Online three-dimensional SLAM by registration of large planar surface segments and closed-form pose-graph relaxation

2010 ◽  
Vol 27 (1) ◽  
pp. 52-84 ◽  
Author(s):  
Kaustubh Pathak ◽  
Andreas Birk ◽  
Narunas Vaskevicius ◽  
Max Pfingsthorn ◽  
Sören Schwertfeger ◽  
...  
Keyword(s):  
Closed Form ◽  
Three Dimensional ◽  
Planar Surface

Solutions to the Vector Tetrahedron Equation

1965 ◽  
Vol 87 (2) ◽  
pp. 228-234 ◽  
Author(s):  
Milton A. Chace
Keyword(s):  
Closed Form ◽  
Digital Computer ◽  
Three Dimensional ◽  
Dimensional Vector ◽  
Spherical Coordinates ◽  
Tetrahedron Equation ◽  
Position Determination ◽  
Closed Form Solutions

A set of nine closed-form solutions are presented to the single, three-dimensional vector tetrahedron equation, sum of vectors equals zero. The set represents all possible combinations of unknown spherical coordinates among the vectors, assuming the coordinates are functionally independent. Optimum use is made of symmetry. The solutions are interpretable and can be evaluated reliably by digital computer in milliseconds. They have been successfully applied to position determination of many three-dimensional mechanisms.

Analysis of tunnels in shaly rock considering three-dimensional stress effects on swelling

2005 ◽  
Vol 42 (1) ◽  
pp. 1-12 ◽  
Author(s):  
B C Hawlader ◽  
K Y Lo ◽  
I D Moore
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Cold Water ◽  
Principal Direction ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Time Dependent ◽  
Stress Effect ◽  
Stress Effects ◽  
Laboratory Test Results

Underground structures in shales or shaly rocks endure time-dependent swelling effects. Laboratory test results show that the swelling of these shales is dependent on three-dimensional stresses; an external stress on a specimen in one principal direction reduces the swelling not only in that direction but also perpendicularly. The effectiveness of a time-dependent swelling model that considers the three-dimensional stress effect is presented in this paper. A finite element algorithm incorporating the new constitutive model is used for a numerical analysis. The finite element program is used to analyze two tunnels in southern Ontario: the Heart Lake storm sewer tunnel, and the Darlington cold-water intake tunnel. The predicted results agree well with the records of field performance of these tunnels. The comparison between present analyses and the existing closed-form solution shows that the existing solution overestimates the time-dependent swelling effects. The three-dimensional stress effects on swelling are not considered in the closed-form solutions and are the cause of this discrepancy. The pseudo-Poisson's effect is a key parameter for modelling the observed time-dependent swelling. The use of these solutions in design is discussed.Key words: time-dependent swelling, shale, modelling, three-dimensional stress effect, finite element method, tunnel.

Induction Proof for a General Exponential Integral Formula

1995 ◽  
Vol 80 (2) ◽  
pp. 424-426
Author(s):  
Frank O'Brien ◽  
Sherry E. Hammel ◽  
Chung T. Nguyen
Keyword(s):  
Closed Form ◽  
Integral Formula ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Form Solution ◽  
Probability Method ◽  
Exponential Integral ◽  
Need To Evaluate ◽  
Three Dimensional Space

The authors' Poisson probability method for detecting stochastic randomness in three-dimensional space involved the need to evaluate an integral for which no appropriate closed-form solution could be located in standard handbooks. This resulted in a formula specifically calculated to solve this integral in closed form. In this paper the calculation is verified by the method of mathematical induction.

scholarly journals Reconstruction of three-dimensional maps based on closed-form solutions of the variational problem of multisensor data registration

2019 ◽  
Vol 484 (6) ◽  
pp. 672-677
Author(s):  
A. V. Vokhmintcev ◽  
A. V. Melnikov ◽  
K. V. Mironov ◽  
V. V. Burlutskiy
Keyword(s):  
Closed Form ◽  
Large Scale ◽  
Three Dimensional ◽  
Dynamic Environment ◽  
Closed Form Solution ◽  
Point Clouds ◽  
Accurate Method ◽  
Form Solution ◽  
Closed Form Solutions ◽  
Reconstruction Methods

A closed-form solution is proposed for the problem of minimizing a functional consisting of two terms measuring mean-square distances for visually associated characteristic points on an image and meansquare distances for point clouds in terms of a point-to-plane metric. An accurate method for reconstructing three-dimensional dynamic environment is presented, and the properties of closed-form solutions are described. The proposed approach improves the accuracy and convergence of reconstruction methods for complex and large-scale scenes.

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