Original Original Articles [13] Newman, D., Defensive Space: People and Design in Received Nov 20 2017; Accepted Jan 24 2018 the Violent City, London, Architectural Press, 1972. [14] Cozens, P., Saville, G., and Hillier, D., Crime Prevention Through Environmental Design (CPTED): DISCUSSION ON THE SHAPING ARRANGEMENT OF A review of Modern Bibiography, Proper Management 23 (5) 328 – 356, 2005 MAJOLICA TILE WITH THE PAPER-CUT [15] Thorpe, A., Gamman, L., Design with society: Why CREATION MODE Social Responsive Design is Good Enough, CoDesign (3-4), 217 – 230, 2011. [16] Villalta, C., El Miedo al Delito en Mexico, Estrutura Yu-Ya WANG *, Chi-Shyong TZENG **, Akiyo KOBAYASHI *** Logica, Bases Emocionales y Recomendaciones

Iniciales de Politica Publica, Gestion Politica, Vol XIX, * Graduate School of Design, National Yunlin University of Science and Technology, Taiwan Num 1, CIDE, Mexico, 2009. * * Graduate School of Design, National Yunlin University of Science and Technology, Taiwan [17] Kessler, El Sentimiento de Inseguridad, Sociologia del * * * Department of Science of Design, Musashino University, Japan Temor al Delito, Siglo XXI, Argentina,35, 2009. [18] Jasso, C., Percepcion de Inseguridad en Mexico, Revista Mexicana de Opinion Publica 15-19, 2013. Abstract: The purpose of the study is to achieve the shaping design with repetitive, symmetric, and [19] INEGI., Encuesta Nacional de Victimización y continuous graphs through papercutting. The researchers used the folding and cutting model of Percepción sobre Seguridad Pública 2016, Mexico, papercutting to build the linkage with the graphic shaping arrangement of the Majolica tile in order to 2016. discover an effective and expeditious design method for the public. The study proposes conclusions as [20] Gobierno del Estado de Sinaloa, Plan de Desarrollo follows: 1) to ensure the relationships between the folding steps and folding lines: the expression of the Estatal 2016, Sinaloa, 2016. shaping arrangement patterns as long as one knows the position of the folding lines in papercutting in [21] Gomez, J., El capital Social Communitario como advance, which significantly enhances the artist’s design efficiency; and 2) the correspondence between herramienta para la seguridad ciudadana: Alarmas papercutting model and the shaping graphic arrangement of the tile: from the 25 single Majolica tile Comunitarias en Peñaleon, Chile, 2014. samples, the folding steps correspond to the Majolica tile, which inspires the design of the shaping graphic [22] Cornero, R., Enriching in-person encounters through arrangement. The study obtains 10 different folding steps and 9 kinds of folding line distribution. social media: A study on family connectedness for the Keywords: Papercutting, Majolica Tile, Shaping Arrangement eldery, Human-Computer Studies, 71: 889-899, 2013.

1. Introduction between figures in shaping, and in the papercutting methods 1. 1. Research Background discussed in this study, new developmental possibilities of The papercutting transmits the information of daily life shaping arrangement are found by folding and cutting. with the skill of cutting “paper shapes”. The application of Judging from the abovementioned study background, it can this technique the construction of figures by paper folding be seen that, with the representation forms of papercutting and cutting, and in the traditional civil papercutting art, creation, symmetrical and repeated patterns can be deigned papercutting is regarded as widespread civil aesthetics, and created. The arrangement designs of shaping patterns while the creation and shaping of its patterns, points, lines, are featured by shaping construction, and through the and surfaces are taken as the basic constitutional elements discussions of this study, the author attempts to determine to further result in a complete figure. For papercutting the developmental process of shaping possibilities to further creators, the design of a pattern can usually be represented develop the relevance of follow-up study design. by their works. Regarding the shaping representation of figures, both In the design-related educational part regarding graphic papercutting and tile have symmetrical, repetitive, and shaping construction, it is indicated that the construction of continual modes. Different shaping arrangement positions shaping elements are based on points, lines, and surfaces. are generated by the papercutting creation modes and the These three elements have different visual effects and figure differences in paper folding for papercutting. Moreover, representation modes. The papercutting creation method extended discussions on the repetitive and symmetrical and representation mode are featured by the relevance shaping of Majolica tiles indicate that the construction of a

