scholarly journals Formation of concepts of point, distance and straight placements of points by means of metric geometry in 7-9 grades

2020 ◽  
Author(s):  
Valerii Kuz’mich ◽  
◽  
Liudmyla Kuzmich ◽  
Keyword(s):  
Metric Geometry ◽  
Point Distance

Teichmuller Geometry

2017 ◽  
Author(s):  
Benson Farb ◽  
Dan Margalit
Keyword(s):  
Uniqueness Theorem ◽  
Existence Theorems ◽  
Quadratic Differentials ◽  
Complex Structures ◽  
Metric Geometry ◽  
Quasiconformal Maps ◽  
Hyperbolic Structures ◽  
Teichmüller Metric ◽  
Uniqueness And Existence ◽  
Teichmüller Mapping

This chapter focuses on the metric geometry of Teichmüller space. It first explains how one can think of Teich(Sɡ) as the space of complex structures on Sɡ. To this end, the chapter defines quasiconformal maps between surfaces and presents a solution to the resulting Teichmüller's extremal problem. It also considers the correspondence between complex structures and hyperbolic structures, along with the Teichmüller mapping, Teichmüller metric, and the proof of Teichmüller's uniqueness and existence theorems. The fundamental connection between Teichmüller's theorems, holomorphic quadratic differentials, and measured foliations is discussed as well. Finally, the chapter describes the Grötzsch's problem, whose solution is tied to the proof of Teichmüller's uniqueness theorem.

scholarly journals A Novel LOS Decision Technique Reflecting 3D DTED for Modeling an Electronic Warfare Environment

2021 ◽  
Vol 11 (1) ◽  
pp. 409
Author(s):  
Jaejoong Lee ◽  
Chiho Lee ◽  
Hyeon Hwi Lee ◽  
Kyung Tae Park ◽  
Hyun-Kyo Jung ◽  
...  
Keyword(s):  
Interpolation Method ◽  
Three Dimensional ◽  
Superior Performance ◽  
Line Of Sight ◽  
Electronic Warfare ◽  
Decision Algorithm ◽  
Elevation Data ◽  
The Republic ◽  
Point Distance ◽  
Terrain Elevation

A new line-of-sight (LOS) decision algorithm applicable to simulation of electronic warfare (EW) is developed. For accurate simulation, the digital terrain elevation data (DTED) of the region to be analyzed must be reflected in the simulation, and millions of datasets are necessary in the EW environment. In order to obtain real-time results in such an environment, a technology that determines line-of-sight (LOS) quickly and accurately is very important. In this paper, a novel algorithm is introduced for determining LOS that can be applied in an EW environment with three-dimensional (3D) DTED. The proposed method shows superior performance as compared with the simplest point-to-point distance calculation method and it is also 50% faster than the conventional interpolation method. The DTED used in this paper is the data applied as level 0 for the Republic of Korea, and the decision of the LOS at approximately 1.8 million locations viewed by a reconnaissance plane flying 10 km above the ground is determined within 0.026 s.

scholarly journals Improving 3D-3D facial registration methods: potential role of three-dimensional models in personal identification of the living

2021 ◽  
Author(s):  
Daniele Gibelli ◽  
Andrea Palamenghi ◽  
Pasquale Poppa ◽  
Chiarella Sforza ◽  
Cristina Cattaneo ◽  
...  
Keyword(s):  
Three Dimensional ◽  
3D Models ◽  
Personal Identification ◽  
Surveillance Systems ◽  
3D Registration ◽  
Three Dimensional Models ◽  
Point To Point ◽  
Point Distance ◽  
Male Subjects

