Interactive design exploration for constrained meshes

Abstract

In architectural design, surface shapes are commonly subject to geometric constraints imposed by material, fabrication or assembly. Rationalization algorithms can convert a freeform design into a form feasible for production, but often require design modifications that might not comply with the design intent. In addition, they only offer limited support for exploring alternative feasible shapes, due to the high complexity of the optimization algorithm.We address these shortcomings and present a computational framework for interactive shape exploration of discrete geometric structures in the context of freeform architectural design. Our method is formulated as a mesh optimization subject to shape constraints. Our formulation can enforce soft constraints and hard constraints at the same time, and handles equality constraints and inequality constraints in a unified way. We propose a novel numerical solver that splits the optimization into a sequence of simple subproblems that can be solved efficiently and accurately.Based on this algorithm, we develop a system that allows the user to explore designs satisfying geometric constraints. Our system offers full control over the exploration process, by providing direct access to the specification of the design space. At the same time, the complexity of the underlying optimization is hidden from the user, who communicates with the system through intuitive interfaces.

Real-Time Deformation of Constrained Meshes Using GPU

“…Besides [6] and [8], other handle-based deformation methods for constrained meshes have been developed in recent years. Zhao et al [26] extended the shape space exploration approach in [25], using curve handles for shape control.…”

“…Section 2 briefly presents the method in [8]. Section 3 gives an overview of the implementation of our system.…”

“…When run on a multi-core CPU, the method achieves interactive results for meshes with about 1K vertices, but still unable to handle large meshes. Recently, this method was extended in [8] to allow both hard and soft constraints. The proposed numerical solver consists of a series of simple subproblems similar to those in [6], enabling speedup from parallelism.…”

“…The proposed numerical solver consists of a series of simple subproblems similar to those in [6], enabling speedup from parallelism. In this paper, we present an implementation of the method in [8] on GPU using CUDA, which provides many more computational cores than CPU. By carefully optimizing for performance, our implementation allows realtime deformation of constrained meshes with up to 20K vertices and 20K constraints.…”

“…This usually leads to nonlinear constrained optimization problems, which are challenging to solve in real time. In this paper, we present a GPU-based shape manipulation tool for constrained meshes, using the parallelizable algorithm proposed in [8]. We discuss the main challenges and solutions for the GPU implementation, and provide timing comparison against a CPU implementation of the algorithm.…”