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Journal of the Science of Design Vol. 2 No. 1 2018 37 shaping arrangement frequently takes on the arrangement of make the graphic shape as precisely as the computer does. continual, repetitive, and symmetrical shaping. This shaping However, it is an undeniable fact that it remains to be a arrangement mode is mostly frequently seen in the figure means of artistic creation, which is less time consuming and designs of the tiles, and the most primary designs and less expensive. creation ideas for tiles is the characteristics of the extended The purpose of the study is to make use of the use of the tile. Tiles can be conveniently used on any planes papercutting model, with its efficiency and easy access, in and spaces, as well as for product designs, thus, achieving order to achieve the shaping design of the repetitive, the unlimited extension of shaping construction and symmetric, and continuous graphs. Through the arrangement. folding-paper techniques, one is capable of understanding 1. 2. Research Purpose the changes of the repetitive, symmetric and continuous In design creation, the shaping changes of symmetrical graphic shaping arrangement. Through the linkage between and repeated figures have a decorative effect, and thus, are the papercutting model and the tile graphic arrangement, frequently adopted in various design-related fields, such as one is capable of finding an efficient and expeditious means ceramics, fabric flowers, , etc. In the traditional era of art creation in order to enhance design efficiency and of manual design, the design and creation processes were offer the basis of mastering the principle of art creation. usually seen as difficult tasks. Currently, with the Meanwhile, it can be used as the design preparation in application functions of the era of computer design and advance before the computer design in order to effectively creation, they can be easily solved with replica technology, achieve the final result of design. thus, designs can be completed more quickly and 1. 3. Research Process and Scope conveniently. The method of finding repeated and In this study, under the concept of the shaping symmetrical figures by papercutting creation has gradually construction design of papercutting creation, the shaping disappeared. Computers and mechanized products are arrangements of the figures on Majolica tiles are analyzed, indifferent to people, and compared with the manual mode, and the generation of shaping arrangements is discussed the papercutting creation mode indeed has existential value. with the paper folding and cutting methods of papercutting With the manual creation mode of papercutting, the design creation. From the shaping arrangement forms of Majolica difficulties of the designers can be solved, and the shaping tile, the representations of shaping arrangement are found, changes of repeated and symmetrical figures can be more and put forward to explain their construction. Therefore, in specifically, effectively, and rapidly achieved. this study, the characteristics of shaping arrangements are The basic material for papercutting is the paper, which is analyzed by descriptions, drawings, and comparisons inexpensive and affordable. The creation of the work uses between creations, in order to learn the arrangement form of the paper to express itself by folding and cutting. The shaping construction. The study process can be divided into shaping work of this sort can be an artistic means of the following stages: convenience, speed, inexpensiveness, and completion. For 1) Investigation of the study sample: beginners of the graphic pattern, they can only learn how As the shaping pattern of a single Majolica tile is the papercutting artwork is done through folding and completed by symmetrical and repetitive cutting in order to find the relations among the graphic arrangements, patterns must be completed by first shaping arrangements. They can make repetitive and producing patterns with unit shapes. The pattern of a symmetric graphic shaping arrangement design. single Majolica tile is taken as the subject of the However, in today’s design concept, computer graphic papercutting creation mode for study and analysis, as design is widely used to conduct the design of artwork. The the positions where the study samples were taken computer graphic design can quickly solve the technical from mainly include the facade and flanking walls of inconvenience caused by many graphic shaping the inner part of the lobby at the front door, and the arrangement, but it requires long time of learning how to representations of the constitutional forms of their use the software before one is capable of actually using it. shaping arrangement are different. Meanwhile, it costs a deal of money to buy the relevant 2) Summary of the study sample: software, which are never cheap. In contrast, the traditional The Majolica tiles in Shuitou Village, Jinmen County, means of papercutting artwork can be an easy and Taiwan are taken as the study sample, the relevance inexpensive means of artistic artwork though it cannot between the number of shaping patterns of the study

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38 Journal of the Science of Design Vol. 2 No. 1 2018 shaping arrangement frequently takes on the arrangement of make the graphic shape as precisely as the computer does. sample and their geographic positions are investigated, NO.14- NO.15 6 in×6 in Facade and flank walls of the inner part of the lobby at front continual, repetitive, and symmetrical shaping. This shaping However, it is an undeniable fact that it remains to be a which also ascertained whether the shaping pattern of

door arrangement mode is mostly frequently seen in the figure means of artistic creation, which is less time consuming and the tile is repeated. According to the positions where Year of decoration Source of the sample designs of the tiles, and the most primary designs and less expensive. study samples were originally found, the shaping 1930 No.82, Qianshuitou, Jincheng Township creation ideas for tiles is the characteristics of the extended The purpose of the study is to make use of the patterns are identified as the basic conditions for the use of the tile. Tiles can be conveniently used on any planes papercutting model, with its efficiency and easy access, in selection of study samples. In this study, five and spaces, as well as for product designs, thus, achieving order to achieve the shaping design of the repetitive, traditional buildings are investigated to obtain the the unlimited extension of shaping construction and symmetric, and continuous graphs. Through the shaping pattern samples used in this study, for a total (NO.14) (NO.15) arrangement. folding-paper techniques, one is capable of understanding of 25 Majolica tiles, of which 21 have the dimensions Sample No. Sample size Position of decoration NO.16- NO.17 6 in×3 in Facade and flank walls of the 1. 2. Research Purpose the changes of the repetitive, symmetric and continuous of 6 in×6 in (15.24cm×15.24cm) (square), and 4 of 6 inner part of the lobby at front In design creation, the shaping changes of symmetrical graphic shaping arrangement. Through the linkage between in×3 in (15.24cm×7.62cm) (rectangle), as shown in door

and repeated figures have a decorative effect, and thus, are the papercutting model and the tile graphic arrangement, (Table 1). Year of decoration Source of the sample 1930 No.82, Qianshuitou, Jincheng Township frequently adopted in various design-related fields, such as one is capable of finding an efficient and expeditious means ceramics, fabric flowers, knitting, etc. In the traditional era of art creation in order to enhance design efficiency and Table 1. List of the Study Samples of Majolica Tiles Obtained in Jinmen County of manual design, the design and creation processes were offer the basis of mastering the principle of art creation. (NO.16) (NO.17) usually seen as difficult tasks. Currently, with the Meanwhile, it can be used as the design preparation in Sample No. Sample size Position of decoration Sample No. Sample size Position of decoration NO.1- NO.5 6 in×6 in Facade and flank walls of the NO.18- NO.21 6 in×6 in Facade and flank walls of the application functions of the era of computer design and advance before the computer design in order to effectively inner part of the lobby at front inner part of the lobby at front creation, they can be easily solved with replica technology, achieve the final result of design. door door thus, designs can be completed more quickly and 1. 3. Research Process and Scope Year of decoration Source of the sample Year of decoration Source of the sample 1935 No.6, Qianshuitou, Jincheng Township conveniently. The method of finding repeated and In this study, under the concept of the shaping 1925 No.17, Qianshuitou, Jincheng Township symmetrical figures by papercutting creation has gradually construction design of papercutting creation, the shaping disappeared. Computers and mechanized products are arrangements of the figures on Majolica tiles are analyzed, indifferent to people, and compared with the manual mode, and the generation of shaping arrangements is discussed (NO.1) (NO.2) (NO.3) (NO.18) (NO.19) (NO.20) the papercutting creation mode indeed has existential value. with the paper folding and cutting methods of papercutting With the manual creation mode of papercutting, the design creation. From the shaping arrangement forms of Majolica difficulties of the designers can be solved, and the shaping tile, the representations of shaping arrangement are found, (NO.4) (NO.5) (NO.21) changes of repeated and symmetrical figures can be more and put forward to explain their construction. Therefore, in specifically, effectively, and rapidly achieved. this study, the characteristics of shaping arrangements are Sample No. Sample size Position of decoration Sample No. Sample size Position of decoration NO.6- NO.11 6 in×6 in Facade and flank walls of the NO.22- NO.25 6 in×6 in Facade and flank walls of the The basic material for papercutting is the paper, which is analyzed by descriptions, drawings, and comparisons inner part of the lobby at front inner part of the lobby at front door door inexpensive and affordable. The creation of the work uses between creations, in order to learn the arrangement form of

