DIGITAL GENERATION OF CHINESE ICE-RAY LAT- TICE DESIGNS

Transcription

1 S. Chien, S. Choo, M. A. Schnabel, W. Nakapan, M. J. Kim, S. Roudavski (eds.), Living Systems and Micro-Utopias: Towards Continuous Designing, Proceedings of the 21st International Conference of the Association for Computer-Aided Architectural Design Research in Asia CAADRIA 2016, , The Association for Computer-Aided Architectural Design Research in Asia (CAADRIA), Hong Kong. DIGITAL GENERATION OF CHINESE ICE-RAY LAT- TICE DESIGNS GUOHUA JI Nanjing University, Nanjing, China 1. Introduction Abstract. Being a rich source of geometric forms, Chinese lattice designs have interested some scholars. With shape grammar and algorithmic approaches, the generation of Chinese lattice designs has been achieved except for that of irregular interdependently structured iceray designs. This paper introduced an algorithmic approach to solve the problem. The algorithm includes crack-track presetting, cracktrack cutting, crack correcting, and bad shape disposing, realized by programming with Grasshopper VB script component. Keywords. Ice-ray; algorithm; designs; generation. In his book A Grammar of Chinese Lattice, Daniel Sheets Dye collected over 1200 Chinese lattice designs and catalogued them into 26 types. Most of the designs have a clearly regular structure except the rustic ice-ray designs, which look sophisticated and mysteriously diversified. The creation of iceray designs has been depending on the skill and aesthetic sensibility of the craftsman. Its development shows a high degree of artistic progress. It is the most careful of lattice design, a genus that is distinct and distinctive. (Dye, 1949) Being a rich source of geometric forms, Chinese lattice designs have interested some scholars. Early in the 1970s, George Stiny introduced shape grammar to generate traditional Chinese lattice designs. Stiny s grammar (Stiny, 1977; 2016) is effective in generating regular patterns. Recently, Lee and Tiong (2013) presented an algorithmic approach of generating Chinese lattice designs by simple procedures, not including ice-ray designs. To generate irregular ice-ray designs, Stiny (1977) defined parametric shape grammar. With a few of rules, his grammar can create a serious of

2 86 G. H. JI beautiful ice-ray patterns, as Figure1 shows. Stiny s ice-ray grammar was expanded by Liew Haldane and Mark Tapia. Haldane further categorized shape grammar rules for ice-ray designs into 4 types: 1) simple parametric grid shape grammar rules; 2) parametric shape grammar rules; 3) constrained parametric shape grammar rules; and 4) unknown shape grammar rules (Shape Grammars of Ice-ray Chinese Lattice Designs, 2005). He also developed an AutoLISP program as an implementation of his ice-ray grammar. Tapia (1992) followed the design intention that Stiny used to describe iceray designs, while defined new shape rules for the ease of computer implementation. Figure 1. Ice-ray designs generated by shape grammar (taken from Stiny, 2006, pp. 336, 339, 340). The above ice-ray grammars can generate regular ice-ray designs and some irregular ice-ray designs, but not all kind of ice-ray designs. Due to the iteration of shape grammar, the generated irregular ice-ray patterns, as Figure1 shows, all have certain hierarchical structure. In reality, we can see that most of ice-ray designs don t have a hierarchical structure, wholly or partly (Figure 2). Their bars are usually interdependent. Such designs belong to Haldane s unknown shape grammar rules and seem to defy any known rule.

3 DIGITAL GENERATION OF CHINESE ICE-RAY LATTICE DESIGNS 87 Figure 2. Interdependently structured ice-ray lattices. Dye (1949, p. 21) described the technique of ice-ray lattice construction as: he divides the whole area into large and equal light spots, and then subdivides until he reaches the size desires. This is followed by Stiny and similar studies. This way obviously doesn t work for interdependently structured ice-ray designs. Yuan et al (2011) noticed the shape at the bar joints, which they called human shape and thought as Chinese cultural intention embodied in ice-ray designs because the shape is similar to a Chinese character 人 which means human, as the key of ice-ray designs. They developed a grammar to generate interdependently structured ice-ray designs, starting from a central hexagon (or other polygon) and repeatedly adding a bar on existing ones with T shaped joints (Figure 3). This method is similar to the drafting process of the carpenters, as briefly introduced in the book Decoration of Chinese Traditional Building (Guo and Chen, 2005, 97-98). Lack of shape control means, this method may only work when the ice-ray pattern is not very complicated and composed by not many lines. Figure 3. Generating process of interdependently structured ice-ray by Yuan et al (2011).

