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Solving Variational Problems Using Nonlinear Rotation-invariant Coordinates

2019
*
Eurographics Symposium on Geometry Processing
*

We consider

doi:10.2312/sgp.20191213
dblp:conf/sgp/SassenHHR19
fatcat:apf3wvuubnhvvb2r4j7s3w56qq
*Nonlinear**Rotation*-*Invariant**Coordinates*(NRIC) representing triangle meshes with fixed combinatorics as a vector stacking all edge lengths and dihedral angles. ... We develop the machinery needed to*use*NRIC for*solving*geometric optimization*problems*. ... Introduction*Variational**problems*are at the core of many applications in geometry processing. Here we consider*Nonlinear**Rotation*-*Invariant**Coordinates*(NRIC) for*solving*them on triangle meshes. ...##
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A Surface-Theoretic Approach for Statistical Shape Modeling
[chapter]

2019
*
Lecture Notes in Computer Science
*

We present a novel approach for

doi:10.1007/978-3-030-32251-9_3
fatcat:7263ok6mujbcpgq3zhi3vtiwdu
*nonlinear*statistical shape modeling that is*invariant*under Euclidean motion and thus alignmentfree. ... We evaluate the performance of our model w.r.t. shape-based classification of pathological malformations of the human knee and show that it outperforms the standard Euclidean as well as a recent*nonlinear*... [26] presented a physically motivated approach based on differential*coordinates*for which the inverse*problem*is well-known and can be*solved*at linear cost. ...##
###
Geometric optimization using nonlinear rotation-invariant coordinates
[article]

2019
*
arXiv
*
pre-print

We consider the

arXiv:1908.11728v1
fatcat:tc6tar7svfa3hdynsaif6kuptq
*Nonlinear**Rotation*-*Invariant**Coordinates*(NRIC) that represent the nodal positions of a discrete triangular surface with fixed combinatorics as a vector that stacks all edge lengths and ... The goal of this paper is to develop the machinery needed to*use*the NRIC for*solving*geometric optimization*problems*. ... Acknowledgements The authors thank Laszlo Bardos from cutoutfoldup.com for the photo of Steffen's polyhedron*used*in Figure 1 . ...##
###
Hamilton-Jacobi Modelling of Relative Motion for Formation Flying

2005
*
Annals of the New York Academy of Sciences
*

*Using*Hamilton's equations, the

*variational*equations for the new constants are found. ... This allows

*us*to treat perturbations in an identical manner as in the classical Delaunay formulation of the two-body

*problem*. ... We do this by

*solving*the

*variational*equations above

*using*a Poincarè-Lindstedt procedure. ...

##
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Page 3953 of Mathematical Reviews Vol. , Issue 93g
[page]

1993
*
Mathematical Reviews
*

Combined with the classical perturbation method, a method for

*solving*the*problem*of*nonlinear*oscillations in a system with sev- eral degrees of freedom is presented. ... Previous studies of the*nonlinear*inverted double pendulum*using*Lyapunov’s di- rect method are not considered by the author. P. ...##
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The Parameters Optimizing Design of Double Suspension Arm Torsion Bar in the Electric Sight-Seeing Car by Random Vibration Analyzing Method

2017
*
Shock and Vibration
*

The suspension stiffness was calculated by

doi:10.1155/2017/8153756
fatcat:d4zfyih7irgsnieyjtze3672da
*using*the virtual work principle, the vector algebra, and tensor of finite*rotation*methods and was verified by the ADAMS software. ... is about the impact of the performance and the sensitivity analysis for parameters of the torsion bar suspension in the electric sight-seeing car, which the authors' laboratory designed and which is*used*... The first step is to*solve*the point*coordinate*of exterior ball joints of upper arms. point*coordinate*is*solved*according to geometric characteristics since the upper exterior point only*rotates*around ...##
###
Page 2604 of Mathematical Reviews Vol. , Issue 97D
[page]

1997
*
Mathematical Reviews
*

[Morgan, Michael Ambrose]
(1-SEAT-P; Seattle, WA)
Geometric angle for

*rotated**rotators*, and the Hannay angle of the world. (English summary)*Nonlinearity*9 (1996), no. 3, 787-799. ... The solution does not rely on*coordinates**used*to describe the sys- tems and is computationally efficient. One illustrative example is presented.” ...##
###
Geometric Collocation Method on SO(3) with Application to Optimal Attitude Control of a 3D Rotating Rigid Body

