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本帖最后由 paperart 于 2012-4-14 09:37 编辑 3.第三章 设计大象 Elephant Design 设计大象 In the beginning—at least,according to some mythologies—there was the Elephant. And so it is with theelephant that we begin our foray into origami design. The elephant—the subjectof Georgeot’s exhibition—is one of the most common subjects for origami.Presumably, this is because it is so readily suggested. Almost any large shapewith a trunk is recognizable as an elephant. If the shape has four legs andlarge, floppy ears, so much the better. But all these features aren’t needed;in fact, it is possible to fold an elephant using a single fold, as Figure 3.1shows (designed by Dave Mitchell). 造物之初（至少据神话记载如此）就有了大象，那么就让我们用大象来开始我们折纸设计的首次尝试吧。大象（若尔若展览的主题）是折纸中最常见的主题之一。大概这是因为大象很容易被表现，只要有个类似象鼻的大体形状就可以辨认出是头大象。如果这个形状有四条腿和大点的松软的耳朵，那就更像了。但所有这些特征都不是必需的，实际上，只折一下就有可能折成大象，像图3.1那样（戴夫.米切尔设计）。 1. Begin with a sheet of writingpaper. Fold the upper right corner down along an edge. 1.拿张打印纸，将右上角沿着边折下来。 2. Finished One-Crease Elephant. 2.一折大象完成。 Figure 3.1. 图 3.1. Dave Mitchell’s One-CreaseElephant. 戴夫.米切尔的一折大象。 Do you see it? The elephant isfacing to the right. 看到了么？一头脸朝右侧的大象出来了。 Yes? Perhaps? This simple model—aboutas simple as you can get—illustrates one of the most important characteristicsof origami models: They simplify the subject. Nearly all origami design isrepresentational, but unlike, say, painting, the constraints of folding with nocuts make it nearly impossible to produce a truly accurate image of thesubject. Origami is, as origami artist and architect Peter Engel has noted, anart of suggestion. Or put another way, it is an art of abstraction. Thechallenge to the origami designer is to select an abstraction of the subjectthat can be realized in folded paper. 是？或许是？这个简单模型（简单得随手可得）是个典型事例，但它表明了折纸模型就是表现主题的最重要特征，也就是折纸简化了主题。差不多所有折纸设计都是具象的，但它不像语言、绘画，在不能剪切的约束下折纸几乎不可能对主题真实完美的再现。折纸艺术家、建筑师彼得.恩格尔指出：折纸是“一门暗示性的艺术。”换句话说，它是一门抽象的艺术。对于折纸设计的挑战就是选择主题的特征并用纸张折叠来实现。 You can also select a subject thatlends itself to abstraction. Elephants are also popular subjects for origamidesign because they offer a range of challenges. What features do you includein the design? Is it a spare representation relying on a few lines to suggest aform, or is it necessary to capture all of the features of the subject? Gettingthe head and trunk may be sufficient for some folders, while others will besatisfied with nothing less than tusks, tail, and toenails. A somewhat moredetailed elephant is shown in Figure 3.2. 你也能选择一个适合于抽象的主题，在折纸设计中，大象之所以流行是因为它提供了一系列挑战。在大象的设计里你应该把握哪些特点呢？是简洁的依赖几道线象征一下？还是必须抓住主题的所有特征呢？折几下弄出头和鼻子就足够了，如果再添上长牙、尾巴和脚趾甲会不会好点呢？图3.2就是这么一头细致点的大象。 Figure 3.2. 图3.2. Base crease pattern and finishedfolded model of my African Elephant. 我设计的非洲象的基本折痕展开图和成品。 These two designs illustrate therange of origami design: Every origami design falls somewhere along a continuumof complexity. Arguably, the one-crease elephant is the simplest possibleorigami elephant. But the complex elephant is almost assuredly not the mostcomplex elephant possible. Complexity in origami is an open-ended scale; thetitle of “most complex” origami design (for any subject) is always transitory. 这两头象说明了折纸设计的范围：每个折纸设计都会在复杂性序列中找到合适的位置。可以证实的是，一折大象是最简单的合理的纸折象，但最复杂的折纸大象却无法确定。折纸的复杂性是没有尽头的，那些名为“最复杂”的折纸设计（任意主题）只会是暂时的。 