中国传统建筑的建造, 是一个按照统一逻辑与规范, 通过制造模数化、标准化构件进行装配的过程。以清式建筑为例, 从总体尺寸到细部构件的设计、模数的确定, 都是在清代编写的《工程做法则例》的指导与规定下完成的 (图1) 。

　　 不过, 拟定的规范在实际建造中常常有灵活变化的空间^[1], 这个现象在中国西南地区更加明显, 并因此形成了西南地区传统建筑的地域性特色。这种灵活变通的现象, 虽是地域文化特色的结晶, 但也给传统的设计模式制造了很大困难:在模数化的标准下, 初始尺寸的改变会影响所有构件的尺寸与位置, 而如果没有计算出所有构件的尺寸与位置并进行可视化呈现, 初始尺寸影响下的最终效果是难以预知的。因此, 设计者常常在初始尺寸的调整中反复计算构件尺寸与位置。这不仅使得设计效率难以提升, 还让设计师额外付出极大的时间成本, 从而阻碍设计施工的精细化, 甚至让设计师在时间的压力下放弃地域性设计。

　　 与此同时, 中国传统建筑的设计与建造, 拥有运用参数化设计的潜力。因为随着参数化设计的发展, 开发能够由计算机自动生成设计方案的参数化模型, 从而减少建筑师将设计构思转化为设计方案的工作负担和时间延迟, 已成为参数化设计公认的优势之一^[2]。因此, 本文的目的在于, 以中国传统建筑的关键构造——翼角为中心, 根据《工程做法则例》中规定的构件尺寸、位置之间的联系, 再基于中国西南地区的地域性特色, 提出一个适用于中国西南地区的传统建筑翼角的自动生成算法, 以提升传统建筑的设计效率, 同时证明参数化设计对于发扬山地传统建筑地域性特色的促进作用。

　　 关于中国传统建筑的参数化设计及算法生形, 已经有一些学者做出了一定研究。例如, 王曦^[3]借助对《营造法式》的研究, 编制出了宋代官式建筑整体架构的生形算法;陈越^[4]基于《工程做法则例》编制了清代官式建筑整体架构与部分细部的生形算法。然而具体来看, 上述研究还有进一步深入的空间。

　　 上述研究主要集中在建筑整体木结构构架的自动生形算法上, 如开间、举架、铺作层的参数化生成。陈越对建筑细部的研究更多一些, 但主要讨论的是台阶、栏板和栏杆的做法。就翼角方面来看主要关注翼角的梁架结构, 翼角具体构件如椽条的定位与尺寸并未充分展开讨论。由于翼角是传统建筑精细化设计的关键部分之一, 对于翼角具体构造的研究缺失, 导致之前的研究成果在实际的精细化设计建造过程中的作用有限。

　　 之前的研究均遵循官式标准做法, 没有考虑实际建造中地域差异带来的设计建造的灵活性。这样也导致了研究的成果并不适应实际设计建造的特点, 限制了成果的实际应用。以“冲出”与“起翘”两个初始尺寸为例, 在官式做法中严格遵循“冲三翘四”规则, 即冲出、起翘的尺寸分别为椽径的三倍和四倍。而在中国西南地区, 冲出、起翘与椽径的比值常常会发生改变。

　　 本文依据《工程做法则例》 (以下简称则例) 与马炳坚所著的《中国古建筑木作营造技术》, 确定翼角各构件尺寸、位置与初始条件的数学关系;同时结合其他参考资料, 通过对上述关系的局部修改并引入部分变量, 把地域差异性纳入考量范围之中;最后, 通过Grasshopper平台把数学关系转化为翼角的生成算法, 并进行翼角的可视化呈现, 从而达到实现参数化设计的目的 (图2) 。

　　 中国传统木建筑的翼角构造中, 主要构件由下至上依次为角梁、枕头木、椽 (分为檐椽与飞椽) 、瓦、脊饰。中国不同地域的木建筑基本都包含以上构件。但是在有些方面, 中国西南地区的翼角构造与《则例》代表的北方官式做法、《营造法原》代表的江南做法差异都很大, 差别主要集中在布椽和起翘做法两个方面。

　　 在布椽方面, 北方官式做法为扇形布椽;而在西南地区, 翼角椽与正身椽相平行。椽条本身也没有官式做法中的撇折扭转变化。椽头下方辅以虾须来稳定椽条, 虾须前端与造角木前端用铁箍铆合在一起, 后尾钉在挑檐檩上, 起承托翼角椽的作用。而在起翘与冲出方面, 与《则例》的“冲三翘四”不同, 西南地区翼角的冲出与起翘都比官式做法更大, 且没有统一标准 (图3) 。