the paper to express itself by folding and cutting. The shaping construction. The study process can be divided into Year of decoration Source of the sample Year of decoration Source of the sample 1921 No.37, Qianshuitou, Jincheng Township 1930 No.4 or 5, Qianshuitou, Jincheng Township shaping work of this sort can be an artistic means of the following stages: convenience, speed, inexpensiveness, and completion. For 1) Investigation of the study sample: beginners of the graphic pattern, they can only learn how As the shaping pattern of a single Majolica tile is the papercutting artwork is done through folding and completed by symmetrical and repetitive (NO.6) (NO.7) (NO.8) (NO.22) (NO.23) (NO.24) cutting in order to find the relations among the graphic arrangements, patterns must be completed by first shaping arrangements. They can make repetitive and producing patterns with unit shapes. The pattern of a symmetric graphic shaping arrangement design. single Majolica tile is taken as the subject of the (NO.9) (NO.10) (NO.11) (NO.25) However, in today’s design concept, computer graphic papercutting creation mode for study and analysis, as design is widely used to conduct the design of artwork. The the positions where the study samples were taken Sample No. Sample size Position of decoration NO.12- NO.13 6 in×3 in Facade and flank walls of the 3) Analysis of shaping arrangement: computer graphic design can quickly solve the technical from mainly include the facade and flanking walls of inner part of the lobby at front To analyze the shaping arrangement patterns of inconvenience caused by many graphic shaping the inner part of the lobby at the front door, and the door arrangement, but it requires long time of learning how to representations of the constitutional forms of their Year of decoration Source of the sample Majolica tiles, the paper folding steps are first use the software before one is capable of actually using it. shaping arrangement are different. 1921 No.37, Qianshuitou, Jincheng Township determined by the folding and cutting concepts of Meanwhile, it costs a deal of money to buy the relevant 2) Summary of the study sample: papercutting, and then, the relative position of shaping software, which are never cheap. In contrast, the traditional The Majolica tiles in Shuitou Village, Jinmen County, (NO.12) (NO.13) construction is found based on the arrangement of the means of papercutting artwork can be an easy and Taiwan are taken as the study sample, the relevance Sample No. Sample size Position of decoration positions and figures of the shaping of a single inexpensive means of artistic artwork though it cannot between the number of shaping patterns of the study Majolica tile. In this way, the shaping distribution of

2 Journal of the Science of Design Vol. xx No. x 20xx Journal of the Science of Design Vol. xx No. x 20xx 3 Journal of the Science of Design Vol. 2 No. 1 2018 39 patterns could be rapidly and effectively completed. unit, which can create a larger inclusive pattern when On the other hand, in order to observe the distribution connected together. They also have high ductility. of the shaping construction of a single Majolica tile, 2. 2. Construction and form of papercutting shaping the overall arrangement modes of the patterns are Regarding the construction representation of the shaping analyzed by combining the folding steps of of a design, three methods, “folding”, “cutting”, and papercutting with tile patterns. “bending” have been used as creation methods [2]. With these three types of methods, paper is free from the 2. Literature Review constraints and images of planes, and three-dimensional 2. 1. Majolica Tile representations can be completed by folding, cutting, “ Majolica tiles” originated in Spain or earlier in bending, etc. Therefore, the shaping form of paper, as Islamic ceramic vessels and tiles. The production of represented by folding, cutting, and bending, is a sort of majolica tiles evolved from Islamic tiles, as Islamic construction process. tiles utilized mosaic to a great extent early on, and Paper represents its shaping through the cut figures, and especially in mosques. Spanish architecture, which was the works represent the creation representation of a sort of later influenced by Islamic styles, and utilized in graphic shaping, if the figures are cut without the paper arranging various patterns to form architectural decorations. being folded first. When folding and cutting are conducted However, this method required a great deal of time and in succession, the final result is a combination of graphic labor, so the Spanish invented a larger tile which shaping forms and three-dimensional representations. The incorporated the entire mosaic within its square area to modes of the construction representations of paper shaping replace the original production method, and this was the are diversified and changing, and such different folding predecessor of the modern majolica tile. methods indicate that the representations of shaping are not just graphic shaping. The other creation mode is to fold different types of shaping forms with the steps of symmetrical and asymmetrical folding lines, squares, polygonal and diagonal lines. After the figure set is cut off, the paper is unfolded, and the arrangement form of graphic shaping is presented. This representation method is called “papercutting”. According to the basic principle of plane formation, this study clarifies that the representations of papercutting shapes is to change the unit form of beauty, and includes Figure 1. Traditional home on Kinmen-Perspective drawing (red spots indicate areas where Majolica Tiles were various forms, such as radiation, symmetry, continuity, applied)Source: Colored Tiles on Structure, Cai repetition, etc. Judging from the four papercutting forms in Rixiang[1] the following figures, the development positions for the Prior to World War II the decoration in residential construction arrangement of figures are determined through housing or contemporary Japanese colonial period paper folding. As shown in (Figure 2), the radiation figure, architecture in Taiwan, and the traditional furniture it can be obviously seen that 8 folds are symmetrically decoration, all had this type of colored Japanese tile. Most generated by using the central point of the paper; the of these ceramic tiles were majolica produced by Japanese unfolded shape arrangement of the cut figures is radioactive, companies and have the “Made in Japan” mark on back, and the arrangement of their shaping regularly tends to be allowing us to know their place of origin. On the front was circular [3]. engraved the companies name or its trademark. Traditional architecture built in Kinmen during the 1930’s, or private residences built by remittances from Kinmen compatriots generally most often use primarily 15 centimeter majolica tile to decorate their walls. These bright color tiles are extremely durable and will not fade despite Figure 2. Representation of Aesthetic Form of Papercutting Creation [4] wind, sun and rain. In addition, each tile is its own graphic

