• Journal of Korean Society of Industrial and Systems Engineering
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• v.42 no.3
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• pp.52-60
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• 2019

This paper presents a numerically robust algorithm to construct a Voronoi diagram of circles in the plane. The circles are allowed to have intersections among them, but one circle cannot fully contain another circle. The Voronoi diagram is a tessellation of the plane into Voronoi regions of given circles. Each circle has its Voronoi region which is defined by a set of points in the plane closer to the circle than any other circles. The distance from a point p to a circle $c_i$ of center $p_i$ and radius $r_i$ is ${\parallel}p-p_i{\parallel}-r_i$, which is the closest Euclidean distance from p to the circle boundary. The proposed algorithm first constructs the point Voronoi diagram of centers of given circles, then it enlarges each point to the circle and expands its Voronoi region accordingly. This region-expansion process is done by local modifications and after completing this process for the whole circles the desired circle Voronoi diagram can be obtained. The proposed algorithm is numerically robust and we provide with a few examples to show its robustness. The algorithm runs in $O(n^2)$ time in the worst case and O(n) time on average where n is the number of the circles. The experiment shows that the region-expansion algorithm is robust and runs fast with strong linear time behavior.

• Korean Journal of Computational Design and Engineering
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• v.6 no.1
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• pp.24-30
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• 2001

An efficient and robust algorithm to compute the exact Voronoi diagram of a circle set is presented. The circles are located in a two dimensional Euclidean space, the radii of the circles are non-negative and not necessarily equal, and the circles are allowed to intersect each other. The idea of the algorithm is to use the topology of the point set Voronoi diagram as a seed so that the correct topology of the circle set Voronoi diagram can be obtained through a number of edge flipping operations. Then, the geometries of the Voronoi edges of the circle set Voronoi diagram are computed. In particular, this paper discusses the topological aspect of the algorithm, and the following paper discusses the geometrical aspect. The main advantages of the proposed algorithm are in its robustness, speed, and the simplicity in its concept as well as implementation. Since the algorithm is based on the result of the point set Voronoi diagram and the flipping operation is the only topological operation, the algorithm is always as stable as the Voronoi diagram construction algorithm of a point set.

• Proceedings of the Society of Korea Industrial and System Engineering Conference
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• 2002.05a
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• pp.467-472
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• 2002

Presented in this paper is an algorithm to compute the Voronoi diagram of a circle set from the Voronoi diagram of a point set. The circles are located in Euclidean plane, the radii of the circles are non-negative and not necessarily equal, and the circles are allowed to intersect each other. The idea of the algorithm is to use the topology of the point set Voronoi diagram as a seed so that the correct topology of the circle set Voronoi diagram can be obtained through a number of edge flipping operations. Then, the geometries of the Voronoi edges of the circle set Voronoi diagram are computed. The main advantages of the proposed algorithm are in its robustness, speed, and the simplicity in its concept as well as implementation.

• Journal of the Korean Institute of Navigation
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• v.7 no.1
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• pp.33-62
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• 1983

A navigator on bridge needs to know every kinds of motion characteristics of his vessel at sea. Generally when a vessel is completely built, the shipyard makes turning circle diagrams from the results of turing circle tests made during the sea trials for the reference of the vessel's owner. But referring only the data of a turning circle diagram, an officer on bridge can not figure out his vessel's maneuvering characteristics sufficiently, So nowadays the shipyard often adds Z test to turning circle test for more detail references. In this paper the author made Z and turning circle tests at the rudder angles of 15 and and 35 degress separately and in each of the case made a turrning circle diagram from the results of the turning circle test and the esults numerically calculated from mathematical formula made on the base of the maneuvering indices got from the Z test and compared them each other for the purpose of finding the correlations between them. Followings are concluded from the results. An actual turning circle diagram and a calculated one from the results of the Z test at same rudder angle coincides each other well when the center of the calculated circle is transferred by 1.7B toward the direction of the initial turning perpendicularly to the original course and 0.5L toward the direction in parallel with original course in case of the rudder angle of 35 degrees and 1.2B and 0.3L toward each of the above mentioned directions in case of rudder angle of 15 degrees.

• Korean Journal of Computational Design and Engineering
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• v.6 no.1
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• pp.31-39
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• 2001

Presented in this paper are algorithms to compute the positions of vertices and equations of edges of the Voronoi diagram of a circle set. The circles are located in a Euclidean plane, the radii of the circles are not necessarily equal and the circles are not necessarily disjoint. The algorithms correctly and efficiently work when the correct topology of the Voronoi diagram was given. Given three circle generators, the position of the Voronoi vertex is computed by treating the plane as a complex plane, the Z-plane, and transforming it into another complex plane, the W-plane, via the Mobius transformation. Then, the problem is formulated as a simple point location problem in regions defined by two lines and two circles in the W-plane. And the center of the inverse-transformed circle in Z-plane from the line in the W-plane becomes the position of the Voronoi vertex. After the correct topology is constructed with the geometry of the vertices, the equations of edge are computed in a rational quadratic Bezier curve farm.

