the user moves the Wii remote. Some experiments are carried out and their performances are compared with an industry-standard PTZ joystick.

Keywords: Bluetooth, Infrared, Pan/Tilt/Zoom, PTZ Camera, Visual Surveillance, Wii Remote

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Authors: Fares Senouci, Bachir Imine

Abstract:

This document provides numerical and experimental optimization of the aerodynamic performance of a drone equipped with three types of horizontal stabilizer. To build this optimal configuration, an experimental and numerical study was conducted on three parameters: the geometry of the stabilizer (horizontal form or reverse V form), the position of the horizontal stabilizer (up or down), and the landing gear position (closed or open). The results show that up-stabilizer position with respect to the horizontal plane of the fuselage provides better aerodynamic performance, and that the landing gear increases the lift in the zone of stability, that is to say where the flow is not separated.

Keywords: Aerodynamics, wind tunnel, turbulence model, lift, drag.

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Authors: C. R. Balamurugan, P. Vijayakumar, P. Kiruba, S. Arun Kanna, E. R. Hariprasath, C. Anu Priya

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This paper studies in details about the need of quadcopter in various fields especially in the place of remote area where the road transportation facility is very less. It is used to monitor and collect data in a specific region. The movement of this quadcopter is controlled by the Raspberry Pi. FPV camera is used for capturing the image and will transmit the image to the receiver which can be monitored using an android smart phone. This is mainly used for surveillance purpose and hidden activities can be captured.

Keywords: FPV camera, A2212 brushless direct current motor, Raspberry Pi, lithium polymer battery.

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Authors: Varin Chouvatut, Suthep Madarasmi, Mihran Tuceryan

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This paper aims to propose a novel, robust, and simple method for obtaining a human 3D face model and camera pose (position and orientation) from a video sequence. Given a video sequence of a face recorded from an off-the-shelf digital camera, feature points used to define facial parts are tracked using the Active- Appearance Model (AAM). Then, the face-s 3D structure and camera pose of each video frame can be simultaneously calculated from the obtained point correspondences. This proposed method is primarily based on the combined approaches of Gradient Descent and Powell-s Multidimensional Minimization. Using this proposed method, temporarily occluded point including the case of self-occlusion does not pose a problem. As long as the point correspondences displayed in the video sequence have enough parallax, these missing points can still be reconstructed.

Keywords: Camera Pose, Face Reconstruction, Gradient Descent, Powell's Multidimensional Minimization.

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Authors: Abdulrahman S. Alturki, John S. Loomis

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This paper discusses a corner detection algorithm for camera calibration. Calibration is a necessary step in many computer vision and image processing applications. Robust corner detection for an image of a checkerboard is required to determine intrinsic and extrinsic parameters. In this paper, an algorithm for fully automatic and robust X-corner detection is presented. Checkerboard corner points are automatically found in each image without user interaction or any prior information regarding the number of rows or columns. The approach represents each X-corner with a quadratic fitting function. Using the fact that the X-corners are saddle points, the coefficients in the fitting function are used to identify each corner location. The automation of this process greatly simplifies calibration. Our method is robust against noise and different camera orientations. Experimental analysis shows the accuracy of our method using actual images acquired at different camera locations and orientations.

Keywords: Camera Calibration, Corner Detector, Saddle Points, X-Corners.

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Authors: S. Malek, N. Zenati-Henda, M. Belhocine, S. Benbelkacem

Abstract:

In geometrical camera calibration, the objective is to determine a set of camera parameters that describe the mapping between 3D references coordinates and 2D image coordinates. In this paper, a technique of calibration and tracking based on both a least squares method is presented and a correlation technique developed as part of an augmented reality system. This approach is fast and it can be used for a real time system

Keywords: Camera calibration, pinhole model, least squares method, augmented reality, strong calibration.