4 88 G. H. JI For interdependently structured ice-ray designs, it seems not easy to generate with the departure from one or several simple shapes. An approach on generating overall layout seems necessary. This paper will introduce an algorithmic approach based on this idea, by which such designs can be achieved. 2. From synchronous cracks to T -shape joint patterns It is easy to find out that an ice-ray design is essentially composed of a set of lines which are T -shape connected. Literally, the Chinese name of iceray means ice crack. Inspired by this, the generation of such a T -shape joint pattern can be achieved with the following idea. Each line in the pattern is considered a crack, which breaks from a point and extends along a straight or curve line. When it meets another crack, the extension will stop at the meeting point. When every crack stops extending, a T -shape joint patterns is resulted. This process can be transformed to the following algorithm: Step 1: The pre-setting of crack tracks. This step sets the break points of a certain amount of cracks as well as the crack tracks. The tracks may be a set of straight of curve lines, and the break point of each crack may be at a certain position of the line, for instance the midpoint (Figure 4(a)). The outer or inner borders of the pattern can be treated as existing cracks, which will not extend but will obstruct the extension of other cracks. (a) Figure 4. Process of generating T -shape joint patterns. Step 2: The blocking-up of crack extensions. Every crack will stop it extension when it meet an early arrived crack or existing crack. This is equivalent to cutting out the segment of the crack tracks beyond the intersection (b) (c)

5 DIGITAL GENERATION OF CHINESE ICE-RAY LATTICE DESIGNS 89 point. For every crack track, we first calculate and record its intersection points with the existing cracks. Then we calculate the intersection point with other crack tracks. When the distance from the intersection to the break point of the crack track is larger than that from the intersection to the other crack track s break point, the intersection point is recorded. Here we assume that the cracks are synchronous, namely they break at the same time and their extending speeds are equal, so that the crack with shorter distance will extend to the intersection point earlier and block the extension of the crack with longer distance. (If asynchronous cracks are considered, we need to calculate the time instead of the distance.) After calculating and recording all the intersection points, each crack track is trimmed, keeping the section between the nearest intersection points on the two sides from its break point. Thus, a T -shape joint pattern is preliminarily obtained, as Figure 4(b) shows. Step 3: The correction of miscut lines. In Figure 4(b), we can see some of the crack endpoints are not on any other crack. The reason is that in the above step, some blocking cracks have been already blocked by other cracks before they extend to the intersection points, so that their effects of blocking don t actually occur. To correct this, we can treat the cracks of which both endpoints are on other cracks as existing cracks and repeat the above step, until all the joints are T -shaped. In most cases, the miscut crack tracks will not block each other, so that we simply extend the miscut cracks to the nearest crack. The result of this step is shown in Figure 4(c). 3. Shape control Due to the randomness of ice-ray designs, it is somehow inevitable to produce small or narrow polygon shapes in the T -shape joint pattern out of the above process. Such shapes are not suitable for a beautiful ice-ray design which normally consists of well-proportioned polygons. To avoid this, we may try to re-preset the crack tracks or let computer deal with this problem. Anyway, the judgment of ill-shaped polygon is needed. Theoretically, it is easy to distinguish such ill-shaped polygons by checking the angles of each polygon if we can extract all the polygons in the T -shape joint pattern. This needs an extra algorithm which is usually complicated. In this study we use a simpler algorithm to distinguish ill-shaped polygon by checking the relation of each couple of crack lines. 1) Find the start point to end point vectors of two cracks, and then calculate the angle between them. Reverse one of the vectors if the angle is larger than 90 degrees, and then get the bisector vector of the two vectors.

6 90 G. H. JI 2) For each crack, construct two planes through the start point and the end point and perpendicular to the bisector vector, and find the intersection points of the two planes with the other crack. If the intersection exists, calculate the distances from the start/end points to the intersection points respectively. The intersection situations differentiate the relations between two cracks as follows: If the two planes of any crack both intersect the other crack, then the relation between the two cracks will be one of the situations shown in Figure 5(a) or Figure 5(b). In this case the two intersection points are recorded. If both cracks have one plane intersecting the other crack, then the relation is among those shown in Figure 5(c), 5(d), and 5(e). It is easy to differentiate them, and the two intersection points are recorded. If the overall number of intersection points is zero, then the situation is that shown in Figure 5(f). (a) (b) (c) (d) (e) (f) Figure 5. Differentiating relations between two cracks based on plans perpendicular to bisector vector. 3) In the situations shown in Figure 5(a), 5(b) and 5(c), the two cracks will most likely be segments of a same polygon in the pattern and they may cause ill-shaped polygon. Two indicators are set to judge whether the polygon is ill-shaped. The first one, d, denotes the distance between the two intersection points for determining whether the area of the polygon is too small. The line connecting the two intersection points is divided into equal length segments, then a serious of planes though the points of division are set. Each plane has two intersection points with the two cracks. The distance between each two intersection points is found, and the average value of the distances dividing by the first indicator, the distance between the original two intersection points, is set as the second indicator r to judge whether the polygon is too narrow. If one of the two indicators values is smaller than the threshold value set by the user, the track of the shorter crack will be deleted and the program will be restart, until all the relations between each two cracks satisfy the demand. Figure 6 shows the results of the pre-set same as in Figure 4, under

