Abstract: Freeform buildings have higher geometric complexity than standard forms. A gap exists between design result and construction methods, resulting in high cost, many modifications, and low efficiency. The reconstruction of freeform architecture is an effective way to solve this problem. Despite this, existing reconstruction techniques demonstrate poor performance, limited applicability, and low success rates due to professional knowledge barriers and interruption of architectural operation processes. From an architectural perspective, discrete modeling and geometric iteration technologies were introduced from other fields. A set of staged freeform architectural reconstruction design methods aligned with freeform construction were proposed to help architects achieve high design efficiency and low construction costs for complicated buildings. 
　　Based on the Rhino&Grassshopper platform, core algorithms for two key planar reconstruction processes of curved surfaces (meshing and plane mesh generation) were explored. Later, a quadrangle planar reconstruction parameter freeform surface model was constructed. Finally, a numerical simulation was carried out to determine the application scope of different reconstruction methods.
　　(1) A reconstruction method for freeform architecture was developed to meet the requirements of architectural scheme design. The method was comprised of four steps: analysis of surface properties, discretization of curved surface, generation of target units, and evaluation & optimization. (2) A principal curvature meshing algorithm for planar reconstruction was developed by focusing on mesh parameterization technology and integrating more robust calculation of meshes, direction field smoothing, and meshing model extraction. (3) A planar mesh generation algorithm based on geometric iteration technology was developed, and an evaluation index system for planar reconstruction structures oriented to architectural curved surfaces was proposed. In addition, a multi-objective optimization process based on the third-party plugins Kangaroo and Octopus was built. (4) According to comparison with the mapping method and the guide line method, the proposed method is superior for high reconstruction efficiency, extensive universality, and good quality. It is applicable to reconstruction of freeform architectures targeting at planar construction.
　　(1) The surface reconstruction modeling technology based on discrete differentiation was introduced, which could increase pertinence of surface reconstruction modeling. (2) Several evaluation indexes aligned with surface reconstruction were proposed, which can guide architects in real-time modification of the reconstruction scheme. (3) The multi-objective optimization mechanism was introduced. This makes it easy for architects to adjust quickly and can also generate several optimization structures to meet expected design goals.
　　(1) It is necessary to verify the proposed method can be scaled to full-scale buildings and multi-layer curved surfaces under real and complicated construction conditions. (2) The reconstruction evaluation indexes must be further perfected, since they lack indexes related to material cost and processing time. (3) The reconstruction problem of architectural surface is closely related with structural performance. Future studies must employ collaborative design of space forms, structural forms, and construction efficiency.

Key words: freeform architecture, surface reconstruction, geometric algorithm, design and construction integration, design method, computational design

摘要： 自由曲面建筑相比标准形体更具几何复杂性，其设计结果与建造系统的脱节问题尤为突出，导致成本高、修改多和效率低的情况。从建筑学视角出发，借鉴并引入其他领域的离散建模与几何迭代技术，整合提出一套面向自由曲面建造的方案阶段建筑曲面重构形体设计方法。以自由曲面的四边形平面化重构形体实现为例，对所提方法中关键环节的几何算法进行具体阐述，并通过与常用方法的对比实验，证明上述方法具有重构效率高、通用性广、形体质量好等优势，由此归纳得到其建筑适用范围，为实现复杂建筑的设计高效率和建造低成本提供方法参考。

关键词: 自由曲面建筑, 曲面重构, 几何算法, 设计建造一体化, 设计方法, 计算性设计