• Journal of architectural history
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• v.14 no.4 s.44
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• pp.157-175
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• 2005

Guarino Guarini(1624-1683) is one of great Baroque architects who developed new spatial concept in architecture. He refused to static space typically appeared in Renaissance architecture. Instead, to make it possible to generate complicate form and moving space, he made use of generative diagram. It provide him with an abstract machine to generate automatically architectural inferiority. His generative diagram consists of three types: single circle diagram, matrix diagram and longitudinal diagram. The first diagram uses single circle as primary generator and develop this by means of overlap and equiangular division. La Cappella della Santissima Sindone, Sanctuary of Chiesa di Oropa, Chiesa dei Padri Somaschi, San Gaetano are designed according to this diagram. The generator of the second diagram is nine circles in $3{\times}3$ matrix, which provide the base for the interpenetration of space in Guarini's architecture. He inspired this diagram from Kepler's $\ulcorner$Harmonices mundi$\lrcorner$. The Churches of San Lorenzo, Ste-Anne-la-Royale, San Filippo Neri, San Gaetano are generated by this diagram. The third diagram has several circles in Lantin-cross plan. Guarini adopted this diagram because he had chances to design several churches in Northern Europe. The churches of Santa Maria di Ettinga, Immacolata Concezione, San Maria della Divina Providenza, Church without Name, San Filippo Neri are representative examples for this diagram.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2010.10a
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• pp.281-284
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• 2010

In this paper, we present Hand-gesture recognition for actual computing into color images from camera. Color images are binarization and labeling by using the YCbCr Color model. Respectively label area seeks the center point of the hand from to search Maximum Inscribed Circle which applies Voronoi-Diagram. This time, searched maximum circle and will analyze the elliptic ingredient which is contiguous so a hand territory will be able to extract. we present the presentation contral system using elliptic element and Maximum Inscribed Circle. This algorithm is to recognize the various environmental problems in the hand gesture recognition in the background objects with similar colors has the advantage that can be effectively eliminated.

• Journal of Power Electronics
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• v.3 no.1
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• pp.55-61
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• 2003

This paper presents parameter measurement for permanent magnet synchronous motors based on the P-Q circle diagram. Three electrical parameters of permanent magnet synchronous motors, i.e., the equivalent iron loss resistance, armature inductance, and electrical motive force (emf) coefficient are simultaneously measured. The advantages of this method are that it can be implemented under constant excitation and it dispenses with the generating test for the emf coefficient. The proposed method is applied to a 160w permanent magnet synchronous motor, and then the measurement results are analyzed.

• 전기의세계
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• v.27 no.5
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• pp.69-75
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• 1978

3 phase induction motor applied in the method of connecting it directly across the line needs large current when it starts. At that time, leakage magnetic pathes of interior of the motor are severely saturated and leakage reactances are decreased because of saturation. Consequently, increased current and raised powerfactor yield increase of starting torque. The author, noticing those phenomena, derived experimentally the raion of decreasing leakage reactance from the fact that when voltage applied to motor is increased under locked condition the magnitude of current and phase angle are varied, and determined tha equations of starting current and starting torque, considering the decrease of leakage reactance by the large starting current. The author calculated the characteristics of Current-Time and Speed-Time with the determined equation at specific load conditions, and compared the values obtained from above calculations with those from circle diagram's method and the practically recorded values at same load conditions. Therefore, the authos got a confidience that the results of the derived theory coincide with the practically measured values more well than circle diagram's results and circle diagram's equation should be modified in order to analize the starting status of a induction motor.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2010.05a
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• pp.389-392
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• 2010

In this paper, it presents to detect location using structural information of hand from the input color images on Webcam and to recognize hand gestures. In this system, based on the skin color, the image changes a binary number and labels. Within each labeled area, we can find the Maximum Inscribed Circle using Voronoi Diagram. This circle can find the center of hand. And the circle extracts hand region from analyzing the ellipse elements to relate Maximum Inscribed Circle. We use the Maximum Inscribed Circle and the ellipse elements as characteristic of hand gesture recognition. In various environments, we cannot recognize the object that have similar colors like the background colors. But the proposed algorithm has the advantage that can be effectively eliminated about it.