• 한국수학교육학회지시리즈A:수학교육
• /
• 제40권1호
• /
• pp.93-102
• /
• 2001

The world we live in is called the age of information. Thus communication and computers are doing the central role in it. When one studies the mathematical problem, the use of tools such as computers, calculators and technology is available for all students, and then students are actively engaged in reasoning, communicating, problem solving, and making connections with mathematics, between mathematics and other disciplines. The use of technology extends to include computer algebra systems, spreadsheets, dynamic geometry software and the Internet and help active learning of students by analyzing data and realizing mathematical models visually. In this paper, we explain concepts of transformation, linear transformation, congruence transformation and homothety, and introduce interesting, meaningful and visual models for teaching of a plane transformation geomeoy which are obtained by using Mathematica. Moreover, this study will show how to visualize linear transformation for student's better understanding in teaching a plane transformation geometry in classroom. New development of these kinds of teaching-learning methods can simulate student's curiosity about mathematics and their interest. Therefore these models will give teachers the active teaching and also give students the successful loaming for obtaining the concept of linear transformation.

• 대한수학교육학회지:학교수학
• /
• 제14권3호
• /
• pp.331-355
• /
• 2012

타원의 지도 방법은 학생들이 직접 두 점으로부터 거리의 합이 같은 점들을 그려서 타원의 모양이 나오는 것을 확인한 후에 두 정점으로부터의 거리의 합이 일정한 점들의 자취라는 타원을 정의를 알게 하는 것이다. 이 과정에서 학생들은 스스로 정의를 생각하거나 만들어 낼 기회를 갖지 못하며 왜 이러한 정의가 만들어 졌는지에 대해 의문을 갖게 된다. 본 논문은 원과 타원의 유사성을 바탕으로 타원을 정의하고 방정식을 유도하는 방법을 소개한다. 이러한 방법은 현재 학교수학에서 다루는 해석기하적인 관점과 더불어 변환 기하학적 관점을 도입함으로서 가능하다. 이를 통해 타원에 대한 본질적인 이해와 직관을 통해 확장 가능한 타원의 성질에 대해 논의하고, 변환 기하학적 관점에서 정의하는 방법이 주는 다양한 이점을 알아보고자 한다.

• 한국수학사학회지
• /
• 제14권1호
• /
• pp.109-114
• /
• 2001

Using Fermi coordinate and Jacobi operator on Kahler manifold, we characterize partially conformal geodesic transformation in Kahler geometry.

• 한국측량학회지
• /
• 제38권5호
• /
• pp.477-486
• /
• 2020

Drone has been widely used for many applications ranging from amateur and leisure to professionals to get fast and accurate 3-D information of the surface of the interest. Most of commercial softwares developed for this purpose are performing automatic matching based on SIFT (Scale Invariant Feature Transform) or SURF (Speeded-Up Robust Features) using nadir-looking stereo image sets. Since, there are some situations where not only nadir and nadir-looking matching, but also nadir and oblique-looking matching is needed, the existing software for the latter case could not get good results. In this study, a matching experiment was performed to utilize images with differences in geometry. Nadir and oblique-looking images were acquired through drone for a total of 2 times. SIFT, SURF, which are feature point-based, and IMAS (Image Matching by Affine Simulation) matching techniques based on affine transformation were applied. The experiment was classified according to the identity of the geometry, and the presence or absence of a building was considered. Images with the same geometry could be matched through three matching techniques. However, for image sets with different geometry, only the IMAS method was successful with and without building areas. It was found that when performing matching for use of images with different geometry, the affine transformation-based matching technique should be applied.

• 정보과학회 논문지
• /
• 제42권2호
• /
• pp.162-168
• /
• 2015

대부분의 영상정보들은 데이터 양이 방대하기 때문에 압축되어 저장되고 전달된다. 이 때문에 영상정보의 변환을 위해서는 사전에 압축을 해제하여 공간정보를 추출한 뒤에 소정의 변환을 하고 다시 압축해야 하는 번거로움과 불편한 점이 있다. 본 논문에서는, JPEG등의 정지영상 압축이나 MPEG-4와 H.264 등의 영상 압축 표준에서 널리 사용되는 DCT 변환에 의한 영상정보의 주파수 영역의 계수 값들의 부호나 이들 간의 상대적 위치를 적절히 바꿈으로써 공간적 영역에서의 원하는 기하학적 변환이 이루어지는 규칙을 발견하고 정리하였다. 본 저자들은 주파수 영역에서의 계수 값 변환 효과가 공간적 영역에 어떻게 나타나는지 수학적으로 유도하고 실제 JPEG 압축 파일에 본 방식을 적용하여 이미지를 변환시켜 그 성능을 검증하였다. 이 방법은 압축을 완전히 해제하지 않고도 공간적 영역에서의 변환을 달성할 수 있기 때문에 대용량의 간단한 이미지 암호화를 위한 경량암호화 시스템에 응용될 수 있다.