　　 图4揭示了在翼角构造中不同构件尺寸与位置之间多样化的数理关系:清式建筑中最基本的模数单位“斗口”确定了建筑中椽条的间距, 而建筑整体的步架、举架、冲出、起翘、出檐等尺寸, 在西南传统建筑中与斗口没有严格数量关系, 可以灵活变化椽条的参量。此外, 檐椽与飞椽的位置比例关系又是一个定值。因此, 受基本模数约束的量、可以自由变化的量、量与量之间的固定比值, 共同决定了每根椽条的尺寸与位置。

　　 如图5, 6是将数理关系整理成为算法之后在Grasshopper下的可视化呈现结果。可以看出, 绝大多数初始参数的影响范围都是非常大的, 任何一个初始条件的调整都会引起大范围的计算。这也从侧面反映了在人工计算状态下, 设计者所面临的工作之繁重。

　　 在翼角具体构造中, 以椽条定位与长度的计算最为复杂繁琐。因为在《则例》中并没有给出具体的计算公式, 仅有总体控制要求。而在当代具体实践中, 虽然有很多人提出了一些公式^[5~8], 但公式提出的背景与目的都是为了简化施工计算, 并非为了准确还原古代建造的导则。因此, 本节将以椽条的确定及算法作为阐述重点。

　　 安装椽条需要以下信息:飞椽的始末点、檐椽的始末点、各椽条的长度。在《则例》中, 椽条位点的控制要求如下:翼角飞椽的外端点首先要与正身部分的端点一起构成连续的曲线, 曲线在翼角上的端点需要与正身部分的端点构成一定的位置关系。飞椽与檐椽需要满足一定的空间位置关系, 而檐椽的起点是由其他参数给定的。上述几何关系的图示可见图7, 算法语言的可视化结果如图8所示, 用几何语言表述如下:

　　 给定点A, H, F与参数a, b

　　 上文提到, 西南地区的传统建筑在实际设计建造过程中, 与官式做法相比具有更大的灵活性。为了引入对地域性的考量, 算法中也引入了更多控制参数, 现以冲出、起翘为例。

　　 通过统计研究得知 (图9左) , 西南地区的冲出与起翘值的确定较官式做法相比更加自由。因此, 为了满足西南地区的实际设计需要, 算法中引入了边数、冲出、起翘等新的参量, 每当冲出、起翘的值被改变的时候, 整个翼角的所有构件的位置、尺寸都将自动更新, 并呈现在设计者的眼前。设计者可以在省去繁重计算的情况下, 对设计进行灵活便捷的调整 (图9右) 。

　　 本文提出了一个适用于中国西南地区的清式建筑翼角自动生成算法。与以往研究重点关注整体构架尺寸的自动推演相比, 本算法对于翼角具体构造的关注有以下特点:首先将以往关于翼角的文本研究整理成逻辑化的算法语言, 给翼角构造的解读带来了一个新的角度;其次, 将翼角具体构件位置、尺寸的计算过程自动化, 为今后中国传统建筑的精细化设计与施工带来了效率提升与错漏减少的可能性, 从而为改变当前传统建筑设计施工中质量粗糙、细节不到位的现状提供了一个可能的解决思路;最后, 本算法对于传统建筑地域性特色的考量, 也证明了地域性特色并不会因为参数化技术的应用而消失。与之相反的是, 参数化技术的应用反而可以促进地域化特色设计更好地应用到实际建造过程之中。

　　 As parametric design develops, reducing the time and labour of the design process by devel-oping a parametric model which can generate building models automatically, has been widely recognized as one of the main advantages of the parametric design. (S.Lyu et all, 2017)

　　 The design and construction process of traditional Chinese architecture has the potential to be applied by parametric design, because the construction of them is an assembling pro-cess, which follows specific rules and makes standardized modular components.For instance, traditional architecture in Qing Dynasty must be built under the guidance of Gongcheng Zuo-fa Zeli (Engineering Practice Rules, a.k.a.Zeli) , which is written in Qing Dynasty.

