A calibration scheme under spherical coordinates is described for a magnetic tracker used in VR (virtual reality) system. A look up table containing data of tracked values for certain positions in the working space, ...A calibration scheme under spherical coordinates is described for a magnetic tracker used in VR (virtual reality) system. A look up table containing data of tracked values for certain positions in the working space, spe cified in spherical coordinates, is generated first, which is then used to calibrate the tracking results by a two dimensional interpolation. The scheme can effectively correct the static errors in the magnetic tracking system. The employment of spherical coordinates significantly reduces the calculation complexity in calibration.展开更多
This study quantifies the main characteristics of a terrain-following, G-coordinate through mathematical analyses of its covariant and contravariant basis vectors as well as the vertical coordinate of σ. A 3-D schema...This study quantifies the main characteristics of a terrain-following, G-coordinate through mathematical analyses of its covariant and contravariant basis vectors as well as the vertical coordinate of σ. A 3-D schematic of the σ-coordinate in a curvilinear coordinate system is provided in this study. The characteristics of the basis vectors were broken down into their ＂local vector charac- teristics＂ and ＂spatial distribution characteristics＂, and the exact expressions of the covariant; in addition, the con- travariant basis vectors of the G-coordinate used to eluci- date their detailed characteristics were properly solved. Through rewriting the expression of the vertical coordi- nate of G, a mathematical expression of all the cr-coor- dinate surfaces was found, thereby quantifying the so- called terrain-following characteristics and lack of flexi- bility to adjust the slope variation of G-coordinate sur- faces for the classic definition of G. Finally, an analysis on the range value of the vertical coordinate demonstrated that the general value range of G could be obtained by eliminating the G-coordinate surfaces below the Earth＇s surface. All these quantitative descriptions of the charac- teristics of G-coordinate were the foundation for improv- ing the G-coordinate or creating a new one.展开更多
Light pen coordinate measuring system(LPCMS)is a kind of portable coordinate measuring technique based on vision metrology.In classical LPCMS,the measuring range is limited to the camera’s field of view.To overcome t...Light pen coordinate measuring system(LPCMS)is a kind of portable coordinate measuring technique based on vision metrology.In classical LPCMS,the measuring range is limited to the camera’s field of view.To overcome this defect,a new LPCMS is designed in this paper to fulfil whole space coordinate measurement.The camera is installed on a turntable instead of a tripod,so that the camera can rotate to track the movement of the light pen.The new system can be applied to large scale onsite measurement,and therefore it notably extends the application of LPCMS.To guarantee the accuracy of the new system,a method to calibrate the parameters of the tracking turntable is also proposed.Fixing the light pen at a stationary position,and changing the azimuth angles of the turntable’s two shafts,so that the camera can capture the images of the light pen from different view angles.According to the invariant spatial relationship between the camera and the pedestal of the tracking turntable,a system of nonlinear equations can be established to solve the parameters of the turntable.Experimental results show that the whole space coordinate measuring accuracy of the new system can reach 0.25 mm within 10 m.It can be concluded that the newly designed system can significantly expand the measuring range of LPCMS without losing too much accuracy.展开更多
文摘A calibration scheme under spherical coordinates is described for a magnetic tracker used in VR (virtual reality) system. A look up table containing data of tracked values for certain positions in the working space, spe cified in spherical coordinates, is generated first, which is then used to calibrate the tracking results by a two dimensional interpolation. The scheme can effectively correct the static errors in the magnetic tracking system. The employment of spherical coordinates significantly reduces the calculation complexity in calibration.
基金supported by the National Natural Science Foundation of China under Grant Nos. 40821092,40633016,and 40875022
文摘This study quantifies the main characteristics of a terrain-following, G-coordinate through mathematical analyses of its covariant and contravariant basis vectors as well as the vertical coordinate of σ. A 3-D schematic of the σ-coordinate in a curvilinear coordinate system is provided in this study. The characteristics of the basis vectors were broken down into their ＂local vector charac- teristics＂ and ＂spatial distribution characteristics＂, and the exact expressions of the covariant; in addition, the con- travariant basis vectors of the G-coordinate used to eluci- date their detailed characteristics were properly solved. Through rewriting the expression of the vertical coordi- nate of G, a mathematical expression of all the cr-coor- dinate surfaces was found, thereby quantifying the so- called terrain-following characteristics and lack of flexi- bility to adjust the slope variation of G-coordinate sur- faces for the classic definition of G. Finally, an analysis on the range value of the vertical coordinate demonstrated that the general value range of G could be obtained by eliminating the G-coordinate surfaces below the Earth＇s surface. All these quantitative descriptions of the charac- teristics of G-coordinate were the foundation for improv- ing the G-coordinate or creating a new one.
基金State Administration of Science,Technology and Industry for the National Defense(No.JSJL2014206B001)。
文摘Light pen coordinate measuring system(LPCMS)is a kind of portable coordinate measuring technique based on vision metrology.In classical LPCMS,the measuring range is limited to the camera’s field of view.To overcome this defect,a new LPCMS is designed in this paper to fulfil whole space coordinate measurement.The camera is installed on a turntable instead of a tripod,so that the camera can rotate to track the movement of the light pen.The new system can be applied to large scale onsite measurement,and therefore it notably extends the application of LPCMS.To guarantee the accuracy of the new system,a method to calibrate the parameters of the tracking turntable is also proposed.Fixing the light pen at a stationary position,and changing the azimuth angles of the turntable’s two shafts,so that the camera can capture the images of the light pen from different view angles.According to the invariant spatial relationship between the camera and the pedestal of the tracking turntable,a system of nonlinear equations can be established to solve the parameters of the turntable.Experimental results show that the whole space coordinate measuring accuracy of the new system can reach 0.25 mm within 10 m.It can be concluded that the newly designed system can significantly expand the measuring range of LPCMS without losing too much accuracy.
