Direct 3D coordinate transformation based on the affine invariance of barycentric coordinates

Liu, Hefeng; Fang, Yi

doi:10.1080/14498596.2019.1658653

Cited by 5 publications

(2 citation statements)

References 46 publications

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“…The linearization of the model and the initial approximation values for the seven parameters are absent from the adjustment model, even though it sets the first three rotation angles to zero. As attitude determination techniques for mobile carriers, including airborne vehicles, ships, and automobiles, these models find extensive application [12][13][14][15][16] .…”

Section: Introductionmentioning

confidence: 99%

A new method for establishing ballistic range spatial benchmark system using total station

yunhua,

bing,

wei

et al. 2024

Fourth International Conference on Sensors and Information Technology (ICSI 2024)

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Several measuring instruments, including CCD photography stations and velocity-coordinate measuring equipment, were arranged at various distances in the ballistic range. To ensure consistency and accuracy, the coordinates of each instrument need to be unified into the ballistic range coordinate system. This paper presents a new method that utilizes a high-precision total station for measuring and positioning, establishing a spatial benchmark system for the ballistic range. The three-dimensional coordinate values of all the equipment's datum points were obtained through the total station and the measuring equipment. The transformation matrix, derived from the coordinates of three non-collinear points in the calibration system, is used to convert between the two coordinate systems. The 3D coordinate transformation process is implemented using the Rodrigues matrix, resulting in direct calculation formulas for the seven parameters. The calibration bracket was used to calibrate all the measuring equipment in the ballistic range, ultimately leading to the establishment of a 1,000-meter benchmark system for light weapons. Experimental results indicate that the spatial benchmark system, based on the total station, effectively eliminates errors caused by human operation and achieves a spatial coordinate precision of less than 15mm. The method's simplicity and efficiency render it suitable for 3D coordinate transformation at any given angle.

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Section: Introductionmentioning

confidence: 99%

A new method for establishing ballistic range spatial benchmark system using total station

yunhua,

bing,

wei

et al. 2024

Fourth International Conference on Sensors and Information Technology (ICSI 2024)

View full text Add to dashboard Cite

show abstract

“…If all the scale factors are the same and after the orthogonality condition in the Equation (10) or Equation (11) is satisfied by the rotation matrix, the affine transformation goes into a transformation by similarity. Various variants of the affine transformation are presented, e.g., in References [ 25 , 26 , 27 ], and in this study, they will not be described in more detail.…”

Section: Introductionmentioning

confidence: 99%

Dimensioning Method of Floating Offshore Objects by Means of Quasi-Similarity Transformation with Reduced Tolerance Errors

Stępień

Tomczak

Loosaar³

et al. 2020

Sensors

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The human activities in the offshore oil and gas, renewable energy and construction industry require reliable data acquired by different types of hydrographic sensors: DGNSS (Differential Global Navigation Satellite System) positioning, attitude sensors, multibeam sonars, lidars or total stations installed on the offshore vessel, drones or platforms. Each component or sensor that produces information, unique to its position, will have a point that is considered as the reference point of that sensor. The accurate measurement of the offsets is vital to establish the mathematical relation between sensor and vessel common reference point in order to achieve sufficient accuracy of the survey data. If possible, the vessel will be put on a hard stand so that it can be very accurately measured using the standard land survey technique. However, due to the complex environment and sensors being mobilized when the vessel is in service, this may not be possible, and the offsets will have to be measured in sea dynamic conditions by means of a total station from a floating platform. This article presents the method of transformation by similarity with elements of affine transformation, called Q-ST (Quasi-Similarity Transformation). The Q-ST has been designed for measurements on such unstable substrates when it is not possible to level the total station (when the number of adjustment points is small (4–6 points)). Such situation occurs, among others, when measuring before the offshore duties or during the jack up or semi-submersible rig move. The presented calculation model is characterized by zero deviations at the adjustment points (at four common points). The transformation concerns the conversion of points between two orthogonal and inclined reference frames. The method enables the independent calculation of the scale factor, rotation matrix and system translation. Scaling is performed first in real space, and then both systems are shifted to the centroid, which is the center of gravity. The center of gravity is determined for the fit points that meet the criterion of stability of the orthogonal transformation. Then, the rotation matrix is computed, and a translation is performed from the computational (centroid) to real space. In the applied approach, the transformation parameters, scaling, rotation and translation, are determined independently, and the least squares method is applied independently at each stage of the calculations. The method has been verified in laboratory conditions as well as in real conditions. The results were compared to other known methods of coordinate transformation. The proposed approach is a development of the idea of transformation by similarity based on centroids.

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Measurement and Adjustment Model of the Reception Ratio of “FAST” Reflector Panel

Wang

et al. 2022

Application of Intelligent Systems in Multi-Modal Information Analytics

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Direct 3D coordinate transformation based on the affine invariance of barycentric coordinates

Cited by 5 publications

References 46 publications

A new method for establishing ballistic range spatial benchmark system using total station

A new method for establishing ballistic range spatial benchmark system using total station

Dimensioning Method of Floating Offshore Objects by Means of Quasi-Similarity Transformation with Reduced Tolerance Errors

Measurement and Adjustment Model of the Reception Ratio of “FAST” Reflector Panel

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