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40 Journal of the Science of Design Vol. 2 No. 1 2018 patterns could be rapidly and effectively completed. unit, which can create a larger inclusive pattern when The basic form of the development of a shaping On the other hand, in order to observe the distribution connected together. They also have high ductility. arrangement, as completed by papercutting, can be regarded of the shaping construction of a single Majolica tile, 2. 2. Construction and form of papercutting shaping as the combination of unit forms, as the unit form is the the overall arrangement modes of the patterns are Regarding the construction representation of the shaping most fundamental unit element of graphic construction. As analyzed by combining the folding steps of of a design, three methods, “folding”, “cutting”, and unit forms appear in most form principles, the unit form can papercutting with tile patterns. “bending” have been used as creation methods [2]. With be regarded as the common basic element in beauty form these three types of methods, paper is free from the principles [5]. During the grouping of unit forms, the 2. Literature Review constraints and images of planes, and three-dimensional integration of forms can occur, and the changes and 2. 1. Majolica Tile representations can be completed by folding, cutting, development of such combination are unlimited. “ Majolica tiles” originated in Spain or earlier in bending, etc. Therefore, the shaping form of paper, as 2. 3. Order of papercutting shaping Islamic ceramic vessels and tiles. The production of represented by folding, cutting, and bending, is a sort of One papercutting creation method is to fold layer by majolica tiles evolved from Islamic mosaic tiles, as Islamic construction process. layer by doubling the paper till the unit form of the paper tiles utilized mosaic to a great extent early on, and Paper represents its shaping through the cut figures, and folding is completed, cut off the set figure, and unfold it to especially in mosques. Spanish architecture, which was the works represent the creation representation of a sort of complete the pattern formed by the paper. This later influenced by Islamic styles, and utilized mosaics in graphic shaping, if the figures are cut without the paper representation of a shaping arrangement can be symmetrical, arranging various patterns to form architectural decorations. being folded first. When folding and cutting are conducted radioactive, repetitive, continual, etc., as shown in (Figure However, this method required a great deal of time and in succession, the final result is a combination of graphic 3). Representation of Papercutting Process and Unfolded Figure 4. Schematic Diagram of Order of Papercutting Shaping labor, so the Spanish invented a larger tile which shaping forms and three-dimensional representations. The Figure of Completed Papercutting. incorporated the entire mosaic within its square area to modes of the construction representations of paper shaping 3. Study and analysis replace the original production method, and this was the are diversified and changing, and such different folding 3. 1. Arrangement relation of shaping patterns between predecessor of the modern majolica tile. methods indicate that the representations of shaping are not folding and cutting of papercutting just graphic shaping. The other creation mode is to fold The representations of the shaping arrangements of different types of shaping forms with the steps of papercutting can be regular or random. The forms of symmetrical and asymmetrical folding lines, squares, shaping arrangements are greatly affected by the procedures polygonal and diagonal lines. After the figure set is cut off, of paper folding. The cutting results, as obtained with Figure 3. Steps of Paper Folding and Cutting [6] the paper is unfolded, and the arrangement form of graphic different paper folding steps and forms, have different shaping is presented. This representation method is called Steps of papercutting creation: Step 1: the completed positions of shaping arrangements, and the different shaping “papercutting”. unit form of paper folding is completed by first folding arrangement forms are represented in the final unfolding. According to the basic principle of plane formation, this square paper; Step 2: the figure is set to be cut; Step 3: the The analysis of this study is shown below, as based on the study clarifies that the representations of papercutting set figure is cut; Step 4: open the folded figure of the steps set for four groups of paper folding. shapes is to change the unit form of beauty, and includes Figure 1. Traditional home on Kinmen-Perspective drawing completed papercutting. Judging from the papercutting Steps for paper folding Groups 1 and 2: Group 2 is (red spots indicate areas where Majolica Tiles were various forms, such as radiation, symmetry, continuity, creation of the figure above, the different angles and folded from the same square diagonal three times. The applied)Source: Colored Tiles on Structure, Cai repetition, etc. Judging from the four papercutting forms in Rixiang[1] numbers of folding lines are represented according to the completed unit form of paper folding is a triangle, and the the following figures, the development positions for the different paper folding processes, and the doubling-up cutting set for this study Groups 1 and 2 are in the same Prior to World War II the decoration in residential construction arrangement of figures are determined through modes could also be divided into square diagonal folding, shape with different positions. The results indicate that, housing or contemporary Japanese colonial period paper folding. As shown in (Figure 2), the radiation figure, parallel folding, and representations of other paper folding while the unfolded figures of paper folding Groups 1 and 2 architecture in Taiwan, and the traditional furniture it can be obviously seen that 8 folds are symmetrically modes, to generate the different positions of shaping and the have ✳-shaped folding lines, the final completed unfolded decoration, all had this type of colored Japanese tile. Most generated by using the central point of the paper; the shaping arrangement of papercutting. figure has different positions of shaping arrangements, as of these ceramic tiles were majolica produced by Japanese unfolded shape arrangement of the cut figures is radioactive, The order of shaping is generated in the arrangement to the set cutting positions are different. companies and have the “Made in Japan” mark on back, and the arrangement of their shaping regularly tends to be show the shaping activity of basic symmetrical forms, as allowing us to know their place of origin. On the front was circular [3]. the folding steps of paper folding are different in engraved the companies name or its trademark. papercutting. The representations of the shaping activity can Traditional architecture built in Kinmen during the be divided into three representations, as shown in (Figure 1930’s, or private residences built by remittances from 4). Kinmen compatriots generally most often use primarily 15 centimeter majolica tile to decorate their walls. These bright color tiles are extremely durable and will not fade despite Figure 2. Representation of Aesthetic Form of Papercutting Figure 5. The Groups 1 and 2 Arrangement relation of shaping Creation [4] patterns between folding and cutting of papercutting wind, sun and rain. In addition, each tile is its own graphic