Furthermore, complexity carrieswith it a special burden. We do not denigrate the one-crease model for itsabstraction; indeed, its abstract nature is part of its elegance and charm. 此外，复杂性承载着它特殊的责任。但我们不能因为抽象就诋毁一折模型，它的抽象正是它的优雅和魅力所在。 But a complex model creates acertain level of expectation in the viewer: an expectation that the model willconvey a richer vision. The more folds we have in the model, the more we canreasonably expect from it. And thus, we must make every fold in the designcount for something in the end result if elegance is to be attained. 但从欣赏的角度来说，对一个复杂的模型总是有一定程度的期待，希望模型能够提供丰富的视觉效果。对模型的折叠越多，这种期望就会越趋于合理。因此，在保证优雅的前提下，我们必须使每次折叠都能对最终的成品奉献其价值。 Georgeot’s exhibition consisted of88 elephants ranging from simple to very complex indeed. But elephants, likerabbits, have a way of multiplying. Once he became known as “the origamielephant guy,” origami elephants continued to come his way. He wrote that hehad accumulated 155 different designs by the year 2000. Many folders have sentmore than one, up to eight different designs from a single artist. 实际上若尔若展览的八十八只大象也是按照从简单到复杂排列的。但大象就和兔子一样，有一个倍增的方式。当若尔若成了知名的“弄纸象那家伙”，折纸大象就一直在奔向他。据若尔若记载，到2000年他一共收到了一百五十五个不同的纸象设计。很多艺术家发的还不止一个，最多的给了他八个不同的设计。 If you were to pick any two ofGeorgeot’s elephants, you would find that they differ in many ways: One couldbe flat, the other three-dimensional; one in profile, one in front view. Theymight differ in the orientation of the paper relative to the model, in thenumber of appendages, or in what part of the paper those appendages come from.They may differ in the level of abstraction versus verisimilitude, incartoonism versus realism, even in the use of curved versus straight lines (andwhich lines are chosen). All of these features are decisions that the designermakes along the way, whether consciously or unconsciously. 如果随便挑两只若尔若的纸象，你会找到很多不同点：可能一个是平面的，另一个是三维的；一个是侧面，一个是正面。对照模型，可能发现它们所取纸张的方向各不相同，附件的数目，或附件来自于纸张的部位也有不同。不同之处还在于抽象的还是写实的，是卡通的还是现实的，是有弧度的还是直线的。不管有意还是无意，设计者们就是根据这些特点来制作模型的。 Of all the artistic criteria thatmay be applied to origami, one of the most important, yet elusive, is elegance.Elegance as it applies to origami is a concept not easily described. It impliesa sense of fitness, of economy of effort. In origami, an elegant fold is onewhose creases seem to go together, in which there is no wasted paper, whose linesare visually pleasing. Elegance cannot be easily quantified, but there is aproperty closely related to elegance that can: efficiency. While elegance is asubjective measure of the quality of a design, efficiency is an objectivemeasure. An efficient model is one in which all of the paper gets used forsomething; nothing is tucked out of the way. Inefficient models are those withunnecessary layers of paper. Such models are thick and bulky, often difficultto fold, and usually less aesthetically pleasing than a model withoutunnecessary layers of paper. 所有的艺术标准一样可以应用于折纸，最重要的一条，也是最难琢磨的，那就是“优雅”。对于折纸，优雅是个很难言传的概念。它蕴藏着一个恰到好处的感觉，精力的合理分配。一个优雅的折叠，折痕看起来很和谐，纸张分配的恰到好处，线条则赏心悦目。优雅无法被轻易量化，但有一个与优雅相关的特性可以量化：效率。可以说优雅是对一个设计的主观评价，那么效率则是客观的。一个高效的模型里，纸张的任意部分都有其用途，没有什么被藏匿。低效的模型则有些多余的纸层，看起来又厚又笨重，而且会很难折叠。从审美角度看，这样的模型通常不如没有多余纸层的模型使人愉悦。 