scholarly journals A study on a line congruence as surface in the space of lines

2021 ◽  
Vol 6 (10) ◽  
pp. 11109-11123
Author(s):  
Rashad A. Abdel-Baky ◽  
◽  
Monia F. Naghi ◽  
Keyword(s):  
Kinematic Geometry ◽  
Line Congruence

<abstract><p>In this work, we introduce a line congruence as surface in the space of lines in terms of the E. Study map. This provides the ability to derive some formulae of surfaces theory into line spaces. In addition, the well known equation of the Plucker's conoid has been obtained and its kinematic-geometry are examined in details. At last, an example of application is investigated and explained in detail.</p></abstract>

On the one-parameter Lorentzian spatial motions

2019 ◽  
Vol 16 (12) ◽  
pp. 1950197 ◽  
Author(s):  
Nadia Alluhaibi ◽  
R. A. Abdel-Baky
Keyword(s):  
Theoretical Expression ◽  
Kinematic Geometry ◽  
Line Congruence ◽  
The One ◽  
Line Trajectory ◽  
Differential Properties ◽  
Explicit Expressions

In this paper, differential properties of the one-parameter Lorentzian spatial motions are developed with explicit expressions independent of coordinates systems. In term of this, we calculate the Disteli formulae of a spacelike line trajectory and derive the connections with kinematic geometry of the axodes. Lastly, a theoretical expression of a spacelike inflection line congruence are investigated in detail.

An efficient method for minimum zone cylindricity error evaluation using kinematic geometry optimization algorithm

Measurement ◽  
2019 ◽  
Vol 135 ◽  
pp. 886-895 ◽  
Author(s):  
Peng Zheng ◽  
Dongliang Liu ◽  
Fengxia Zhao ◽  
Linna Zhang
Keyword(s):  
Efficient Method ◽  
Optimization Algorithm ◽  
Geometry Optimization ◽  
Error Evaluation ◽  
Kinematic Geometry ◽  
Minimum Zone ◽  
Cylindricity Error

Visual Perception of Apparent Motion Abides by Minimization Principles of Geometry

2021 ◽  
Author(s):  
Yaxin Liu ◽  
Stella F. Lourenco
Keyword(s):  
Visual Perception ◽  
Target Detection ◽  
Apparent Motion ◽  
Visual Space ◽  
Detection Task ◽  
Newtonian Physics ◽  
Kinematic Geometry ◽  
Shed Light ◽  
Target Detection Task ◽  
Perceptual Phenomenon

Apparent motion is a robust perceptual phenomenon in which observers perceive a stimulus traversing the vacant visual space between two flashed stimuli. Although it is known that the “filling-in” of apparent motion favors the simplest and most economical path, the interpolative computations remain poorly understood. Here, we tested whether the perception of apparent motion is best characterized by Newtonian physics or kinematic geometry. Participants completed a target detection task while Pacmen- shaped objects were presented in succession to create the perception of apparent motion. We found that target detection was impaired when apparent motion, as predicted by kinematic geometry, not Newtonian physics, obstructed the target’s location. Our findings shed light on the computations employed by the visual system, suggesting specifically that the “filling-in” perception of apparent motion may be dominated by kinematic geometry, not Newtonian physics.

Internalized constraints in the representation of spatial layout

2001 ◽  
Vol 24 (4) ◽  
pp. 677-678 ◽  
Author(s):  
Helene Intraub
Keyword(s):  
Theoretical Framework ◽  
Spatial Layout ◽  
Kinematic Geometry

Shepard's (1994) choice of kinematic geometry to support his theory is questioned by Todorovic, Schwartz, and Hecht. His theoretical framework, however, can be applied to another domain that may be less susceptible to some of their concerns. The domain is the representation of spatial layout. [Hecht; Schwartz; Shepard; Todorovič]

The internalization of physical constraints from a developmental perspective

2001 ◽  
Vol 24 (4) ◽  
pp. 681-682
Author(s):  
Horst Krist
Keyword(s):  
Developmental Perspective ◽  
Evolutionary Perspective ◽  
Developmental Research ◽  
Physical Constraints ◽  
Kinematic Geometry

Shepard's internalization concept is defended against Hecht's criticisms. By ignoring both Shepard's evolutionary perspective and the fact that internalization does not preclude modularization, Hecht advances inconclusive evidence. Developmental research supports Shepard's conclusion that kinematic geometry may be more deeply internalized than physical dynamics. This research also suggests that the internalization concept should be broadened to include representations acquired during ontogeny. [Hecht; Shepard]

Measurement theory is a poor model of the relation of kinematic geometry and perception of motion

2001 ◽  
Vol 24 (4) ◽  
pp. 705-706
Author(s):  
Dejan Todorovič
Keyword(s):  
Measurement Theory ◽  
Relational Structures ◽  
Kinematic Geometry

The Kubovy-Epstein proposal for the formalization of the relation between kinematic geometry and perception of motion has formal problems in itself. Motion phenomena are inadequately captured by the relational structures and the notion of isomorphism taken over from measurement theory. [Kubovy & Epstein]

scholarly journals Internalization: A metaphor we can live without

2001 ◽  
Vol 24 (4) ◽  
pp. 618-625 ◽  
Author(s):  
Michael Kubovy ◽  
William Epstein
Keyword(s):  
Natural Selection ◽  
Apparent Motion ◽  
Evolutionary History ◽  
Motion Path ◽  
The World ◽  
Kinematic Geometry ◽  
Innate Knowledge ◽  
History Of ◽  
The Mind ◽  
Internal Knowledge

Shepard has supposed that the mind is stocked with innate knowledge of the world and that this knowledge figures prominently in the way we see the world. According to him, this internal knowledge is the legacy of a process of internalization; a process of natural selection over the evolutionary history of the species. Shepard has developed his proposal most fully in his analysis of the relation between kinematic geometry and the shape of the motion path in apparent motion displays. We argue that Shepard has made a case for applying the principles of kinematic geometry to the perception of motion, but that he has not made the case for injecting these principles into the mind of the percipient. We offer a more modest interpretation of his important findings: that kinematic geometry may be a model of apparent motion. Inasmuch as our recommended interpretation does not lodge geometry in the mind of the percipient, the motivation of positing internalization, a process that moves kinematic geometry into the mind, is obviated. In our conclusion, we suggest that cognitive psychologists, in their embrace of internal mental universals and internalization may have been seduced by the siren call of metaphor.

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