• Journal for History of Mathematics
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• v.32 no.1
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• pp.17-25
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• 2019

This essay elucidates the way the geometries of space-time theories explain material bodies' motions. A conventional attempt to interpret the way that space-time geometry explains is to consider the geometrical structure of space-time as involving a causally efficient entity that directs material bodies to follow their trajectories corresponding to the laws of motion. Newtonian substantival space is interpreted as an entity that acts but is not acted on by the motions of material bodies. And Einstein's curved space-time is interpreted as an entity that causes the motions of bodies. This essay argues against this line of thought and provides an alternative understanding of the way space-time geometry explain the laws of motion. The workings of the way that Newton's flat and Einstein's curved space-time explains the law of motion is such that space-time geometry encodes the principle of inertia which specifies straight lines of moving bodies.

• Journal for History of Mathematics
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• v.22 no.3
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• pp.273-292
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• 2009

According to historical commentators such as Newton and Einstein, bodily behaviors are causally explained by the geometrical structure of space-time whose existence analogous to that of material substance. This essay challenges this conventional wisdom of interpreting space-time geometry within both Newtonian and Einsteinian physics. By tracing recent historical studies on the interpretation of space-time geometry, I defends that space-time structure is a by-product of a more fundamental fact, the laws of motion. From this perspective, I will argue that the causal properties of space-time cannot provide an adequate account of the theory-change from Newtoninan to Einsteinian physics.

• Korean Institute of Interior Design Journal
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• v.14 no.5 s.52
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• pp.98-105
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• 2005

Through advanced computer technology, our physical environment became a flexible and liquid space that is a multi-functional space structure, hetero-alliance, formless, interactivity. We attempt to interpretate Deleuze's Other geometry as a space designer. Hence first, the aim of this study is to define the meaning of the Other and Other geometry. Second, to extract keywords out of the Other geometry to analyze the work. Third, to analyze the work using the space formative languages(blob, blurring, distortion, folding, layering, lightness, nesting, repetition, shear, transparency, twisting, unfolding, warping, waving, and weaving). The 13 works were selected which have been issued after year 2000 with the focus on liquid space studies. The methods of this study are literature research and contents analysis. The results of the analysis were as follows. First, the source is the Other who is a hidden potentials in the surrounding environment, and this source has the capability of making it part of reality anytime. Other geometry means it is a theory that is comprised of various lines that with the kind of experiences that one has in life. Second, the key words that were extracted from the theory of Deleuze's Other geometry were of (1)hetero-alliance(reflected in a sculptured shape or a fluid abstract form), (2)dis-form(by speculating the user's movements, and combining space elements with external forces), (3)interactivity (information was exchanged real time between the user and his environment where the space took on a sensory institution). Finally, after studying the works using the space formative languages, we found that blob, warping, waving were used externally, and repetition, warping and waving for mostly used internally.

• Journal of Mechanical Science and Technology
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• v.18 no.1
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• pp.92-105
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• 2004

A new algorithm for planning a collision-free path based on algebraic curve is developed and the concept of collision-free Path Space (PS) is introduced. This paper presents a Geometry Mapping (GM) based on two straight curves in which the intermediate connection point is organized in elliptic locus ($\delta$, $\theta$). The GM produces two-dimensional PS that is used to create the shortest collision-free path. The elliptic locus of intermediate connection point has a special property in that the total distance between the focus points through a point on ellipse is the same regardless of the location of the intermediate connection point on the ellipse. Since the radial distance, a, represents the total length of the path, the collision-free path can be found as the GM proceeds from $\delta$=0 (the direct path) to $\delta$=$\delta$$\_$max/(the longest path) resulting in the minimum time search. The GM of elliptic workspace (EWS) requires calculation of interference in circumferential direction only. The procedure for GM includes categorization of obstacles to .educe necessary calculation. A GM based on rectangular workspace (RWS) using Cartesian coordinate is also considered to show yet another possible GM. The transformations of PS among Circular Workspace Geometry Mapping (CWS GM) , Elliptic Workspace Geometry Mapping (EWS GM) , and Rectangular Workspace Geometry Mapping (RWS GM), are also considered. The simulations for the EWS GM on various computer systems are carried out to measure performance of algorithm and the results are presented.

• Journal of KIBIM
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• v.9 no.2
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• pp.21-28
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• 2019

Recently, many scan projects are gradually increasing for maintenance, construction. The scan data contains useful data, which can be generated in the target application from the facility, space. However, modeling the scan data required for the application requires a lot of cost. In example, the converting 3D point cloud obtained from scan data into 3D object is a time-consuming task, and the modeling task is still very manual. This research proposes Scan-to-Geometry Mapping Rule Definition (S2G-MD) which maps point cloud data to geometry for irregular building plane objects. The S2G-MD considers user use case variability. The method to define rules for mapping scan to geometry is proposed. This research supports the reverse engineering semi-automatic process for the building planar geometry from the user perspective.