The most efficient models are thelargest possible for a given sheet of paper. If you have folded two figuresfrom ten-inch squares of paper and one figure is three inches across and theother is two inches across, then the smaller figure must by necessity have morelayers of paper on average in any given flap. The smaller model will generallybe thicker; it will hold together less well; and it will show more edges, whichwill break up the lines of the model. In short, the less efficient a model is,the poorer its visual appeal. Thus, efficiency is an aesthetic goal as well asa mathematical goal. For a base with a fixed number of flaps, the mostefficient base is that base in which the flaps are as large as possible. 最有效率的模型是对特定纸张最为合理的设计。如果你用十英寸的纸折两个（一样形状的）作品，一个三英寸大小、另一个二英寸。可以断言，小的作品中对应纸翼的纸层的平均数肯定会大一些。小的模型通常会厚一些，不容易聚合，会看到更多的纸边，模型上的线条看起来也会很凌乱。简言之，低效的模型看起来没什么吸引力。因此，效率既是美学目标又是数学目标。对于纸翼数目确定的基底，纸翼在合理范围内最大的基底就是最有效率的基底。 The tools of origami design cannot(yet) directly address elegance, but they can address its close relative,efficiency, by quantifying what is possible and impossible and providingdirection for maximally efficient structures. To wield the tools of origamidesign, one must have some tools to start with. The way to build a set of toolsis to examine some examples of design and deconstruct the model, identifyingand isolating specific techniques. To get started and to illustrate some basicprinciples of origami design, let’s add three more elephants to the roster. 折纸设计工具（暂时还）不能直接确定优雅，但它可以找到优雅的近亲——效率，通过量化什么可能、什么不可能最终直接给出效率最大化的结构。为了掌握折纸设计工具，怎么也要有个开端。检验一套工具的方法是检验一些设计实例和解构模型，识别和分离特殊的技巧。作为开场，下面就例举一些折纸设计的基本原理，让我们在花名册里再增加三头大象吧。 3.1. Elephant Design 1 3.1.大象设计1 The first design shown in Figure3.3 is for an Elephant’s Head. It is very simple and takes only five creases. 第一个设计是如图3.3所示的一个象头。它非常简单只需要五个折痕。 This is very simple—it’s perhapsone step up from the One-Crease Elephant, although, you might note, it tookfive steps. Can you devise an elephant using exactly two creases? Exactlythree? 就这么简单，它可以说是对一折大象的升级，另外你可能已经注意——它只需要五个步骤。那么你能用两道精确的折痕设计出一头大象么？三道折痕呢？ 3.2. Elephant Design 2 3.2.大象设计2 On the scale of origami complexity,both the One-Crease Elephant and the Elephant’s Head fall into the “simple”category. But as we add more features to a model, it almost invariablyincreases in complexity. As an illustration, let’s take the same basic designas the Elephant’s Head and add a pair of tusks to it. 按照折纸复杂性的比例，一折大象和上面的象头都只能在“简单”级别上。但随着我们在模型上增加点特征，它的复杂性也会随之提升。举个例子，让我们来做个简单的设计——为那象头加上一对象牙。 The amount of folding increasedsubstantially, just to create two tiny points for tusks. But I also added a fewsteps to give definition to the ears (step 9). Why? Why not just leave the facea flat surface as we did in the previous model? Two reasons. In the firstElephant’s Head, the ears came almost for free—there were two flaps (thecorners of the square) available to work with. But in this design, we needed tocreate side flaps (in steps 8 and 9) to define the ears, which required morefolding. 只为了增加两个小角来做象牙，折叠的数量已经大体上成倍增长了。另外我还加了几步来定义耳朵（步骤9）。为什么呢？为什么不像前一个模型那样做一个平整的脸部呢？有两个原因，在第一个象头里耳朵差不多是随意得来的——正好有两个纸翼（方形的纸角）可以用。但这个设计里，我们必须建立侧面的纸翼来定义耳朵，因此需要额外的折叠。 There’s a second reason, however,which is a bit more subtle. There is an aesthetic balance that needs to bemaintained across an origami design. The tusks introduce some small, finefeatures into the model. The contrast between those fine features and thebroad, flat, featureless expanse of the face is jarring, so we introduced twofolds to break up the surface of the face a bit and bring some balance to thelines of the model. 