• The Mathematical Education
• /
• v.46 no.1 s.116
• /
• pp.81-96
• /
• 2007

This study was conducted to investigate the possibility of teaching tessellations' mathematical principles in elementary school mathematics. A survey was carried out and the two hours of the instructional experiment were developed for this study triangular tessellation activity and rectangular tessellation activity. Six fifth graders from W elementary school participated voluntarily in the instructional experiment. It was shown from the survey that teachers and students both know what the tessellation is, but they don't know what the mathematical principles really are in the tessellation. This is because they have just done the covering up-activities in class. It was seen from the instructional experiments that even ordinary students were able to understand the mathematical principles of the tessellation if teachers could throw the suitable focusing questions like 'how to move the rectangles making sides equal' and 'how to gather vertexes making angle $360^{\circ}$'. Furthermore, it is desirable to teach the rectangular tessellation prior to the triangular tessellation since the rectangular tessellation is more easy to deal with than the triangular tessellation.

• Journal of the Korean Society of Clothing and Textiles
• /
• v.30 no.6 s.154
• /
• pp.948-960
• /
• 2006

Chogakpos are highly artistic works created by Korean women as a part of the Kyubang culture in the Chosun Dynasty from the late 19th century to the early 20th. Tessellation is a plaid pattern composed of squares that covers a surface or a space with figures completely without any gap or overlap. The present study purposed to make a comparative analysis of the formative pattern of Chogakp and tessellation in order to show the superiority of Korean Kyubang(the women's quarters called Kyubang in the Chosun Dynasty) culture. As for the research method, we analyzed relevant materials to examine the geometric characteristics and formative principles of tessellation. In addition, we analyzed the formative pattern of Chogakpo using Photographs. The scope of this study was limited to 148 old Chogakpos contained in Huh Dong-hwa's 'Yetpojagi'. According to the results of this research, similarities between Chogakpo and tessellation were as follows. First, in a regular polygon, the face was divided into regular triangles, squares and two or more regular polygons. Second, in a polygon, the face was divided into triangles and quadrangles. Third, the symmetry of tessellation was applied to Cintamani pattern Pojagi. Differences between Chogakpo and tessellation were as follows. First, different from Chogakpo, tessellation had various formative patterns utilizing different regular polygons including hexagons. Second, there was no overlapping repetition in tessellation. Third, there was no free pattern in tessellation.

• Korean Journal of Computational Design and Engineering
• /
• v.11 no.3
• /
• pp.205-210
• /
• 2006

Curve tessellation, which generates a sequence of points from a curve, is very important for curves rendering on a computer screen and for NC machining. For the most case the sequence of discrete points is used rather than a continuous curve. This paper deals with a method of tessellation by calculating the maximal deviation of a curve. The maximal deviation condition is introduced to find the point with the maximal chordal deviation on a curve segment. In the previous research a curve tessellation was tried by the subdivision method, that is, a curve is subdivided until the maximal chordal deviation is less than the given tolerance. On the other hand, a curve tessellation by sequential method is tried in this paper, that is, points are generated successively by using the local property of a curve. The sequential method generates relatively much less points than the subdivision method. Besides, the sequential method can generate a sequence of points from a spatial curve by approximation to a planar curve. The proposed method can be applied for high-accuracy curve tessellation and NC tool-path generation.

• Education of Primary School Mathematics
• /
• v.5 no.1
• /
• pp.1-11
• /
• 2001

The purpose of the study is to introduce how tessellation can be used and integrated to connect geometry to pattern in elementary mathematics educations. Tessellation examples include transformations such as translational symmetry, rotational symmetry, reflection symmetry, and glide reflection symmetry. In addition, many examples of tessellation using softwares such as Escher, TesselMania!, and LOGO programs. Further, future study will continue to foster students and teachers to try to construct their alive mathematics knowledge. The study of geometry and patterns require a rich teaching and learning environment provided by in-depth understanding of thinking connections to objects in real world.

