Reciprocal frame structures made easy

Abstract

Figure 1: A large reciprocal frame (RF) AbstractA reciprocal frame (RF) is a self-supported three-dimensional structure made up of three or more sloping rods, which form a closed circuit, namely an RF-unit. Large RF-structures built as complex grillages of one or a few similar RF-units have an intrinsic beauty derived from their inherent self-similar and highly symmetric patterns. Designing RF-structures that span over large domains is an intricate and complex task. In this paper, we present an interactive computational tool for designing RF-structures over a 3D guiding surface, focusing on the aesthetic aspect of the design.There are three key contributions in this work. First, we draw an analogy between RF-structures and plane tiling with regular polygons, and develop a computational scheme to generate coherent RF-tessellations from simple grammar rules. Second, we employ a conformal mapping to lift the 2D tessellation over a 3D guiding surface, allowing a real-time preview and efficient exploration of wide ranges of RF design parameters. Third, we devise an optimization method to guarantee the collinearity of contact joints along each rod, while preserving the geometric properties of the RF-structure. Our tool not only supports the design of wide variety of RF pattern classes and their variations, but also allows preview and refinement through interactive controls.

An Interactive Computational Design Tool for Large Reciprocal Frame Structures

“…Our tool supports a wide variety of RF patterns and their variations, and it allows users to design RF-structures over guiding surfaces of many different shapes. Figure 6 shows some new RF-structures that we have not presented in (Song et al 2013): (a) CYLINDER with a 4-rod RF pattern, (b) HEMISPHERE with the bug-shaped RF pattern, (c) HYPERBOLOID with a 6-rod RF pattern, (d) TORUS Fig. 5 Procedure of using our tool to design a large 3D RF-structure.…”

“…This paper supplements (Song et al 2013) and details our interactive computational tool for RF designs with the followings: the implementation detail of our software tool; the procedure of using its user interface; new results of RF-structures derived from our tool; and a preliminary study of using our tool to create an RF-structure.…”

“…3a, b). So after a design is done, we can apply the optimization toolbox in RF Creator, which is the two-stage optimization method described in (Song et al 2013), to solve for the rods positions in 3D so that we can ensure collinear rods contacts (see Fig. 3c), as well as preserve the RF pattern against distortion.…”

“…Our interactive tool (Song et al 2013) for designing RF-structures has the following three key contributions: (1) it develops coherent 2D RF-tessellations by connecting RF-structures and plane tiling; (2) it lifts the 2D RF-tessellation to 3D over a guiding surface and forms an approximated RF-structure by conformal mapping for interactive preview; and (3) since conformal mapping cannot ensure collinear contact joints along each rod, we devise further a novel optimization model to ensure collinear contacts while preserving the geometric properties of RFstructures. Please refer to (Song et al 2013) for details.…”

Real-Time Deformation of Constrained Meshes Using GPU

“…Recently, computational design shape exploration tools have also been proposed for other types of architecture, such as reciprocal frame structures [21] and building layouts [1]. As these problems require other representations than polygonal meshes, they cannot be handled by our method.…”