2015
*
Mathematical Problems in Engineering
*

In addition, the numerical method is applied to

doi:10.1155/2015/790409
fatcat:5chqlfmgrnf7he3uau4fmjp6pi
*solve*a constrained OAC*problem*on SO(3). ... The optimal control*problem*is transcribed into a*nonlinear*programming*problem*, in which the equivalent Lie algebra equation is being considered as the defect constraints instead of the configuration ... referred to as a Lie group*variational*integrator and then*use*Lagrange's method to derive the discrete necessary conditions (i.e., two-point boundary-value*problem*) which are*solved*by a standard*nonlinear*...##
###
Page 5331 of Mathematical Reviews Vol. , Issue 82m
[page]

1982
*
Mathematical Reviews
*

Some functions of p which are

*invariant*under*rotation*of the*coordinate*axes are obtained.” Babaev, M. A.; Salmanov, V. ... The author derives the basic*variational*principles of finite elasticity*using*the principle of virtual work. ...##
###
Dynamic analysis of planar flexible beams with finite rotations by using inertial and rotating frames

1995
*
Computers & structures
*

*Nonlinear*effects appear only in the transformation of displacement components between global and local

*coordinates*. ... Since the exact solutions for linear static theory of Timoshenko's beam are

*used*to obtain the strain energy, the present stiffness operator is free from the locking

*problem*without

*using*any special technique ... There have been many methods to

*solve*the

*nonlinear*algebraic equations. ...

##
###
Page 2966 of Mathematical Reviews Vol. , Issue 90E
[page]

1990
*
Mathematical Reviews
*

This study is of great interest to researchers

*using*group-*invari*- ance to*solve*differential equations and to those interested in the*nonlinear*superposition principle. G. A. ... [Rogers, Colin] (3-WTRL); Ramgulam, U. (3-WTRL) A*nonlinear*superposition principle and Lie group*invariance*: application in*rotating*shallow water theory. Internat. J. ...##
###
2D/3D rotation-invariant detection using equivariant filters and kernel weighted mapping

2012
*
2012 IEEE Conference on Computer Vision and Pattern Recognition
*

In many vision

doi:10.1109/cvpr.2012.6247766
dblp:conf/cvpr/LiuWDR12
fatcat:lx2nyy5w5nbkvg3yg4j3akctqm
*problems*,*rotation*-*invariant*analysis is necessary or preferred. ... We demonstrate its performance on 2D object detection with in-plane*rotations*, and a 3D application on*rotation*-*invariant*landmark detection in microscopic volumetric data. ...*Invariance*and equivariance In detection tasks, the*rotation**invariance*is defined w.r.t. to the object*coordinate*system. ...##
###
Pose Space Surface Manipulation

2012
*
International Journal of Computer Games Technology
*

We encode example deformations with a

doi:10.1155/2012/596953
fatcat:to7rerasnjbi7fozyjp5ardr4u
*rotation*-*invariant*mesh representation which handles large*rotations*in examples. ... To incorporate example deformations, we infer a pose from the handle translations/*rotations*and perform pose space interpolation, thereby avoiding involved*nonlinear*optimization. ... Storing*rotation*-*invariant*encodings requires a relatively large amount of memory. To*solve*this*problem*, we propose a multiresolution approach. ...##
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A Second-Order Symplectic Integrator for Guiding-Center Equations
[article]

2018
*
arXiv
*
pre-print

Algorithm for finding a solution to a set of

arXiv:1809.05498v1
fatcat:s5pqo2mfirbk7jgcyrvnpfvkla
*nonlinear*equations Newton's method is commonly*used*for finding a solution to a set of*nonlinear*equations, F j (z=(z 1 ,...z 2n ))=0. ... The integrator, which requires a*nonlinear*equation*solve*at each step, is discussed in Sec. III. A fast method for performing this*solve*is described in Sec. IV. ...##
###
Page 2297 of Mathematical Reviews Vol. 52, Issue 6
[page]

1976
*
Mathematical Reviews
*

Surveying in

*rotating*systems. J. Phys. A 9 (1976), no. 1, 35-43. Authors’ summary: “The principles of radar are applied to the*problem*of measuring distances in*rotating*systems. ... Two applications*using*the above expansion of > are given: (i) If, in the*coordinate*system*used*in this paper, # is set equal to zero, the space has hypersurface-orthogonal geodesic rays with nonvanishing ...
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