4 Journal of the Science of Design Vol. xx No. x 20xx Journal of the Science of Design Vol. xx No. x 20xx 5 Journal of the Science of Design Vol. 2 No. 1 2018 41 The shaping arrangement of Group 1 is uniformly shaping arrangement for cutting, and if the position of cut distributed symmetrically. The shaping cut represents shaping is exchanged, the arrangement position of the re-cut triangular and diamond forms. The shaping of the triangle is shaping of the unfolded figure after cutting will change. distributed at four directions of the outer frame, while that 3. 2. Analysis of the shaping form of Majolica tile of the diamond is arranged in the middle. As a result of Judging from the shaping arrangement of single changing the cutting position of Group 2, its shaping Majolica tiles in the study samples, the analysis of this arrangement position is dramatically different. The shaping study can be divided into the following arrangement forms arrangement positions of the cut patterns are concentrated of shaping: in the center, while the positions of the arrangement forms A. Layout of a single shape: look like a surrounding square, where all cut shapes are Symmetrical type -- consists of absolute and relative distributed on the ✳ -shaped folding line. The symmetry. representations of shaping after cutting are square and 1) Absolute symmetry: It means shaping is required on diamond, respectively. the left and right, as well as above and below a central line, to be absolutely the same, while the color matching corresponding to the shaping is changeable. 2) Relative symmetry: The arrangement and construction are mainly required to have the same shaping, but the figures of some parts can slightly change; thus, the arrangement of the entire shaping maintains

Figure 6. The Groups 3 and 4 Arrangement relation of shaping symmetry. patterns between folding and cutting of papercutting

The steps of paper folding for Groups 3 and 4 are the same: a square is folded twice in parallel and then, diagonally once. The final form unit of the completed paper fold is triangular, the cutting set is in the same shape, but with a different position, the unfolded folding line figure is the same, and represents the diamond and cruciform (middle) folding lines, while the shaping arrangement Figure 7. Layout of a Single Shape: a. Absolute Symmetry position, as obtained after cutting, is in a different position. b. Relative Symmetry

The setting forms of Groups 3 and 4 are designed to be B. Layout of combined shapes: compared with the shaping forms and shaping arrangement 1) Vertical type -- shapes are arranged from bottom to positions of Groups 1 and 2, and the completed unit form top within a scope suitable for the arrangement. and cutting position of the paper folding of Group 2 are set 2) Radioactive type -- shapes are laid out towards the to be the same. surrounding areas by centering on one central point Judging from the comparison between the unfolded and feature radioactive arrangement. figures of Groups 1 and 3, the represented folding line figures are different, as the steps of paper folding are different. However, the shaping arrangement position and figure form after cutting are the same. The unfolded figure and shaping arrangement positions after cutting of Groups 2 and 4 are different: it is found that the shaping arrangement positions cut inside had obviously changed, and the positions of all cut figures of Group 2 correspond to the folding lines. However, the folding lines do not traverse all unit forms cut of the remaining three groups 1, 3, and 4.

Thus, based on these comparisons, it can be definitely known that folding lines affect all the positions of the Figure 8. Layout of Radioactive Combination of Single Majolica Tiles

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42 Journal of the Science of Design Vol. 2 No. 1 2018 The shaping arrangement of Group 1 is uniformly shaping arrangement for cutting, and if the position of cut This shaping arrangement form can be based on one distributed symmetrically. The shaping cut represents shaping is exchanged, the arrangement position of the re-cut square, and the arrangement of shaping is achieved with the triangular and diamond forms. The shaping of the triangle is shaping of the unfolded figure after cutting will change. ✳-shaped or #-shaped grids on the square. The structural distributed at four directions of the outer frame, while that 3. 2. Analysis of the shaping form of Majolica tile representations of the shaping in the grids are evenly of the diamond is arranged in the middle. As a result of Judging from the shaping arrangement of single distributed to indicate the balance of the arrangement of the changing the cutting position of Group 2, its shaping Majolica tiles in the study samples, the analysis of this shaping. This balancing mode can result in the image arrangement position is dramatically different. The shaping study can be divided into the following arrangement forms having a sense of stability to achieve balance. arrangement positions of the cut patterns are concentrated of shaping: 3.3. Analysis of the correspondence of papercutting in the center, while the positions of the arrangement forms A. Layout of a single shape: folding lines to the shaping pattern of a single Majolica look like a surrounding square, where all cut shapes are Symmetrical type -- consists of absolute and relative tile distributed on the ✳ -shaped folding line. The symmetry. Based on the study samples---25 separate Majolica tiles, representations of shaping after cutting are square and 1) Absolute symmetry: It means shaping is required on including the shaping of the pattern of each tile that diamond, respectively. the left and right, as well as above and below a central correspond to the process resulting in the most paper line, to be absolutely the same, while the color folding steps, the Paper Folding Steps figure, Display matching corresponding to the shaping is changeable. Figure of Shaping of Paper Folding of Tile and Display 2) Relative symmetry: The arrangement and construction Figure of Step Folding Lines of Tile are drawn, respectively, are mainly required to have the same shaping, but the and a total of 4 classes, 10 paper folding steps, and 9 Figure 10. The graphs of the 2nd and the 3rd papercutting steps correspond to those of Majolica tiles, and their tile figures of some parts can slightly change; thus, the folding line distribution modes are studied. Thus, the sample are NO.20 and NO.5 arrangement of the entire shaping maintains following study and analysis results are put forward. The paper folding processes of Steps (2) and (3) of Figure 6. The Groups 3 and 4 Arrangement relation of shaping symmetry. 1) There are three diagonal folding methods, and the patterns between folding and cutting of papercutting completed unit form of paper folding took on isosceles paper folding: the square is diagonally doubled up twice