第二个原因有一点微妙。那就是美感平衡必须在折纸设计中贯穿始终。象牙做得很小，整个模型就要突出这一精美的特征。宽的、平的、无特色的脸部和其对照就一点冲突，所以我们增加两个折叠将脸部来分出来一点，以此使得模型的线条变得平衡。 1. Begin with the colored side up.Fold and unfold along the vertical diagonal. Turn the paper over. 1.在纸的彩色面开始。沿着垂直对角线折后展开。翻转纸张。 2. Fold edges AC and BC in to lie along the center line DC. 2.折叠边AC与BC对齐中心线DC。 3. Fold corners A and B down sothat their outer edges are vertical. 3.向下折叠角A和B使它们的外部纸边与水平垂直。 4. Fold down about 1/3 of point D(the exact amount isn’t critical) and turn the model over. 4.将顶角D的（大约）三分之一向下折叠，然后翻转模型。 5. Finished Elephant’s Head. 5.完成象头。 Figure 3.3. Folding sequence for an Elephant’sHead. 图 3.3. 象头的折序图。 1. Begin with the colored side up.Fold and unfold along both diagonals. Turn the paper over. 1.纸的彩色面朝上开始。依照折图折后展开。翻转纸张。 2. Fold edges AC and BC in to liealong the center line DC and unfold. Repeat with edges AD and BD. 2.将边AC、BC折向中间与DC对齐。边AD、BD重复该步骤。 3. Fold rabbit ears from corners Aand B. 3.对角A、B做兔耳折。 4. Fold corners A and B to theoutside edges. 4.折叠角A、B到外纸边。 5. Fold corner D down so that it lieson an imaginary line running between points A and B. 5.向下折叠角D使其与点A、B之间的假设线对齐。 6. Fold corners A and B in half. Foldcorners E and F down (the exact amount isn’t critical). 6.二分角A、B。向下折叠角E、F（大约位置即可）。 7. Turn the model over. 7.翻转模型。 8. Pleat the front flap upward. Themountain fold will run from corner G to corner H. 8.前纸翼向上打褶。峰折线落在角D到角H上。 9. Pleat the sides of the head toform ears. 9.头部的两边打褶形成耳朵。 10. Finished Elephant’s Head. 10.大象头完成。 Figure 3.4. Folding sequence for the morecomplex Elephant’s Head. 图3.4. 略复杂的象头的折序图。 1. Begin with the colored side up.Fold and unfold along the diagonals. Turn the paper over. 1. 纸的彩色面朝上开始。依照折图折后展开。翻转纸张。 2. Fold and unfold. 2.折后展开。 3. Bring the four corners togetherat the bottom to make a Preliminary Fold. 3.使四个纸角全部到底部制作成序折基底。 4. Fold edges AD and CD in to thecenter line and unfold. Then fold point B down and unfold. 4.折纸边AD、CD对齐到中心线，展开。向下折叠点B，展开。 5. Petal-fold front and back tomake a Bird Base. 5.前后花瓣折做成鹤型基底。 6. Fold and unfold on the nearflap. Each crease lies directly over a folded edge. 6.在近纸翼折后展开。每道折痕直到折边结束。 7. Fold corner D down while pullingpoints A and C out to the sides; flatten. 7.向下折叠角D同时向外拉出点A、C到两侧；压平。 8. Turn the paper over. 8.翻转纸张。 9. Reverse-fold the two bottompoints out to the sides. 9.翻折两的底部的角到两侧。 10. Narrow the two points withvalley folds in front and behind. 10.通过前后谷折将两个角弄细。 11. Fold point E down. 11.向下折叠点E。 12. Fold point B down. 12. 向下折叠点B。 13. Fold the corners down and turnthe model over. 13.向下折叠纸角，翻转模型。 14. Curve the tusks. 14.弯曲象牙。 15. Finished Elephant’s Head. 15. 大象头完成。 Figure 3.5. Folding sequence for yet anotherElephant’s Head. 图3.5. 另一种象头的折序图。 3.3. Elephant Design 3 3.3.大象设计3 We can take another step up theladder of complexity. Now we’ll make the tusks a bit longer. 在复杂性的阶梯上，我们还能获得另一种提升方式。现在我们把象牙再弄长点儿。 These three models depict the samesubject, but with progressively greater anatomical accuracy (although theystill leave a lot to be desired—like a body). They are simple, but illustratesome basic principles of origami design that are worth identifying: Generally, the more long points a model has, the more complex itsfolding sequence must be. Generally, the more long points a model has, the smaller the finalmodel will be relative to the size of the square. 