Computing self-supporting surfaces by regular triangulation

Yang Liu, Hao Pan, John Snyder, Wenping Wang, Baining Guo
2013 ACM Transactions on Graphics  
Figure 1 : Left: self-supporting surfaces with unsupported (top) and supported (bottom) boundary constraints. Unsupported boundary vertices and their corresponding power cells are colored in orange. Top right: initial self-supporting mesh. Spikes appear due to extremely small reciprocal areas. Bottom right: applying our smoothing scheme (5 iterations) improves mesh quality. The power diagrams (black) show how power cell area is distributed more evenly. Abstract Masonry structures must be
more » ... ures must be compressively self-supporting; designing such surfaces forms an important topic in architecture as well as a challenging problem in geometric modeling. Under certain conditions, a surjective mapping exists between a power diagram, defined by a set of 2D vertices and associated weights, and the reciprocal diagram that characterizes the force diagram of a discrete self-supporting network. This observation lets us define a new and convenient parameterization for the space of self-supporting networks. Based on it and the discrete geometry of this design space, we present novel geometry processing methods including surface smoothing and remeshing which significantly reduce the magnitude of force densities and homogenize their distribution.
doi:10.1145/2461912.2461927 fatcat:pbdow7f2vjcqbilqonh3gnakwu