Rectangulations include packings of rectangles in two dimensions and packings of cuboids (3-rectangles) in three dimensions. Spatial layouts of this type are used in architectural and engineering design. In this paper we examine the spatial relations between the lines, planes, and volume...

Comment and discussion on the method proposed for generating the graphs for enumerating architectural arrangements by Baybars and Eastman (1980).

Structures of graph theory are compared with those of q-analysis and there are many similarities. The graph and simplicial complex defined by a relation are equivalent in terms of the information they represent, so that the choice between graph theory and <I>q</I>-analysis depends on which gives the...</i>

Representations are developed for kinematic chains in terms of the incidence between the component links both at pairs and at joints. Coplanar kinematic chains with only revolute pairs are considered in this paper.

A design world describes knowledge about possible designs. The characteristics of design worlds in engineering and architecture are compared. An implementation of three-dimensional shape grammars is outlined and the description of composite spatial relations which arise in generated shapes is...

Atkin's conjecture that a simplicial complex might be uniquely determined by its structured vectors is disproved by counterexample.

The generation algorithm for rectangular dissections given by Mitchell et al (1976) is shown not to be exhaustive, and a formal procedure is presented for the exhaustive generation of the class of 'nonaligned' rectangular dissections.

The subshape recognition problem for three-dimensional shapes under linear transformations is considered. The problem is analysed in a series of cases, some that provide a determinate number of solutions and others that have indeterminately many solutions. Procedures for its solution for general...

Shapes and shape grammars use algebras of subshapes in the description and generation of designs. Different types of boundary, including element boundaries, closure boundaries, and specially defined boundary shapes, are defined in shape algebra descriptions. These are compared to boundaries in...

Architectural plans whose walls lie along two perpendicular directions are represented by rectangular shapes. The rectangular shapes are classified according to the types of endpoints and the intersection of their component maximal lines. Shape grammars are used to construct members of the...