• Journal of The Korean Digital Architecture Interior Association
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• v.7 no.1
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• pp.15-20
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• 2007

This study is aimed to analyze the method of movement expression in the Space-Time of Modern Visual Art. According to the results of analysis. the following is obtained. (1) The still object is perceived by the sense or optical illusion, and its whole image is made through the information processing prodedure. The concept of Space-Time is integrated into the constructivist works by the composition of image through transforming the position of the fundamental geometry and projecting it. (2) The traditional notion that the work of art is still concept of is changed. The movement of observer is caused by inducing the direction and concept of time through the object in three dimensional space.

• International Journal of Aeronautical and Space Sciences
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• v.14 no.2
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• pp.183-192
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• 2013

This paper presents formation reconfiguration using impulsive control input for spacecraft formation flying. Spacecraft in a formation should change the formation size and/or geometry according to the mission requirements and space environment. To modify the formation radius and geometry with respect to the leader spacecraft, the follower spacecraft generates additional control inputs; the two impulsive control inputs are general control type of the spacecraft system. For the impulsive control input, Lambert's problem is modified to construct the transfer orbit in relative motion, given two position vectors at the initial and final time. Moreover, the numerical simulation results show the transfer trajectories to resize the formation radius in the radial/along-track plane formation and in the along-track/cross-track plane formation. In addition, the maneuver characteristics are described by comparing the differential orbital elements between the reference orbit and transfer orbit in the radial/along-track plane formation and along-track/cross-track plane formation.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.29B no.11
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• pp.36-45
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• 1992

A numerical trajectory planning method for path-constrained trajectory planning is proposed which ensures collision-free and time-optimal motions for two robotic manipulators with limited actuator torques and velocities. For each robot, physical constraints of the robots such as limited torques or limited rotational velocities of the actuators are converted to the constraints on velocity and acceleration along the path, which is described by a scalar variable denoting the traveled distance from starting point. Collision region is determined on the coordination space according to the kinematic structures and the geometry of the paths of the robots. An Extended Coordination Space is then constructed` an element of the space determines the postures and the velocities of the robots, and all the constraints described before are transformed to some constraints on the behaviour of the coordination-velocity curves in the space. A dynamic programming technique is them provided with on the discretized Extended Coordination Space to derive a collision-free and time-optimal trajectory pair. Numerical example is included.

• Journal of the Korea Society for Simulation
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• v.11 no.4
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• pp.1-14
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• 2002

This paper presents bounding space(BS) management for real-time visual simulation when using GK-DEVS models. Since GK-DEVS, extended from DEVS formalism, has information of 3D geometry and 3D hierarchical structure, we employs three types of bounding spaces: BS of its own shape, BS of its children GK-DEVS, and total BS. In addition to next-event scheduling functionality of previous GK-Simulator, its abstract simulation algorithms is extended to manage the three types of BSs so that BSs can be utilized in the rendering process of a renderer, so called GK-Renderer, We have implemented the method and evaluated it with an automated manufacturing system. In the case study, the proposed BSs management method showed about 2 times improvement in terms of rendering process speed.

• Korean Institute of Interior Design Journal
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• v.17 no.2
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• pp.22-29
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• 2008

Johannes Vermeer is one of the masters in the 17th century Dutch Genre Painting. Genre Painting represented the mundane everyday life and humble domestic spaces of the time. It was so unique in the history of western art. Most common subjects of the medieval art had been myths, historical heroes, and the christianity up to that time. However, Dutch Genre Painting that was originated from the 16th century Flandre art has fundamentally changed perception of art. Genre Painting was related to the prosperous development of civil society and early capitalism in the Netherlands of the time. In the paintings of Vermeer, there are unique spatial characteristics. This study aims to 'spatially' analyze the representation of everyday space perceived by the painter himself. Three analytical elements were chosen: light, space, and geometry. These elements have crucial roles to construct a space together within which Vermeer tried to express his discoveries as well as perception of the world. Four paintings were selected to be further analyzed in detail: $\ulcorner$A Maid Asleep$\lrcorner$ (1656-57), $\ulcorner$The Little Street$\lrcorner$ (1658-60), $\ulcorner$The Music Lesson$\lrcorner$ (1662-1665), and $\ulcorner$Young Woman with a Water Pitcher$\lrcorner$ (1662). It has been found that there are distinct spatial aspects in his paintings: Structure of Frontal Layers, Diffusion of Light, and Subtle Geometrical Tension. It is hoped that this sort of interdisciplinary research could enrich the related studies in the field of architecture & interior design, and could help to rediscover the everyday world that we live in here and now.