Visual Perception of Apparent Motion Abides by Minimization Principles of Geometry

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.

Sweeping surfaces according to type-2 Bishop frame in Euclidean 3-space

This work is concerned with the study of the kinematic-geometry of a special kind of tube surfaces, so-called sweeping surface in Euclidean 3-space [Formula: see text]. It is generated by a plane curve moving through space such that the movement of any point on the surface is always orthogonal to the plane. In particular, the type-2 Bishop frame is considered and some important theorems are obtained. Also, the problem of singularity and convexity of such sweeping surface is discussed. Finally, an application is presented and plotted using computer aided geometric design.

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

<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>

Kinematic geometry of hyperbolic dual spherical motions and Euler–Savary’s equation

In this paper, differential properties of the one-parameter hyperbolic dual spherical kinematics are developed with explicit expressions independent of coordinates systems. We calculate Euler–Savary equations of spherical kinematics in the dual Lorentzian 3-space [Formula: see text]. Then from E. Study’s map new proofs are directly attained for the Disteli’s formulae and their spatial equivalents are examined in detail. Lastly for spherical and planar motions, the point trajectories theoretical expressions of the point trajectories are investigated with a certain value of acceleration and velocity, which are regarded as different forms of Euler–Savary equation form.

Kinematic Geometry Description of a Line With Four Positions and Its Application in Dimension Synthesis of Spatial Linkage

In the dimension synthesis of the spatial linkages, the geometric characteristics of floating links in mechanisms reveal the geometric relationship between the motion task and the dimensions of the mechanisms. In order to establish the kinematic geometry rules corresponding to the motion of the floating link, this paper transforms the kinematic problems of geometric elements on the floating link into geometric problems and uses the geometric procedure to solve the spatial linkages synthesis problem with four given positions. In a previous work, we have extracted the kinematic geometry rules of a line with two and three positions. However, as the number of task positions increases, the kinematic characteristics representing the position transformation become more complicated. The method proposed in this paper extends the previous work to four given positions and builds up the geometric relationships among the kinematic rules for two, three, and four positions. The establishment of this geometric relationship is helpful to unify the synthesis procedure of synthesis problems with different number of positions. After that, the two-plane projection system and the transformation of projection are introduced to establish a procedural graphical synthesis method.