Mathematical Algorithms of Patterns for Free-Form Panels

Free-Form buildings provide a wide range of diverse and beautiful spaces supported by the development of digital technology. However, there are many difficulties and challenges in realizing free-form curved surfaces at the design and construction phase. Accordingly, panelizing of most free-form buildings is performed only in consideration of reducing the construction cost, or constructability. This panelizing process results in curved surfaces that are against the designer’s intention, and this makes it difficult for the designers to come up with the planned beauty. This may happen because the process of designing a free-form building differs from that of a specifically-formed building, and it is difficult to mathematically define the curved surfaces designed. Thus, the purpose of this study is to define mathematical algorithms of patterns for finish panels of free-form buildings based on the basic principles of building design forms such as repetition and gradation. The study results will be used to mathematically review various methods of dividing curved surfaces at the initial design phase of actual free-form building projects, as well as to automatically extract accurate production information and to respond to technical problems that may arise in the construction process.