Theoretically Based Robust Algorithms for Tracking Intersection Curves of Two Deforming Parametric Surfaces

2006 ◽  
pp. 101-114
Author(s):  
Xianming Chen ◽  
Richard F. Riesenfeld ◽  
Elaine Cohen ◽  
James Damon
Keyword(s):  
Parametric Surfaces ◽  
Robust Algorithms ◽  
Intersection Curves

scholarly journals Intersection Curves of Implicit and Parametric Surfaces in R<sup>3</sup>

2011 ◽  
Vol 02 (08) ◽  
pp. 1019-1026 ◽  
Author(s):  
Mohamed Abdel-Latif Soliman ◽  
Nassar Hassan Abdel-All ◽  
Soad Ali Hassan ◽  
Sayed Abdel-Naeim Badr
Keyword(s):  
Parametric Surfaces ◽  
Intersection Curves

Parametric Surface Intersections for Geometric Modeling

1992 ◽  
Author(s):  
J.-M. Chen ◽  
Yu Wang ◽  
E. L. Guroz ◽  
Fritz B. Prinz
Keyword(s):  
Geometric Modeling ◽  
Parametric Surface ◽  
Parametric Surfaces ◽  
B Spline ◽  
Surface Intersection ◽  
Spline Surfaces ◽  
Intersection Algorithm ◽  
Intersection Curves ◽  
Surface Intersections

Abstract A surface-surface intersection algorithm is an important element in the development of a geometric modeler. This paper presents a new algorithm for calculating the intersection curves of two parametric surfaces. Combining the merits of subdivision and global exploration methods, this algorithm is efficient and robust in dealing with the issues related to small loops and singularities. This algorithm is demonstrated with examples of non-uniform rational B-spline surfaces.

Robust algorithms for relative orientation

2001 ◽  
Vol 36 (1) ◽  
pp. 35-38 ◽  
Author(s):  
Judit Somogyi ◽  
L. Battha
Keyword(s):  
Relative Orientation ◽  
Robust Algorithms

Mathematical Method to Unfolding Couplings

2019 ◽  
Vol 17 (17) ◽  
pp. 63-64
Author(s):  
Carmen Popa ◽  
Ivona Petre ◽  
Ruxandra-Elena Bratu
Keyword(s):  
Mathematical Method ◽  
Mathematical Methods ◽  
Intersection Curves ◽  
Four Cylinders

AbstractThe purpose of this paper is to establish the intersection curves between cylinders, using Mathematica program. The equations curves which are inferred by mathematical methods are introduced in this program. This paper takes into discussion the case of four cylinders.

Centered error entropy Kalman filter with application to satellite attitude determination

2021 ◽  
pp. 014233122110198
Author(s):  
Baojian Yang ◽  
Lu Cao ◽  
Dechao Ran ◽  
Bing Xiao
Keyword(s):  
Kalman Filter ◽  
Gaussian Noise ◽  
Attitude Determination ◽  
Complexity Analysis ◽  
Iteration Algorithm ◽  
Robust Algorithms ◽  
Convergence Conditions ◽  
Satellite Attitude ◽  
Heavy Tailed ◽  
Non Gaussian

Due to unavoidable factors, heavy-tailed noise appears in satellite attitude estimation. Traditional Kalman filter is prone to performance degradation and even filtering divergence when facing non-Gaussian noise. The existing robust algorithms have limited accuracy. To improve the attitude determination accuracy under non-Gaussian noise, we use the centered error entropy (CEE) criterion to derive a new filter named centered error entropy Kalman filter (CEEKF). CEEKF is formed by maximizing the CEE cost function. In the CEEKF algorithm, the prior state values are transmitted the same as the classical Kalman filter, and the posterior states are calculated by the fixed-point iteration method. The CEE EKF (CEE-EKF) algorithm is also derived to improve filtering accuracy in the case of the nonlinear system. We also give the convergence conditions of the iteration algorithm and the computational complexity analysis of CEEKF. The results of the two simulation examples validate the robustness of the algorithm we presented.

Admissible Measurements and Robust Algorithms for Ptychography

2021 ◽  
Vol 27 (2) ◽  
Author(s):  
Brian Preskitt ◽  
Rayan Saab
Keyword(s):  
Robust Algorithms

Computation of Self-Intersections of Offsets of Be´zier Surface Patches

1997 ◽  
Vol 119 (2) ◽  
pp. 275-283 ◽  
Author(s):  
Takashi Maekawa ◽  
Wonjoon Cho ◽  
Nicholas M. Patrikalakis
Keyword(s):  
Differential Geometry ◽  
Distance Function ◽  
Polynomial Equations ◽  
Intersection Curve ◽  
Parameter Domain ◽  
Surface Patches ◽  
Intersection Curves

Self-intersection of offsets of regular Be´zier surface patches due to local differential geometry and global distance function properties is investigated. The problem of computing starting points for tracing self-intersection curves of offsets is formulated in terms of a system of nonlinear polynomial equations and solved robustly by the interval projected polyhedron algorithm. Trivial solutions are excluded by evaluating the normal bounding pyramids of the surface subpatches mapped from the parameter boxes computed by the polynomial solver with a coarse tolerance. A technique to detect and trace self-intersection curve loops in the parameter domain is also discussed. The method has been successfully tested in tracing complex self-intersection curves of offsets of Be´zier surface patches. Examples illustrate the principal features and robustness characteristics of the method.

scholarly journals A Note on Parametric Surfaces in Minkowski 3-Space

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Esra Betul Koc Ozturk
Keyword(s):  
Linear Combination ◽  
Sufficient Conditions ◽  
Ruled Surface ◽  
Necessary And Sufficient Conditions ◽  
Frenet Frame ◽  
Parametric Surface ◽  
Parametric Surfaces ◽  
Null Curve ◽  
Necessary And Sufficient

With the help of the Frenet frame of a given pseudo null curve, a family of parametric surfaces is expressed as a linear combination of this frame. The necessary and sufficient conditions are examined for that curve to be an isoparametric and asymptotic on the parametric surface. It is shown that there is not any cylindrical and developable ruled surface as a parametric surface. Also, some interesting examples are illustrated about these surfaces.

Sign in / Sign up

Export Citation Format

Share Document