AbstractPersonal identification of the living from video surveillance systems usually involves 2D images. However, the potentiality of three-dimensional facial models in gaining personal identification through 3D-3D comparison still needs to be verified. This study aims at testing the reliability of a protocol for 3D-3D registration of facial models, potentially useful for personal identification. Fifty male subjects aged between 18 and 45 years were randomly chosen from a database of 3D facial models acquired through stereophotogrammetry. For each subject, two acquisitions were available; the 3D models of faces were then registered onto other models belonging to the same and different individuals according to the least point-to-point distance on the entire facial surface, for a total of 50 matches and 50 mismatches. RMS value (root mean square) of point-to-point distance between the two models was then calculated through the VAM® software. Intra- and inter-observer errors were assessed through calculation of relative technical error of measurement (rTEM). Possible statistically significant differences between matches and mismatches were assessed through Mann–Whitney test (p < 0.05). Both for intra- and inter-observer repeatability rTEM was between 2.2 and 5.2%. Average RMS point-to-point distance was 0.50 ± 0.28 mm in matches, 2.62 ± 0.56 mm in mismatches (p < 0.01). An RMS threshold of 1.50 mm could distinguish matches and mismatches in 100% of cases. This study provides an improvement to existing 3D-3D superimposition methods and confirms the great advantages which may derive to personal identification of the living from 3D facial analysis.

The Effect of Extended Sensory Range via the EyeCane Sensory Substitution Device on the Characteristics of Visionless Virtual Navigation

2014 ◽  
Vol 27 (5-6) ◽  
pp. 379-397 ◽  
Author(s):  
Shachar Maidenbaum ◽  
Shelly Levy-Tzedek ◽  
Daniel Robert Chebat ◽  
Rinat Namer-Furstenberg ◽  
Amir Amedi
Keyword(s):  
Single Point ◽  
Visual Navigation ◽  
Assistive Technologies ◽  
Sensory Substitution ◽  
Distance Information ◽  
Navigation Patterns ◽  
White Cane ◽  
Blind User ◽  
Mobility Training ◽  
Point Distance

Mobility training programs for helping the blind navigate through unknown places with a White-Cane significantly improve their mobility. However, what is the effect of new assistive technologies, offering more information to the blind user, on the underlying premises of these programs such as navigation patterns?We developed the virtual-EyeCane, a minimalistic sensory substitution device translating single-point-distance into auditory cues identical to the EyeCane’s in the real world. We compared performance in virtual environments when using the virtual-EyeCane, a virtual-White-Cane, no device and visual navigation. We show that the characteristics of virtual-EyeCane navigation differ from navigation with a virtual-White-Cane or no device, and that virtual-EyeCane users complete more levels successfully, taking shorter paths and with less collisions than these groups, and we demonstrate the relative similarity of virtual-EyeCane and visual navigation patterns. This suggests that additional distance information indeed changes navigation patterns from virtual-White-Cane use, and brings them closer to visual navigation.

Fourier Integrals and Metric Geometry

1988 ◽  
pp. 146-171
Author(s):  
J. Von Neumann ◽  
I. J. Schoenberg
Keyword(s):  
Metric Geometry ◽  
Fourier Integrals

scholarly journals Newman’s Error Analysis Dalam Geometri Ruang Ditinjau dari Kecerdasan Visual Siswa SMA

2019 ◽  
Vol 3 (2) ◽  
pp. 447-461
Author(s):  
Ardina Fahriyanti Maharani ◽  
Erlina Prihatnani
Keyword(s):  
High School ◽  
Error Analysis ◽  
Transformation Process ◽  
Intelligence Test ◽  
Solid Geometry ◽  
Visual Intelligence ◽  
The Difference ◽  
Point Distance ◽  
Different Levels ◽  
Geometry Test

In solid geometry needed the ability to visualize space that cannot be seen so differences in visual intelligence can trigger errors in solving geometry problems. Therefore, this study aimed to determine the types of errors made by students and the factors that cause errors in working on geometry problems based on Newman's Error Analysis (NEA) in terms of visual intelligence. This research chose the subjects of class XII high school who had studied the material distance points to lines in space with different levels of visual intelligence, namely high and low. The process of collecting data used visual intelligence test questions, geometry test questions, and interviews. The results of this study indicated that the level of students' visual intelligence affects the difference in location and the factor that causes errors in the stage of transformation especially on determining the distance in dimension 3. Students with high visual intelligence made mistakes at the stage of transformation and encoding that caused by the students’ carelessness. However, students with low visual intelligence made mistakes at the stage of comprehension, transformation, process skills, and encoding due to the concept of the point distance to the line and the concept of the Pythagorean theorem.

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