triangles. and once, respectively. By comparing the paper folding The steps of paper folding for Groups 3 and 4 are the process to a single Majolica tile, it is found that, in Step (2) same: a square is folded twice in parallel and then, of paper folding, the square is doubled up twice diagonally, diagonally once. The final form unit of the completed paper and the X-shaped folding line indicates that the square is fold is triangular, the cutting set is in the same shape, but uniformly divided into left, right, upward, and downward with a different position, the unfolded folding line figure is areas. Through the folding process of step (2), the folding the same, and represents the diamond and cruciform lines of arrangement will be generated. After the (middle) folding lines, while the shaping arrangement Figure 7. Layout of a Single Shape: a. Absolute Symmetry comparative analysis about the samples of the tile, the study position, as obtained after cutting, is in a different position. b. Relative Symmetry discovers that the means of papercutting can achieve the

The setting forms of Groups 3 and 4 are designed to be same shaping graphic arrangement, as the following B. Layout of combined shapes: compared with the shaping forms and shaping arrangement Figure 9. The graph of the 1st papercutting steps corresponds to numbers show: NO.2, NO.7, NO.8, NO.9, NO.10, NO.11, 1) Vertical type -- shapes are arranged from bottom to that of the Majolica tiles, and its tile sample is NO.2 positions of Groups 1 and 2, and the completed unit form top within a scope suitable for the arrangement. NO.15, NO.19, and NO.20. and cutting position of the paper folding of Group 2 are set Step (3) of paper folding: the square is doubled up once 2) Radioactive type -- shapes are laid out towards the In Step (1) of paper folding, the square is doubled up to be the same. surrounding areas by centering on one central point three times diagonally, the final completed unit form of diagonally. The folding lines are presented as the Judging from the comparison between the unfolded and feature radioactive arrangement. paper folding took on isosceles triangles, its folding lines symmetrical arrangement of two isosceles triangles, and figures of Groups 1 and 3, the represented folding line are displayed as ✳, and the paper is divided into eight such symmetrical arrangement forms one square. This study figures are different, as the steps of paper folding are equal blocks centering on a central point. This distribution finds that this folding line form would result in the different. However, the shaping arrangement position and mode of folding lines corresponds to the pattern of a single arrangement shaping pattern of a single Majolica tile, which figure form after cutting are the same. The unfolded figure Majolica tile. This study finds that there are symmetrical only has the representation of a shaping arrangement with and shaping arrangement positions after cutting of Groups 2 figures in four directions, left, right, up, and down. Through diagonal reflection, and the arrangement representations of and 4 are different: it is found that the shaping arrangement the folding process of step (1), the folding lines of patterns do not have the left, right, upward, and downward positions cut inside had obviously changed, and the arrangement will be generated. After the comparative or radioactive position. Through the folding process of step positions of all cut figures of Group 2 correspond to the analysis about the samples of the tile, the study discovers (3), the folding lines of arrangement will be generated. folding lines. However, the folding lines do not traverse all that the means of papercutting can achieve the same After the comparative analysis about the samples of the tile, unit forms cut of the remaining three groups 1, 3, and 4. shaping graphic arrangement, as the following numbers the study discovers that the means of papercutting can

Thus, based on these comparisons, it can be definitely show: NO.2, NO.7, NO.8, NO.9, NO.10, NO.11, NO.15, achieve the same shaping graphic arrangement, as the known that folding lines affect all the positions of the Figure 8. Layout of Radioactive Combination of Single Majolica Tiles NO.19. following numbers show: NO.2, NO.5, NO.7, NO.8, NO.9,

6 Journal of the Science of Design Vol. xx No. x 20xx Journal of the Science of Design Vol. xx No. x 20xx 7 Journal of the Science of Design Vol. 2 No. 1 2018 43 NO.10, NO.11, NO.15, NO.19, and NO.20. extended on the left and right, as well as up and down. 2) There are two upward, downward, left, and right 3) There are two methods that require folding parallel parallel folding methods, and the final completed unit from left to right, from up to down, and then, form of paper folding takes on squares. diagonally. The final completed unit form of paper folding took on isosceles triangles.

Figure 11. The graph of the 4th papercutting steps corresponds to that of Majolica tiles, and its tile sample is NO.15 Figure 13. The graph of the 6th papercutting steps corresponds

to that of Majolica tiles, and its tile sample is NO.7 Step (4) of paper folding: the square is doubled up twice from up to down and from left to right, thus, cruciform Step (6) of paper folding: the square is doubled up folding lines appear. The square is uniformly divided into twice parallel from left to right and from up to down to four equal small squares. Through the folding process of form a smaller square, and then, doubled up diagonally step (4), the folding lines of arrangement will be generated. three times. The completed unit form of paper folding After the comparative analysis about the samples of the tile, took on isosceles triangles. The completed unfolded the study discovers that the means of papercutting can folding lines are displayed as ✳ and a radioactive achieve the same shaping graphic arrangement, as the shaping arrangement centered on a central point. This following numbers show: NO.2, NO.7, NO.8, NO.9, NO.10, display result of folding lines is the same as Step (1) of NO.11, NO.15, NO.19, and NO.20. paper folding, which also indicates that the arrangement positions of the shaping of patterns will be the same if the final display of the folding lines is the same, despite of the different steps of paper folding. Step (6) of paper folding corresponds to the same shaping arrangement tile sample as Step (1) of paper folding, as their folding lines are the same.