　　 However, rules written in the book may be slightly changed in actual practice (D.Yang, 2007) , which is widely seen in South West China, forming the regional features.These vari-ations are both part of regional culture and big trouble for design:Because of the feature of modularity, any change of the initial parameter will affect all the positions and the sizes of most components.In addition, the final visual effect can be evaluated only when all the calculations have been done.So designers have to repeat the entire calculation work for visual control.Such low efficiency with limited time can often lead to the poor quality of design and the absence of regional features.

　　 Therefore, focusing on upturned roof-ridge, the key component of traditional Chinese ar-chitecture, this paper aims to establish an automatic modelling algorithm of it, which can also suit for the requirements of South West China.By doing this, the paper try to find a method to increase design efficiency of traditional architecture, as well as try to prove that parametric design can also advocate the apply of the regional features in architecture.

　　 Previous research have proved the potential of parametric design in the general wooden structure design under the rules of Song Dynasty and Qing Dynasty. (X.Wang, 2017;Y.Chen, 2002) But further research need to be done.

　　 Previous research mainly focus on general wooden structure of traditional architecture, while Chen (2002) has gone a little further, extending the parametric method to the design of steps, railings, and the structure of upturned roof-ridge.However, some of the key parts of it, like the position and the size of rafter, are not thoroughly discussed.

　　 In addition, previous study only deals with the official rules of traditional architecture, omitting the variations in different parts of China, which result in the conflict to re-gional culture and practice.

　　 Based on Gongcheng Zuofa Zeli and Zhongguo gu jian zhu mu zuo ying zao ji shu (Construction Techniques of Chinese Traditional Wooden Structure) written by Bingjian Ma, the math corre-lations of the sizes and positions between every upturned roof-ridge component is summa-rized and initial algorithm is put forward.Then, by modifications of the correlations ac-cording to others’research, initial algorithm can be extended to the appliance of regional practice.Finally, the algorithm is developed in Grasshopper platform, enabling the visualization of upturned roof-ridge.

　　 A typical upturned roof-ridge mainly consists of Jiaoliang (cantilevered corner beam) , Zhen-toumu, Yanchuan (eave-rafter) , Feichuan (flying-rafter) and tilework.But in South West China, the layout and the rise of rafters are so different from what is ruled in official style written in Zeli.

　　 As for the layout of rafters, rafters are installed in a fan-shape in North China, while artisans in South West China prefer to lay them in parallel and support them with a batten called Xiaxu.When it comes to Chongchu and Qiqiao (the rise and extending of rafters) , South West China also shows its variability.

　　 5.1 IN GENERAL

　　 Figure 4 illustrates complex correlations between different components in upturned roof-ridge:Doukou (Bracket unit) , the basic unit in traditional architecture in Qing Dynasty, determines the space between rafters.And general parameters like Bujia (Panel) , Jujia, Chongchu, and Qiqiao, also affect the position and length of rafters indirectly.Along side fixed positioning ratios between two types of rafters, positions and lengths of every sin-gle rafter can be calculated.

　　 Moreover, the correlations above can be translated into algorithm, which is developed in Grasshopper.

　　 While specific formulas are not included in Zeli, nor previous relative research is aimed for the concise restoration of ancient practice (D.Wang, 2008;C.Li, 1998;Z.Li, 1996;J.Yan, 1989) .Geometry correlations are summarized by the authors and translated into formu-las below:

　　 Point A, H, F and parameter a, b is given

　　 As is mentioned above, in order to make the algorithm suitable for regional practice, more parameters need to be put into it.Chongchu and Qiqiao are taken as examples down below:

　　 The plot in Figure 5 shows the diversity of the actual value of Chongchu and Qiqiao in South West China practice.Therefore, the two parameters are integrated into the algorithm, achieving the goal that the rest of the component sizes and positions can automatically up-dated and visualized when parameters change.

　　 In this paper, an automatic modelling algorithm for the upturned roof-ridge of traditional Chinese architecture is developed.Compared to previous research, which focus on the auto-matic calculation of general wooden structure, this paper translate the paper research of upturned roof-ridge into algorithm which has logical and clear expression, providing a new perspective of understanding the structure of upturned roof-ridge.

　　 In addition, by making the complex calculation work automatic, the algorithm offer a new method for the design and construction process of traditional Chinese architecture to in-crease the efficiency and accuracy.It may be a possible solution to address the poor qual-ity of design and construction in many cases.

　　 Finally, by making the algorithm suitable for appliance of regional practice, this paper also proves that the appliance of parametric design will not eliminate regional features of architecture.Actually, it is parametric design that can help architects to integrate regional features to real constructions.