Minimal Surfaces through Skeletal Graphs

This research develops a computational design method and design interface that allows anyone to generate, explore and visualize minimal surfaces intuitively in real-time instead of having to manipulate mathematical expressions. This method generates a minimal surface in a 3D Euclidean space for any given two sets of curves, which represent the minimal surface medial graph. 

Most methods use mathematical expressions or computational physics simulation with mesh relaxation to generate minimal surfaces in 3D design space, which can be difficult to use when a high degree of formal control and articulation is needed. This newly developed approach uses skeletal graphs to generate, alter, and manipulate minimal surfaces intuitively, enabling their geometric adaptation to functional and program requirements. A skeletal graph of a minimal surface can be viewed as a curve resulting from the shrinking of a minimal surface along the direction of its normal vectors while avoiding any pinching off that would change the topology of the surface.