现在我们有了描绘同一题材的三个模型，而且结构渐进精确（虽然它们一直有所保留——例如身体）。它们虽然简单，但是作为折纸设计基本原理的例证还是有其价值的： 通常，一个模型的点距越长，它的折序就会越复杂； 通常，一个模型的点距越长，成品的尺寸相对于所用纸张就越小。 These principles were widely knownin the origami world of the 1960s and 1970s, but it was not until the 1980s and1990s that they could be quantified. Those two decades saw the appearance of anew type of origami, the “technical fold.” It is hard to define precisely whatconstitutes technical folding; technical folding tends to be fairly complex anddetailed, encompassing insects, crustaceans, and other point-ridden animals. Itis often geometric, as in box-pleated models and polyhedra. The earlypractitioners of what we call technical folding—Neal Elias, Max Hulme, KoshoUchiyama, and a handful of others—were joined by a host of other folders—Montroll, Engel, and myself in the U.S., Fujimoto, Maekawa, Kawahata, Yoshino,Kamiya, Meguro, and many others in Japan—an expansion of the art that continuestoday. In fact, technical folding has its own name in Japan: origami sekkei. Itis difficult to pin down a unique characteristic of a model that defines it asorigami sekkei, but I have a candidate criterion: A fold is a technical foldwhen its underlying structure shows clear evidence of intentional design. 这些原理早在十九世纪六十、七十年代就已在折纸界广为流传，但直到十九世纪八十、九十年代才被量化。在这中间出现了一种全新的划时代的折纸类型——艺术折纸。很难精确的定义艺术折纸的构成，艺术折纸倾向于更加复杂与精细，题材涉及昆虫、甲壳动物和其它顶点较多的动物。它经常是与几何学相关的，像箱式折叠（蛇腹折）模型和多面体。艺术折纸的先驱有——尼尔.伊莱亚斯、马科斯.胡尔默、内山兴正，其后一些其它种类折纸的顶尖人物加入了这一行列——美国有蒙特利尔、恩格尔还有我本人，其他更多的在日本，有藤本、前川、川畑、吉野、目黒，直到今天这一群体还在不断地增长。实际上，艺术折纸有其自己的日文称谓：“origami sekkei”（折纸设计）。虽然很难确定究竟具备哪些显著的特征才能称之为艺术折纸，但是我有一个候选标准：如果一个折纸作品的基础结构可以明显看出是有目的性的设计出来的，那么它就可以称为艺术折纸。 The first steps of design, however,do not require use of any specialized techniques or mathematical theorems.Anyone who can fold origami can design origami. In fact, if you folded one ofthe three elephant designs, you were calling upon your design skill. A sequenceof folding diagrams—no matter how detailed—can still only provide a set ofsamples of what is a continuous process. In following a folding sequence, thereader must interpolate; he must connect the steps in his mind to form acontinuous process. Depending on the amount of detail into which the steps arebroken down, this process can be easy, as in Figure 3.6, or it can bedifficult, as in Figure 3.7. 设计的第一步不需要任何专门的技巧或数学理论，能折纸就可以设计。事实上，如果你折了上面设计的三头大象，哪怕一个，你的设计技能就已经提升了。折序图（无论多详尽）只能提供一个连续过程的一系列片段。按照折序图，读者必须有所添加，必须将片段按照自己的想法联系起来变成一个连续的过程。把细节添加到被拆解的步骤中去，这个过程可能很容易，像图3.6那样，或者有点困难，试试图3.7。 A good origami diagrammer, balancingthe needs of brevity and clarity, strives to match the level of detail to thecomplexity of the fold and to the intended audience. In this book, I have aimedfor a middle ground, along the lines of Figure 3.8. 一个不错的折序图需要在简洁与细致中找到平衡，努力使其复杂程度与目标受众的理解能力相匹配。本书中，我做了一个折衷选择，就像图3.8中我所给出的那样。 When you begin following diagrams,you require each instruction to be broken down into the smallest possiblesteps. 当你开始按照折序图学习的话，需要注意一下文字说明，它有助于你将折图分解成更好理解的几个小步骤。 1. Begin with the colored side up.Fold and unfold along the diagonals. Turn the paper over. 1. 纸的彩色面朝上开始。依照折图折后展开。翻转纸张。 2. Fold and unfold. 2.折后展开。 3. Bring the four corners togetherat the bottom to make a Preliminary Fold. 3.