• Communications of Mathematical Education
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• v.22 no.4
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• pp.545-556
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• 2008

In this paper we study Gergonne's point and its adjoint points of triangle using the principle of the lever. We prove existence of Gergonne's point and its adjoint points, suggest new proof method of a equality related with Gergonne's point. We find new equalities related with adjoint points of Gergonne's points, and prove these using the principle of the lever.

• Journal of the Korean School Mathematics Society
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• v.12 no.4
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• pp.365-388
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• 2009

In this paper we solve various triangle construction problems given by three points(a midpoint of side and other two points). We investigate relation between these construction problems, draw out a base problem, and make hierarchy of solved construction problems. In detail we describe analysis for searching solving method, and construction procedure of required triangle.

• Proceedings of the IEEK Conference
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• 2002.06d
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• pp.263-266
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• 2002

This paper describes extraction procedure for the center coordinates of steam generator tubes of Youngkwang NPP #6, which are arrayed in triangular patterns. Steam generator tube images taken with wide field-of-view lens and low-light lamp mounted on a ccd camera tend to have low contrast, because steam generator is sealed and poorly illuminated. The extraction procedures consists of two steps. The first step is to process the region with superior contrast in entire image of steam generator tubes and to extract the center points. Using the extracted coordinates in the first step and the geometrical array characteristics of tubes lined up in regular triangle forms, the central points of the rest region with low contrast are estimated. The straight lines from center point of a tube to neighbour points in horizontal and 60, 120$^{\circ}$ degree directions are derived. The intersections of straight line In horizontal direction and slant line in regular triangle direction are selected as the center coordinates of steam generator tubes. The Chi-square interpolation method is used to determine the line's coefficients in horizontal and regular triangle direction.

• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.433-444
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• 2024

Our study explores the connection between the Pythagorean theorem and the Fixed-point theorem in metric spaces. Both of which center around the concepts of distance transformations and point relationships. The Pythagorean theorem deals with right triangles in Euclidean space, emphasizing distances between points. In contrast, fixed-point theorems pertain to the points that remain unchanged under specific transformations thereby preserving distances. The article delves into the intrinsic correlation between these concepts and presents a novel study in Euclidean metric spaces, examining the relationship between contraction mapping and Pythagorean Right Triangles. Practical applications are also discussed particularly in the context of image compression. Here, the integration of the Pythagorean right triangle paradigm with contraction mappings results in efficient data representation and the preservation of visual data relation-ships. This illustrates the practical utility of seemingly abstract theories in addressing real-world challenges.

• Journal of Korea Multimedia Society
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• v.12 no.11
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• pp.1623-1628
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• 2009

This paper presents the development of certain highly efficient and accurate method for computing tangent curves for two-dimensional vector fields. Unlike convention methods, such as Runge-Kutta, for computing tangent curves which produce only approximations, the method developed herein produces exact values on the tangent curves based on piecewise linear variation over a triangle in 2D. This new method assumes that the vector field is piecewise linearly defined over a triangle in 2D. It is also required to decompose the rectangular cell into two triangular cells. The critical points can be easily found by solving a simple linear system for each triangle. This method is to find exit points by producing a sequence of points on the curve with the computation of each subsequent point based on the previous. Because points on the tangent curves are calculated by the explicit solution for each triangle, this new method provides correct topologies in visualizing 2D vector fields.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.901-909
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• 2014

It is well known that the area U of the triangle formed by three tangents to a parabola X is half of the area T of the triangle formed by joining their points of contact. In this article, we study some properties of U and T for strictly convex plane curves. As a result, we establish a characterization for parabolas.

• Journal of the Korea Society of Computer and Information
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• v.11 no.3
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• pp.151-159
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• 2006

In this paper. we Present an estimation method of a face pose by using two camera images. First, it finds corresponding facial feature points of eyebrow, eye and lip from two images After that, it computes three dimensional location of the facial feature points by using the triangulation method of stereo vision techniques. Next. it makes a triangle by using the extracted facial feature points and computes the surface normal vector of the triangle. The surface normal of the triangle represents the direction of the face. We applied the computed face pose to display a 3D face model. The experimental results show that the proposed method extracts correct face pose.

• Journal of Korea Game Society
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• v.14 no.2
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• pp.55-66
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• 2014

Image warping is a technology to transform input images to be suitable for given conditions and has been recently utilized in changing face shape of characters in the field of movies or animation. Mesh warping which is one of warping methods that change shapes based on the features of face forms warping images by forming rectangular mesh groups around the eyes, nose, and mouth and matching them 1:1. This method has a problem in the resultant images are distorted in the segments of boundaries between meshes when there are errors in mesh control points or when meshes have been formed as many small area meshes. This study proposes a triangle based image interpolation technique to minimize the occurrence of errors in the process of forming natural warping images of face and process accurate results with a small amount of arithmetic operation and a short time. First, feature points that represent the face are found and these points are connected to form basic triangle meshes. The fact that the proposed method can reduce errors occurring in the process of warping while reducing the amount of arithmetic operation and time is shown through experiments.

• Communications of Mathematical Education
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• v.23 no.4
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• pp.1059-1078
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• 2009

In this paper we study metric equalities related with distance between excenter and other points of triangle. Especially we find metric equalities between excenter and incenter, circumcenter, center of mass, orthocenter, vertex, prove these formulas, and transform these formulas into new formula containing another elements of triangle. We in detail describe proof process of these equalities, indicate references of some formulas that don't exist within secondary school curriculum.

• Korean Journal of Computational Design and Engineering
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• v.10 no.3
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• pp.168-178
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• 2005

The Delaunay triangular net is primarily characterized by a balance of the whole by improving divided triangular patches into a regular triangle, which closely resembles an equiangular triangle. A triangular net occurring in certain, point-clustered, data is unique and can always create the same triangular net. Due to such unique characteristics, Delaunay triangulation is used in various fields., such as shape reconstruction, solid modeling and volume rendering. There are many algorithms available for Delaunay triangulation but, efficient sequential algorithms are rare. When these grids involve a set of points whose distribution are not well proportioned, the execution speed becomes slower than in a well-proportioned grid. In order to make up for this weakness, the ids are divided into sub-grids when the sets are integrated inside the grid. A method for finding a mate in an incremental construction algorithm is to first search the area with a higher possibility of forming a regular triangular net, while the existing method is to find a set of points inside the grid that includes the circumscribed sphere, increasing the radius of the circumscribed sphere to a certain extent. Therefore, due to its more efficient searching performance, it takes a shorer time to form a triangular net than general incremental algorithms.