Figure 12. The graph of the 5th papercutting steps corresponds to that of Majolica tiles, and its tile sample is NO.12

Step (5) of paper folding: the rectangle is first doubled up from left to right twice, and then horizontally from up to down, thus, three cruciform folding lines appear (only one folding line appeared on the study sample, a single Majolica tile (NO.12). As the pattern of study sample (NO.12) is a Figure 14. The graph of the 7th papercutting steps corresponds to that of Majolica tiles, and its tile sample is NO.12 shape that is repeated and symmetrical on the left and right and up and down, it is an arrangement form of quadrilateral Step (7) of paper folding: the rectangle is doubled up continuity at the corresponding position. This study finds twice from left to right to form a smaller square, and then, that the shaping pattern of tile (NO.12) can be quickly doubled up once from up to down horizontally. The obtained by only completing the smallest symmetrical completed unit form of paper folding took on isosceles pattern of shaping in the steps of paper folding. This triangles. There are 4 folds, which is the largest in the paper arrangement form of shaping represents that the shaping folding steps of this study, and its folding lines are arrangement of quadrilateral continuity can be unlimitedly displayed as the arrangement of two ✳ . Regarding the

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44 Journal of the Science of Design Vol. 2 No. 1 2018 NO.10, NO.11, NO.15, NO.19, and NO.20. extended on the left and right, as well as up and down. shaping arrangement of 25 tiles, Steps (7) and (5) of paper bilateral symmetry and is horizontally arranged for 2) There are two upward, downward, left, and right 3) There are two methods that require folding parallel folding only correspond to (NO.12) study sample. From the continual shaping. Regarding the shaping arrangement that parallel folding methods, and the final completed unit from left to right, from up to down, and then, comparison between them, the folding lines are displayed corresponds to Step (10) of paper folding, 2 study samples form of paper folding takes on squares. diagonally. The final completed unit form of paper differently due to the diagonal doubling up of the square; are found to meet the condition (NO.12, NO.16). These two folding took on isosceles triangles. however, in papercutting, Step (7) can more quickly result study samples display figures with two-side continuity and in the shaping of the final pattern, thus, enhancing the speed repetition. of creation and conception. Analysis of the three paper folding steps finds that the 4) There are three left-to-right parallel folding methods, smallest symmetrical and repeated figure can be found first, and their final completed unit forms of paper folding and the corresponding arrangement of the shaping pattern are rectangles. could be obtained by horizontal paper folding, cutting, and unfolding. This form of shaping is arranged from left to right, and is an unlimited extension of two-side continuity.

Figure 11. The graph of the 4th papercutting steps corresponds to that of Majolica tiles, and its tile sample is NO.15 Table 2.The category of the graphic arrangement of the Figure 13. The graph of the 6th papercutting steps corresponds Majolica tile sample to that of Majolica tiles, and its tile sample is NO.7 Step (4) of paper folding: the square is doubled up twice 1. Absolute Symmetry of Shaping Arrangement from up to down and from left to right, thus, cruciform Step (6) of paper folding: the square is doubled up Longitudinal and Bilateral Diagonal folding lines appear. The square is uniformly divided into twice parallel from left to right and from up to down to Quantity bilateral symmetry symmetry symmetry four equal small squares. Through the folding process of form a smaller square, and then, doubled up diagonally NO.2, NO.7, NO.8, NO.9, NO.6, NO.12, 14 NO.10, NO.11, NO.15, NO.5 step (4), the folding lines of arrangement will be generated. three times. The completed unit form of paper folding NO.13, NO.16 After the comparative analysis about the samples of the tile, took on isosceles triangles. The completed unfolded NO.19, NO.20 the study discovers that the means of papercutting can folding lines are displayed as ✳ and a radioactive 2. Partly Absolute Symmetry of Shaping Arrangement Four-side symmetry Middle symmetry with achieve the same shaping graphic arrangement, as the shaping arrangement centered on a central point. This Quantity with middle asymmetry four-side asymmetry following numbers show: NO.2, NO.7, NO.8, NO.9, NO.10, display result of folding lines is the same as Step (1) of NO.1, NO.3, NO.4, NO.22 NO.11, NO.15, NO.19, and NO.20. paper folding, which also indicates that the arrangement NO.21, NO.24 positions of the shaping of patterns will be the same if 10 Bilateral symmetry Middle symmetry with the final display of the folding lines is the same, despite with middle asymmetry four-side asymmetry of the different steps of paper folding. Step (6) of paper NO.14, NO.18, NO.25 NO.17 folding corresponds to the same shaping arrangement tile 3. Relative Symmetry of Shaping Arrangement sample as Step (1) of paper folding, as their folding lines Quantity 1 NO.23 are the same. Judging from (Table 2) above, regarding the shaping arrangement modes of tiles divided into three categories, Figure 12. The graph of the 5th papercutting steps corresponds the first one is the absolute symmetry of the shaping to that of Majolica tiles, and its tile sample is NO.12 Figure 15. The graphs of the 8th, 9th or 10th papercutting steps arrangement of tile, which is further divided into bilateral