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Authors: Hao Wang, Yanming Zou

Abstract:

Two-dimensional (2D) bar codes were designed to carry significantly more data with higher information density and robustness than its 1D counterpart. Thanks to the popular combination of cameras and mobile phones, it will naturally bring great commercial value to use the camera phone for 2D bar code reading. This paper addresses the problem of specific 2D bar code design for mobile phones and introduces a low-level encoding method of matrix codes. At the same time, we propose an efficient scheme for 2D bar codes decoding, of which the effort is put on solutions of the difficulties introduced by low image quality that is very common in bar code images taken by a phone camera.

Keywords: 2D bar code reading, camera phone, low-level encoding, mixed model

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Authors: Norihiro Nishio, Yuki Deguchi, Takahiro Sugiyama, Yoichi Takebayashi

Abstract:

We developed a multi-camera control system that a (one) cameraman can operate several cameras at a compact studio. we analyzed a workflow of a cameraman of some program shootings with two cameras and clarified their heavy tasks. The system based on a dynamic workflow which adapts a program progressing and recommends of cameraman. we perform the automation of multicamera controls by modeling of studio environment and perform automatic camera adjustment for suitable angle of view with face detection. Our experiment at a real program shooting showed that one cameraman can carry out the task of shooting sufficiently.

Keywords: Camera work, compact studio, dynamic workflow, shooting support.

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Authors: Won-Ho Kim

Abstract:

In this paper, a design of H.263 based wireless video transceiver is presented for wireless camera system. It uses standard WIFI transceiver and the covering area is up to 100m. Furthermore the standard H.263 video encoding technique is used for video compression since wireless video transmitter is unable to transmit high capacity raw data in real time and the implemented system is capable of streaming at speed of less than 1Mbps using NTSC 720x480 video.

Keywords: Digital signal processing, H.263 video encoder, surveillance camera, wireless video transceiver.

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Authors: Somkiat Wangsiripitak

Abstract:

Virtual touch screen using camera is an ordinary screen which uses a camera to imitate the touch screen by taking a picture of an indicator, e.g., finger, which is laid on the screen, converting the indicator tip position on the picture to the position on the screen, and moving the cursor on the screen to that position. In fact, the indicator is not laid on the screen directly, but it is intervened by the cover at some intervals. In spite of this gap, if the eye-indicator-camera angle is not large, the mapping from the indicator tip positions on the image to the corresponding cursor positions on the screen is not difficult and could be done with a little error. However, the larger the angle is, the bigger the error in the mapping occurs. This paper proposes cursor position estimation model for virtual touch screen using camera which could eliminate this kind of error. The proposed model (i) moves the on-screen pilot cursor to the screen position which locates on the screen at the position just behind the indicator tip when the indicator tip has been looked from the camera position, and then (ii) converts that pilot cursor position to the desirable cursor position (the position on the screen when it has been looked from the user-s eye through the indicator tip) by using the bilinear transformation. Simulation results show the correctness of the estimated cursor position by using the proposed model.

Keywords: Bilinear transformation, cursor position, pilot cursor, virtual touch screen.

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Authors: Peter Podbreznik, Božidar Potocnik

Abstract:

The camera parameters are changed due to temperature variations, which directly influence calibrated cameras accuracy. Robustness of calibration methods were measured and their accuracy was tested. An error ratio due to camera parameters change with respect to total error originated during calibration process was determined. It pointed out that influence of temperature variations decrease by increasing distance of observed objects from cameras.

Keywords: camera calibration, perspective projection matrix, epipolar geometry, temperature variation.

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Authors: Umar Alhaji Mukhtar, Abubakar Mohammed El-jummah

Abstract:

This research involved the utilization of fluid flow energy to predict power output using Lead Zirconate Titanate (PZT) piezoelectric stacks. The aim of this work is to extract energy from a controlled level of pressure fluctuation in single-phase flow which forms a part of the energy harvesting technology that powers flow meters. A device- Perspex box was developed and fixed to 50.8 mm rig to induce pressure fluctuation in the flow. An experimental test was carried out using the single-phase water flow in the developed rig in order to measure the power output generation from the piezoelectric stacks. 16 sets of experimental tests were conducted to ensure the maximum output result. The acquired signal of the pressure fluctuation was used to simulate the expected electrical output from the piezoelectric material. The results showed a maximum output voltage of 12 V with an instantaneous output power of 1 µW generated, when the pressure amplitude is 2.6 kPa at a frequency of 2.4 Hz.