7 DIGITAL GENERATION OF CHINESE ICE-RAY LATTICE DESIGNS 91 the control of the two indicators (6(a): d=0, r=0.2; 6(b): d=0, r=0.4; 6(c): d=a certain value, r=0.4). (a) (b) (c) Figure 6. Shape control results. 4. From T -shape joint patterns to ice-ray designs The algorithm except the pre-setting step is realized with VB scripting on Rhino Grasshopper, which can generate various T -shape joint patterns based on users different presetting of crack breakpoints and tracks with control on polygon shapes. Figure 7 shows some computational results based on randomly set crack tracks. Those T -shape joint patterns embody some attributes of traditional Chinese ice-ray designs, but they still look different in the aspect of selfsimilarity. Figure 7. Ice-ray designs based on randomly preset crack traces. The solution is in the presetting process. Observing various ice-ray designs, one may discover that each irregular ice-ray pattern has certain simi-

8 92 G. H. JI larity with certain regular ice-ray pattern. If the crack tracks are preset with a slightly transformed regular ice-ray pattern, then such similarity will be achieved. Figure 8 (left) shows one of the common regular grids of ice-ray designs. Based on it, the crack tracks is preset by randomly moving the lines with small distances, rotating with small angles (less than 15 degrees), and extending to a relatively long length. The crack break points are at the middle points of the original grid lines. The program can successfully generate a serious of designs similar to traditional ice-ray designs, one of which is shown in Figure 8 (right). Figure 9 shows another example out of a regular grid composed by hexagon. Figure 8. Ice-ray designs based on a frequently-used regular ice-ray grid. Figure 9. Ice-ray designs based on a regular grid composed by hexagons. Regular ice-ray patterns can be generated by the program as well. Based on an array of regular polygon, by locating each crack point at one end of each polygon segment and extending the other side, the program generates a regular ice-ray design. Based on it, slightly randomized ice-ray designs can be further achieved. This forms a two-step-generating process, as Figure 10 and 11 shows.

9 DIGITAL GENERATION OF CHINESE ICE-RAY LATTICE DESIGNS 93 Figure 10. Two-step generating of Ice-ray designs based on square array. Figure 11. Two-step generating of Ice-ray designs based on pentagon array. 5. Conclusion This paper presents an algorithm of T -shape joint patterns that consist of straight or curve lines, on plane of curve surface. The algorithm is based on the concept of cracks, as well as their occurrence and development. Based on regular ice-ray grids, it can generate irregular traditional Chinese ice-ray lattice designs with interdependent structure. With two-step generating process, such designs can also be got from array of regular polygons. Since the purpose is to generate Chinese ice-ray lattice designs, the principle of crack invoked in this study is very conceptual, and the algorithm is much simplified. By carefully studying cracking phenomena, other crack

10 94 G. H. JI patterns as those on earths and glasses may be generated with the same idea. This will be an interesting topic for the further study. References Dye, D. S.: 1949, A Grammar of Chinese Lattice, Harvard University Press, Cambridge, Mass. Guo, H. & Chen, J.: 2005, Gu Jianzhu Zhuangzhe (Decoration Of Chinese Traditional Building), Beijing: China Architecture & Building Press, Lee, S. Y., & Tiong, K. M.: 2013, Algorithmic generation of Chinese lattice designs. International Journal of Computer & Communication Engineering, 2(6), Shape Grammars of Ice-ray Chinese Lattice Designs : Available from: Open Source Repository < (accessed 15 May 2015). Stiny, G.: 1977, Ice-ray: A note on the Generation of Chinese Lattice Designs, Environment and Planning B, (4), Stiny, G.: 2006, Shape: Talking about Seeing and Doing, The MIT Press, Tapia, M.: 1992, Chinese lattice designs and parametric shape grammars. Visual Computer, 9(9), Yuan, X., Lee, J., & Wu, Y.: 2011, A new perspective to look at ice-ray grammar, Circuit Bending, Breaking and Mending: Proceedings of the 16th International Conference on Computer-Aided Architectural Design Research in Asia,