A Study On Surface Planarizartion Of Hexagonal Grid

With development of technology and aesthetic standard,more and more architecture of complex form has appeared in public vision.As an important design language,curved surface is accepted by architects and widely used in design.The geometrical properties of curved architectural surface are far more complicated than the properties of“square boxes”under the traditional orthogonal system.Many problems such as non-standard components,installation and positioning,and construction costs generated by curved surfaces need to be optimized and solved.The planarizartion of surface is a common method for the optimization of architectural surface.It uses flat panel to fit the original surface under the premise of meeting the design requirements,in order to achieve low cost,high efficiency of production and construction optimization purposes.In the general workflow,the designer will kick the problem to the curtain wall design company,which will weaken the designer’s control over the surface form construction to some extent.The generation of a digital model that is close to reality during the design process has a significant bearing on the actual construction of curved surfaces.This article starts with the background of digital design and construction,architectural geometry,and building industrialization.First,I study domestic and foreign related literature,and summarize the methods of planarization from triangle,quadrilateral,and hexagonal grid;Secondly,I summarize the tools that can realize the planarization reconstruction in Rhinoceros platform,the popular digital design software,and comparing the characteristics of different tools;With practical examples,the application of triangular,quadrilateral and hexagonal flat plate in current practice is demonstrated.Because there are few hexagonal planarization results in the application,I use this as a starting point.Based on Rhinoceros and Grasshopper platform,a planar hexagon reconstruction algorithm based on the tangent plane method is proposed,and two reconstruction algorithms of non-continuous planar hexagons are proposed as a supplement.Afterwards,experiments were performed on the algorithm using different types of surfaces,and satisfactory results were obtained.Finally,three real cases are simulated using the different algorithm.This study provides an intuitive and fast algorithm for surface planarization reconstruction, freeing from the difficulties of overly complex mathematical optimization. In the designing phase of thecurved surface architecture, the designer can control the construction result of the project, reducethe gap between the virtual model and the actual construction, and bring about reasonable and beautiful architectural forms. It is of great significance for designers to understand themathematical rules behind surface planarization optimization, to improve thsurface geometry properties and to enhance the control of the surface in the modeling phase.