A method for implementing parametric shape grammars is presented. Subgraph detection is used to find subshapes. Parametric shapes are described by restricting topologies.

Generative design is emerging as an important approach for design exploration and design analysis in architectural practice. At the interior design scale, although many approaches exist, they do not meet many requirements for implementing generative design in practice. These requirements include the need for end-user accessible tools and skills, rapid execution, the use of standard inputs and outputs, and being scalable and reusable. In this paper, we describe a hybrid process that uses both space allocation and shape grammar algorithms to solve workplace and space planning interior design problems. Space allocation algorithms partition spaces according to program requirements while shape grammar automates the placement of inventory and the production of high-resolution drawings. We evaluate using three real world example projects how this hybrid approach meets the identified requirements of generative space planning in architectural practice.

Shape queries based on shape embedding under a given Euclidean, affine, or linear transformation are absent from current CAD systems. The only systems that have attempted to implement shape embedding are the shape grammar interpreters albeit with promising but inconclusive results. The work here identifies all possible 14 cases of shape embedding with respect to the number of available registration points, four for determinate cases and ten for indeterminate ones, and an approach is sketched to take on the complexities underlying the indeterminate cases. All visual calculations are done with shapes consisting of straight lines in the Euclidean plane within the algebra Uij for i = 1 the dimension of lines and j = 2 the dimension of space in which the lines are defined, transformed and combined. Aspects of interface design and integration to current work design workflows are deliberately left aside.