The space layout of a reasonable modular building prototype is a time consuming and complex process. Many studies have optimised automatic spatial layouts based on spatial adjacency simulation. Although machine-produced plans satisfy the adjacency and area constraints, people still need further manual modifications to meet other spatially complex design requirements. Motivated by this, we provide a human–machine collaborative design workflow that simulates the spatial adjacency relationship based on physical models. Compared with previous works, our workflow enhances the automated space layout process by allowing designers to use environment anchors to make decisions in automatic layout iterations. A case study is proposed to demonstrate that the solution generated by our workflow can initially complete different customised design tasks. The workflow combines the advantages of the designer's decision-making experience in manual modelling with the machine's ability in rapid automated layout. In the future, it has the potential to be developed into a designer-machine collaboration tool for completing complex building design tasks.

No abstract

No abstract

No abstract

Cosmic expansion is an important concept in astronomy. For ease of understanding, astronomers generally draw an analogy between cosmic expansion and the expansion of a spherical surface in 3D space. This study theoretically and experimentally investigates the laws governing the motion of particles on the surface of a balloon during expansion. Firstly, the relevance of Hubble’s law to the movement of the surface particles is analyzed. The results of this analysis show that the receding velocity of a particle relative to another particle is proportional to the arc length between the two particles. Secondly, variation in the Hubble constant with time is examined and thirdly, the variation in arc length between two particles with time during balloon expansion is investigated. Finally, the peculiar motion of a small object on the surface of an expanding balloon is investigated. The experimental data are in good agreement with the results of the theoretical analysis. This comparison between cosmic expansion and the expansion of a balloon suggests that these two processes exhibit essential differences but that the expansion of a balloon can be regarded as an appropriate metaphor for cosmic expansion. The experiment described here requires only simple materials, making it convenient for the in-class exploration of cosmic expansion by middle-school students or junior undergraduates.