使四个纸角全部到底部制作成序折基底。 4. Fold edges AD and CD in to thecenter line and unfold. Then fold point B down and unfold. 4.折纸边AD、CD对齐到中心线，展开。向下折叠点B，展开。 5. Petal-fold front and back to makea Bird Base. 5. 前后花瓣折做成鹤型基底。 6. The Bird Base. 6. 鹤型基底。 Figure 3.6. Detailed sequence for folding aBird Base. 图3.6. 鹤型基底的详细折序图。 As you gain experience in followingdiagrams, the jumps between steps become larger. Instead of seeing everyindividual crease, the creases start to come in groups of two or three. As wehave seen, the most common groups of creases have been given names: reversefolds, rabbit-ear folds, petal folds. More advanced folds may have groups of 10or 20 creases that must be all brought together at once, or several differentfolds must occur simultaneously, or not all creases may be visible in thediagram. Following such a sequence is even more a process of design. Followinga folding sequence is, in effect, resolving a series of small design problemsgoing from one configuration of the paper to the next. Designing an entirelynew model is the same task, merely scaled up. 随着你折图经验的积累，所遇到的折图里步骤之间的跳跃也会增大。每个步骤里不再是一条折痕，而是俩三个一组的出现。我们已经看过，这些常见的折叠组合都有其特定称谓：翻折、兔耳折、花瓣折。接着还会出现十几二十道折痕的组合需要一次完成，或者几个不同的折叠同时出现，或者并非所有折痕在折图中都能看到。按照这样的折图练习更接近一个设计的过程。它使你不断地分辨前后纸张结构一类的小型的设计问题。设计一个全新的模型也是同样的任务，只是规模更大一些。 1. Divide the square in half verticallyand horizontally with creases. Crease all angle bisectors at the corners, thenassemble using the creases shown. 1.用折痕在垂直方向与水平方向将纸张平分。在纸角做出所有角分线折痕，如图示聚拢所有折痕。 2. The Bird Base. 2.鹤型基底。 Figure 3.7. Compact sequence for folding a BirdBase. 图 3.7. 鹤型基底的简洁折序图。 1. Begin with a square with creaseddiagonals. Bring the four corners together at the bottom and flatten. 1.按照图示在纸张中做出折痕。使四个纸角全部到底部然后压平。 2. Petal-fold front and back. 2.前后花瓣折。 3. The Bird Base. 3.鹤型基底。 Figure 3.8. Intermediate sequence for folding aBird Base. 图 3.8. 鹤型基底的折衷折序图。 Origami design runs along acontinuous scale ranging from minor modification of an existing design to the“ground-up” creation of an entirely new model. Just as a beginning foldershould begin to fold simple models from diagrams, the beginning designer shouldchoose simple shapes to design. 折纸设计是一个循序渐进的过程，从对已有设计的小规模修改一直到将原有设计完全粉碎创造出一个全新的模型。就为一个折纸新手，应该先从按折序图折叠简单的模型开始，如果开始设计的话，就从一个简单的形状开始吧。 And now is as good a time as any tostart. The elephants in Figures 3.4 and 3.5 have colored tusks. Can you find away to alter each model so that the tusks become white as shown in Figure 3.9?(Hint: Turn a flap inside-out.) The first stage of origami design is to modifysomeone else’s work, as you can with the elephants. Origami design is, in largepart, built on the past. The origami designers of the present have created newtechniques, but in doing so, they used techniques of those anonymous Japanesefolders of history (as well as those of their contemporaries, of course). Itbehooves us to spend some time studying how prior generations of folders designedtheir models. 现在就有个开始设计的好时机。图3.4和图3.5的大象的象牙都是彩色的。你能够找到一种使象牙的颜色变成白色的方式么？就像图3.9那样。（小提示：纸翼内外变换。）折纸设计的第一阶段就是修改其他人的作品，像你改变象牙颜色这样。折纸设计很大程度上都是建立在原有的基础之上的，当代的折纸设计者们虽然创造了一些新的技巧，但即使这样，历史上无名的日本折纸者的技巧（当然，还包括同辈的技巧）仍在被使用。理所当然，我们也该花些时间来学习一下历代的折纸者们如何设计他们的模型。 Figure 3.9. Two variations on the Elephant’s Heads. 图 3.9. 大象头的两个变体。
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