Keywords: Energy harvesting, experimental test, perspex rig, pressure fluctuation.

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Authors: C. C. Wang, N. S. Pai, H. T. Yau, T. T. Liao, M. J. Jang, C. W. Lee, W. M. Hong

Abstract:

Horizontal platform system (HPS) is popularly applied in offshore and earthquake technology, but it is difficult and time-consuming for regulation. In order to understand the nonlinear dynamic behavior of HPS and reduce the cost when using it, this paper employs differential transformation method to study the bifurcation behavior of HPS. The numerical results reveal a complex dynamic behavior comprising periodic, sub-harmonic, and chaotic responses. Furthermore, the results reveal the changes which take place in the dynamic behavior of the HPS as the external torque is increased. Therefore, the proposed method provides an effective means of gaining insights into the nonlinear dynamics of horizontal platform system.

Keywords: horizontal platform system, differentialtransformation method, chaotic.

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Authors: Yongsei Lee, Hyunsu Park, Youngseob Yu, Heechan Yoo, Sungin Yoo

Abstract:

A horizontal anaerobic digester was developed and tested in pilot scale for Korean food waste with high water contents (>80%). The hydrogen sulfide in the biogas was removed by a biological desulfurization equipment integrated in the horizontal digester. A mixer of the horizontal digester was designed to easily remove the sediment in the bottom and scum layers on surface in the digester. Experimental result for 120 days of operation of the pilot plant showed a high removal efficiency of 81.2% for organic substance and high stability during the whole operation period were acquired. Also food waste was treated at high organic loading rates over 4 kg•VS/m3∙day and a methane gas production rate of 0.62 m3/kg•VSremoved was accomplished. The biological desulfurization equipment inside the horizontal digester was proven to be an economic and effective method to reduce the biogas desulfurization cost by removing hydrogen sulfide more than 90% without external desulfurization equipments.

Keywords: Biogas, Biological desulfurization, Horizontal anaerobic digester, Korean food waste

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Authors: Stephan Rupp, Matthias Elter, Michael Breitung, Walter Zink, Christian Küblbeck

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Camera calibration is an indispensable step for augmented reality or image guided applications where quantitative information should be derived from the images. Usually, a camera calibration is obtained by taking images of a special calibration object and extracting the image coordinates of projected calibration marks enabling the calculation of the projection from the 3d world coordinates to the 2d image coordinates. Thus such a procedure exhibits typical steps, including feature point localization in the acquired images, camera model fitting, correction of distortion introduced by the optics and finally an optimization of the model-s parameters. In this paper we propose to extend this list by further step concerning the identification of the optimal subset of images yielding the smallest overall calibration error. For this, we present a Monte Carlo based algorithm along with a deterministic extension that automatically determines the images yielding an optimal calibration. Finally, we present results proving that the calibration can be significantly improved by automated image selection.

Keywords: Camera Calibration, Discrete Optimization, Monte Carlo Method.

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Authors: Hasan Hassoun, Jaafar Hallal, Denis Duhamel, Mohammad Hammoud, Ali Hage Diab

Abstract:

This paper aims to prove the accuracy of an inexpensive smartphone camera as a non-contact vibration sensor to recover the vibration modes of a vibrating structure such as a cantilever beam. A video of a vibrating beam is filmed using a smartphone camera and then processed by the motion magnification technique. Based on this method, the first two natural frequencies and their associated mode shapes are estimated experimentally and compared to the analytical ones. Results show a relative error of less than 4% between the experimental and analytical approaches for the first two natural frequencies of the beam. Also, for the first two-mode shapes, a Modal Assurance Criterion (MAC) value of above 0.9 between the two approaches is obtained. This slight error between the different techniques ensures the viability of a cheap smartphone camera as a non-contact vibration sensor, particularly for structures vibrating at relatively low natural frequencies.

Keywords: Modal Analysis, motion magnification, smartphone camera, structural vibration, vibration modes.

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