Performative Surfaces: Generating complex geometries using planar flow patterns

This research explains the development process of a design tool that can construct complex surface geometries using only two-dimensional plan drawings. The intention behind this tool is to address certain complex behavior of surface geometries such as hydrological characteristics. This paper briefly explains the historic and mathematic description of surface data structures, according to Cayley, Maxwell and Morse. This is followed by a brief introduction of the surface network/critical graph extraction technique in GIS. Additionally, the algorithm of contour extraction from asimple critical graph to reconstruct a surface is explained. In the final section the lessons learnedfrom the previous sections are used to develop algorithms for a tool which uses only plan drawings to construct complex surfaces. Three algorithms are explained in the final section among which the third one is considered to be the most complete and promising approach. Therefore,some design examples are presented to show the flexibility of the tool. At the end, this paper provides suggestions and discussions to reflect further ideas in order to improve the tool in future.