scholarly journals Computing the Angularity Tolerance

1998 ◽  
Vol 08 (04) ◽  
pp. 467-482 ◽  
Author(s):  
Mark De Berg ◽  
Henk Meijer ◽  
Mark Overmars ◽  
Gordon Wilfong
Keyword(s):  
Restricted Problem ◽  
Dimensional Space ◽  
Similar Time ◽  
3 Dimensional ◽  
Computational Metrology ◽  
The Given ◽  
Time Bounds ◽  
Extract Information

In computational metrology one needs to compute whether an object satisfies specifications of shape within an acceptable tolerance. To this end positions on the object are measured, resulting in a collection of points in space. From this collection of points one wishes to extract information on flatness, roundness, etc. of the object. In this paper we study one particular feature of objects, the angularity. The angularity indicates how well a plane makes a specified angle with another plane. We study the problem in 2-dimensional space (where the planes become lines) and in 3-dimensional space. In 2-dimensional space the problem is equivalent to computing the smallest wedge of the given angle that contains all the points. We give an O(n2 log n) algorithm for this problem. In 3-dimensional space we study the more restricted problem where one of the planes is known (a datum plane). In this case the problem is equivalent to asking for the smallest width 3-dimensional strip that contains all the points and makes a given angle with the datum plane. We give an O(n log n) algorithm to solve this version. We also show that in the case of uncertainty in the measured points, upperbounds and lowerbounds on the width can be computed in similar time bounds.

scholarly journals Mannheim Curves in Nonflat 3-Dimensional Space Forms

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Wenjing Zhao ◽  
Donghe Pei ◽  
Xinyu Cao
Keyword(s):  
Linear Relationship ◽  
Dimensional Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
De Sitter ◽  
Space Forms ◽  
3 Dimensional ◽  
Constant Coefficients ◽  
Necessary And Sufficient ◽  
The Given

We consider the Mannheim curves in nonflat 3-dimensional space forms (Riemannian or Lorentzian) and we give the concept of Mannheim curves. In addition, we investigate the properties of nonnull Mannheim curves and their partner curves. We come to the conclusion that a necessary and sufficient condition is that a linear relationship with constant coefficients will exist between the curvature and the torsion of the given original curves. In the case of null curve, we reveal that there are no null Mannheim curves in the 3-dimensional de Sitter space.

Association algorithm with bearing-only measurements in 3-dimensional space

2009 ◽  
Author(s):  
Xiu Jianjuan ◽  
Li Yuli ◽  
He You ◽  
Wang Guohong
Keyword(s):  
Dimensional Space ◽  
3 Dimensional ◽  
Association Algorithm

Triharmonic Riemannian submersions from 3-dimensional space forms

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Tomoya Miura ◽  
Shun Maeta
Keyword(s):  
Existence Theorem ◽  
Space Form ◽  
Dimensional Space ◽  
Riemannian Submersion ◽  
Partial Answer ◽  
Riemannian Submersions ◽  
Space Forms ◽  
3 Dimensional

Abstract We show that any triharmonic Riemannian submersion from a 3-dimensional space form into a surface is harmonic. This is an affirmative partial answer to the submersion version of the generalized Chen conjecture. Moreover, a non-existence theorem for f -biharmonic Riemannian submersions is also presented.

Combo separability criteria and lower bound on concurrence

2021 ◽  
Author(s):  
Zangi Sultan ◽  
Jiansheng Wu ◽  
Cong-Feng Qiao
Keyword(s):  
Lower Bound ◽  
Correlation Matrix ◽  
Density Operator ◽  
Singular Values ◽  
Quantum Information Theory ◽  
Separability Criteria ◽  
The Given ◽  
Ky Fan ◽  
Natural Way ◽  
Extract Information

Abstract Detection and quantification of entanglement are extremely important in quantum information theory. We can extract information by using the spectrum or singular values of the density operator. The correlation matrix norm deals with the concept of quantum entanglement in a mathematically natural way. In this work, we use Ky Fan norm of the Bloch matrix to investigate the disentanglement of quantum states. Our separability criterion not only unifies some well-known criteria but also leads to a better lower bound on concurrence. We explain with an example how the entanglement of the given state is missed by existing criteria but can be detected by our criterion. The proposed lower bound on concurrence also has advantages over some investigated bounds.

The early attentional pancake: Lack of selection in depth for rapid exogenous cueing

2021 ◽  
Author(s):  
Ryan Edward O'Donnell ◽  
Kyrie Murawski ◽  
Ella Herrmann ◽  
Jesse Wisch ◽  
Garrett D. Sullivan ◽  
...  
Keyword(s):  
Reaction Time ◽  
Binocular Disparity ◽  
Dimensional Space ◽  
Exogenous Attention ◽  
3 Dimensional ◽  
Exogenous Cueing ◽  
Different Depths ◽  
Depth Cueing ◽  
The Difference ◽  
Attentional Selectivity

There have been conflicting findings on the degree to which exogenous/reflexive visual attention is selective for depth, and this issue has important implications for attention models. Previous findings have attempted to find depth-based cueing effects on such attention using reaction time measures for stimuli presented in stereo goggles with a display screen. Results stemming from such approaches have been mixed, depending on whether target/distractor discrimination was required. To help clarify the existence of such depth effects, we have developed a paradigm that measures accuracy rather than reaction time in an immersive virtual-reality environment, providing a more appropriate context of depth. Four modified Posner Cueing paradigms were run to test for depth-specific attentional selectivity. Participants fixated a cross while attempting to identify a rapidly masked letter that was preceded by a cue that could be valid in depth and side, depth only, or side only. In Experiment 1, a potent cueing effect was found for side validity and a weak effect was found for depth. Experiment 2 controlled for differences in cue and target sizes when presented at different depths, which caused the depth validity effect to disappear entirely even though participants were explicitly asked to report depth and the difference in virtual depth was extreme (20 vs 300 meters). Experiments 3a and 3b brought the front depth plane even closer (1 m) to maximize effects of binocular disparity, but no reliable depth cueing validity was observed. Thus, it seems that rapid/exogenous attention pancakes 3-dimensional space into a 2-dimensional reference frame.

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