• 방송공학회논문지
• /
• 제18권1호
• /
• pp.31-42
• /
• 2013

본 논문에서는 고품질의 3D 콘텐츠 제작에 있어 입체피로를 최소화하기 위한 영상의 수직시차 교정방법으로, 베이지안 접근방식을 적용한 사진측량기반의 강인 편위수정 기법을 제안하고자 한다. 영상의 수직시차 제거 과정은 크게 기하추정 단계와 에피폴라 변환 단계로 구성된다. 본 논문에서는 기하추정을 위해 사진측량에서 널리 활용되고 있는 공면조건 기반의 상대표정 알고리즘을 적용한다. 이때 상대표정 알고리즘에는 자동 정합점 추출에 따른 오정합과 위치오차에 강인성을 확보하기 위해 제약조건을 도입한 베이지안 접근방식을 적용하고자 하며, 이를 바탕으로 수행되는 에피폴라 변환에는 영상의 왜곡과 원 영상 대비 변형을 최소화하기 위한 공선조건기반의 중심투영변환기법을 적용하고자 한다. 알고리즘의 성능검증을 위한 비교 알고리즘으로, 기하추정에는 일반적인 상대표정 알고리즘과 컴퓨터비전분야의 8점 알고리즘 및 스테레오 캘리브레이션 기법이 사용되었으며, 에피폴라 변환에는 Hartley 방법과 Bouguet 방법이 사용되었다. 실험결과는 제안 알고리즘의 높은 정확도와 여러 오차요인들에 대한 강인성, 그리고 최소화된 영상변형의 결과를 보여주었다.

• 아동학회지
• /
• 제32권2호
• /
• pp.71-85
• /
• 2011

This study was carried out in order to better understand how cooperative learning effects the geometric understanding of young children. The geometry tasks used in the study included the geometric relationship between two dimensional shapes and three dimensional shapes, coordination, symmetry and transformation visualization and spacial reasoning. The subjects were composed of children aged five years and were taken from two kindergartens in a relatively new city close to Seoul. The experimental group of children the comparative learning in geometry. The comparative group of children were enrolled in a kindergarten that uses an the intergrated curriculum. The results indicated that cooperative learning impacted positively on the children's understanding of geometry. The specific results are as follows : The scores that the experimental acquired were higher in terms of p < .001 level. than the scores of the comparative group studying the geometric relationships between two dimensional shapes and three dimensional shapes, coordination, symmetry and transformation visualization & spacial reasoning.

• 대한전자공학회:학술대회논문집
• /
• 대한전자공학회 2006년도 하계종합학술대회
• /
• pp.989-990
• /
• 2006

This paper presents a design of 3D Graphics Geometry processor. A geometry processor needs to cope with a large amount of computation and consists of transformation processor and lighting processor. To deal with the huge computation, a vector processing structure based on pipeline chaining is proposed. The proposed geometry processor performs 4.3M vertices/sec at 100MHz using 11 floating-point units.

• 대한전자공학회:학술대회논문집
• /
• 대한전자공학회 2005년도 추계종합학술대회
• /
• pp.711-714
• /
• 2005

We propose floating point arithmetic units for geometry operation of mobile 3D graphic processor. The proposed arithmetic units conform to the single precision format of IEEE standard 754-1985 that is a standard of floating point arithmetic. The rounding algorithm applies the nearest toward zero form. The proposed adder/subtraction unit and multiplier have one clock cycle latency, and the inversion unit has three clock cycle latency. We estimate the required numbers of arithmetic operation for Viewing transformation. The first stage of geometry operation is composed with translation, rotation and scaling operation. The translation operation requires three addition and the rotation operation needs three addition and six multiplication. The scaling operation requires three multiplication. The viewing transformation is performed in 15 clock cycles. If the adder and the multiplier have their own in/out ports, the viewing transformation can be done in 9 clock cycles. The error margin of proposed arithmetic units is smaller than $10^{-5}$ that is the request in the OpenGL standard. The proposed arithmetic units carry out operations in 100MHz clock frequency.

• 한국수학교육학회지시리즈D:수학교육연구
• /
• 제9권3호
• /
• pp.285-294
• /
• 2005

The author has been teaching with an instructional module consisting of many mathematical concepts, based on designs formed by personal names or words to arouse students' interesting in learning mathematics. This module has been growing since it was first used as a supplementary lesson for calculus students. Now it consists of concepts that connect with mathematical topics such as number sense, algebraic thinking, geometry, and statistical reasoning, as well as other subjects such as art and quilt design. With its content we can provide our students the basic mathematical knowledge needed for further study in their own fields. In this article, we will demonstrate the latest development of this instructional module, which makes connections between mathematical knowledge and the design of personal quilt patterns. We will exhibit a 'Quilt of Nations' which consists of the designed quilt blocks of different countries, such as USA, Japan, Taiwan, Korea and others, as well as a quilt design using the abbreviation of this seminar. Then we will talk about how the connections are built, and how to design these mathematically rich, uniquely created, beautifully designed, and personalized quilt block patterns.