correspond to those of Majolica tiles, and their tile and longitudinal symmetry, bilateral symmetry, and Step (5) of paper folding: the rectangle is first doubled sample are NO.6, NO.13, and NO.16 diagonal symmetry; a total of 14 study samples have up from left to right twice, and then horizontally from up to The three paper folding steps (8, 9, 10) or shaping absolutely symmetrical shaping arrangement down, thus, three cruciform folding lines appear (only one arrangement modes are obviously constituted by representations, thus, the shaping activity featuring line and folding line appeared on the study sample, a single Majolica horizontally repetitive continuity, and is the representation point symmetry and parallel movement could be achieved tile (NO.12). As the pattern of study sample (NO.12) is a Figure 14. The graph of the 7th papercutting steps corresponds to that of Majolica tiles, and its tile sample is NO.12 of a sort of two-sided continuity. Step (8) of paper folding by paper cutting and folding. shape that is repeated and symmetrical on the left and right could correspond to shaping arrangement tile samples: The second one is the partly absolute symmetry of the and up and down, it is an arrangement form of quadrilateral Step (7) of paper folding: the rectangle is doubled up NO.2, NO.6, NO.7, NO.8, NO.9, NO.10, NO.11, NO.15, shaping arrangement. A total of four classes of study continuity at the corresponding position. This study finds twice from left to right to form a smaller square, and then, NO.19, and NO.20, with 10 in total. There is only one samples are found in this part, namely: four-side symmetry that the shaping pattern of tile (NO.12) can be quickly doubled up once from up to down horizontally. The shaping arrangement (NO.13) that corresponds to Step (9) with middle asymmetry, middle symmetry with four-side obtained by only completing the smallest symmetrical completed unit form of paper folding took on isosceles of paper folding, as the corresponding pattern is divided asymmetry, bilateral symmetry with middle asymmetry, and pattern of shaping in the steps of paper folding. This triangles. There are 4 folds, which is the largest in the paper into three equal parts, where the folding lines are displayed middle symmetry with bilateral asymmetry, with a total of arrangement form of shaping represents that the shaping folding steps of this study, and its folding lines are as three equal parts of a rectangle, which has a relation of ten corresponding study samples. These tiles could not be arrangement of quadrilateral continuity can be unlimitedly displayed as the arrangement of two ✳ . Regarding the

8 Journal of the Science of Design Vol. xx No. x 20xx Journal of the Science of Design Vol. xx No. x 20xx 9 Journal of the Science of Design Vol. 2 No. 1 2018 45 totally created by papercutting; however, as part of the mode, the shaping patterns of tiles can be correspondingly shaping arrangement had a symmetrical relation, it could be designed and created, and the shaping arrangement form of applied to the pattern design of a tile by the papercutting the figure can be rapidly created. From the 25 units of study creation mode. sample tiles, 10 paper folding steps were studied and The third one is the relative symmetry of the shaping analyzed from the shaping arrangements of 4 tiles and the arrangement. Only one study sample corresponds to relative display of nine folding lines. By virtue of the papercutting symmetry, the representation of its shaping arrangement is a creation mode, the repetition, symmetry, continuity, etc., in sort of balanced pattern, and no representations of bilateral the representations of the shaping of tile patterns can be or longitudinal symmetry occurred. This shaping rapidly formed. In the design of traditional tile patterns, arrangement form could not be designed or conceived by artisans inherit skills through mentorship or learn from the papercutting creation mode, since absolute symmetry is others’ experiences for creation. generated by this method. In current tile designs, creators usually consider the basic shaping principles to complete their shaping 4. Conclusion arrangement designs for tile figures. Design creation, With the papercutting creation mode, this study used 25 conception, and drawing requires a long time. This study Majolica tiles for analysis. It also conducted paper folding found that the shaping arrangement result can be quickly and cutting that corresponded to the shaping arrangement achieved by virtue of the papercutting creation mode, which forms of Majolica tiles. With the steps of paper folding and has become one of the creation and conception methods for papercutting, the final completed unit forms of paper designers to design tile figures or other graphic shaping. folding were found, and the cutting results obtained. By virtue of the folding and cutting creation modes of According to the papercutting creation mode, this study papercutting, materials can be economically and obtained the regularity and logics of the shaping conveniently obtained. In addition, creations and designs arrangements of Majolica tiles. Based on the analysis are diversified and their conception is rapid. With regard to results, the proofs to this study can be provided. The study the technical aspect of creation, operations can be carried results are described below: out without skilled drawing techniques. This creation and 1) Steps of paper folding and confirmation of the conception mode is quite suitable for the beginners of basic relation between folding lines and shaping shaping for graphic construction, and can be taken as a arrangements after cutting guide for learning the design and creation methods of basic In this study, under the circumstance of paper folding, graphic shaping to effectively improve creation extensions two types of steps for paper folding were developed in a in the design of shaping arrangements, as well as by the limited manner, and the cutting form patterns of the two creators of relevant graphic basics. types of steps led to four groups of papercutting creations. The representations of the final unfolded figures of the four References groups of papercutting can be obviously compared and [1] Miao, H. C., Condensing Time and Light into Ceramic analyzed. This study found that the completed unit forms of - Old Tiles from Taiwan and the Netherlands, Taipei: paper folding are the same; while the unfolded figure of a Taipei County Yingge Ceramics Museum, 112-121, completed papercutting may not be the same. If the final 2003 (in Chinese) completed unit forms of paper folding and pattern cuts are [2] Naomi, A., Paper: Basic design, art, and design, Taipei: the same, different shaping arrangements can occur, even if New Image Publisher, 2007 (in Chinese) the folding lines displayed are the same. This study also [3] Chen, P. Y., ’s folk paper-cutting, Taipei: Woolin found that the steps of paper folding can affect the shaping Publisher, 1987 (in Chinese) arrangement result of paper cutting. This is because [4] Chan, K., Learning paper-cutting is so simple, different symmetrical positions can be found in the paper Shenyang: Liaoning Science and Technology folding due to the folding modes of the square, resulting in Publishing House, 2012 (in Chinese) different folding lines on the inner layer of the folded paper. [5] Yeh, K. S., The fundamental structure of graphic design, 2) Correspondence between papercutting creation Taipei: Yi Fong Tang Publisher, 1999 (in Chinese) mode and arrangement of shaping patterns of tile [6] Chiang, K. W., Paper-cutting skills, Tainan: Tafu This study found that with the papercutting creation Bookstore, 2007 (in Chinese)

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