• Journal of the Korea Fashion and Costume Design Association
• /
• v.23 no.3
• /
• pp.57-71
• /
• 2021

When teaching traditional pattern-themed textile design, it has been found that many students struggle during the investigation stage of traditional patterns and complete the development of patterns in relatively simple layout methods, such as block patterns and half drop patterns. Until now, digital textile design textbooks lack content on how to develop patterns. Judging that the current teaching method leads to difficulties in developing a new sense of textile design, this study focused on Heesch-tiling tessellation and software called TESS, a program that can transform patterns themselves. This study is an academic study on the methodology of first developing patterns through TESS, a tessellation program developed for elementary school students in the U.S., and then applying various lines and colors to the complete patterns and textures using Adobe Illustrator. In this study, the concept, formative characteristics, and generative principles of Heesch-tiling tessellation were examined, and the process of developing new patterns using the TESS program, which can be used to create patterns through Heesch-tiling principles, was intended to help in textile design education. Therefore, after analyzing the comprehensive concepts and principles of tessellation, the next step is to understand the principles and the characteristics of pattern making only for Heesch-tiling tessellation, and then ultimately to develop new patterns. While patterns using traditional tessellation layouts have been characterized mainly by repeated geometric shapes, Heesch-tiling tessellation can express surrealistic attributes, such as those by painter M. C. Escher or style elements such as those in neo-pop.

• Communications of the Korean Mathematical Society
• /
• v.18 no.1
• /
• pp.1-20
• /
• 2003

본 요약논문에서는 단순 연결된 리만곡면들의 isometry군, 그 군의 이산부분군을 이용한 리 만곡면들의 tessellation 그리고 regular map에 대해 소개하고 그 응용과 상호연관성들에 대해 살펴본다. 그리고, 여러가지 관점에서의 regular map의 분류에 대해 소개하고, 최근까지 연구되어진 바에 대해 정리해 보고자 한다.

• Proceedings of the Korea Society of Design Studies Conference
• /
• 2005.10a
• /
• pp.110-111
• /
• 2005

• Korean Journal of Computational Design and Engineering
• /
• v.9 no.2
• /
• pp.158-163
• /
• 2004

Curve tessellation, which generates a sequence of points from a curve, is very important for curve rendering on a computer screen and for NC machining. For the most case the sequence of discrete points is used rather than a continuous curve. This paper deals with a method of tessellation by calculating the maximal deviation of a curve. The maximal deviation condition is introduced to find the point with the maximal deviation. Our approach has two merits. One is that it guarantees satisfaction of a given tolerance, and the other is that it can be applied in not only a polynomial curve but its offset. Especially the point sequence generated from an original curve can cause over-cutting in NC machining. This problem can be solved by using the point sequence generated from the offset curve. The proposed method can be applied for high-accuracy curve tessellation and NC tool-path generation.

• International Journal of CAD/CAM
• /
• v.6 no.1
• /
• pp.139-148
• /
• 2006

Catmull-Clark subdivision scheme provides a powerful method for building smooth and complex surfaces. But the number of faces in the uniformly refined meshes increases exponentially with respect to subdivision depth. Adaptive tessellation reduces the number of faces needed to yield a smooth approximation to the limit surface and, consequently, makes the rendering process more efficient. In this paper, we present a new adaptive tessellation method for general Catmull-Clark subdivision surfaces. Different from previous control mesh refinement based approaches, which generate approximate meshes that usually do not interpolate the limit surface, the new method is based on direct evaluation of the limit surface to generate an inscribed polyhedron of the limit surface. With explicit evaluation of general Catmull-Clark subdivision surfaces becoming available, the new adaptive tessellation method can precisely measure error for every point of the limit surface. Hence, it has complete control of the accuracy of the tessellation result. Cracks are avoided by using a recursive color marking process to ensure that adjacent patches or subpatches use the same limit surface points in the construction of the shared boundary. The new method performs limit surface evaluation only at points that are needed for the final rendering process. Therefore it is very fast and memory efficient. The new method is presented for the general Catmull-Clark subdivision scheme. But it can be used for any subdivision scheme that has an explicit evaluation method for its limit surface.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.61 no.1
• /
• pp.130-134
• /
• 2012

In this paper, we propose a space partitioning technique for swarm robots by using the Centroidal Voronoi Tessellation. The proposed method consists of two parts such as space partition and collision avoidance. The space partition for searching a given space is carried out by a density function which is generated by some accidents. The collision avoidance is implemented by the potential field method. Finally, the numerical experiments show the effectiveness and feasibility of the proposed method.