Embedding Shapes without Predefined Parts

Abstract

For a practical computer implementation of part embedding in shapes that is also true to their continuous character and the shape grammar formalism, shapes and their boundaries are handled together in composite shape and label algebras. Temporary representations of shapes, termed ‘overcomplete graphs’, comprise boundary elements of shapes and how they are assembled, and are utilized in a two-phase algorithm that systematically searches for embedded parts. The associated implementation is developed to receive user-defined constraints for an interactive search. In particular, the user-defined reference shape extends the search to nondeterministic cases.

Embedding parts in shape grammars using a parallel particle swarm optimization method on graphics processing units

“…Although each one uses different representations for shapes and different approaches for part embeddings, they all treat shapes that contain straight lines, circular arcs, or free-form curves or all, equally such that the shape representations become invariant to constituting analytical forms. They either use some registration points as vertices to shape graphs to resolve structure and perform part matchings for graph edges (Keles et al, 2010; Grasl & Economou, 2013); use pixel-based representation and image processing algorithms (Jowers et al, 2010); use weighted representation of shapes and evolutionary optimization algorithms (Keles et al, 2012; Keles, 2015). In all these approaches, shapes are not treated as a composition of a set of pre-defined analytical forms but treated as continuous entities.…”

“…Keles et al (2010) represented shapes using over-complete graphs and determined part embeddings using the attributes of the graph nodes which define the geometric relations among the nodes in the spatial domain. Another graph-based solution is proposed by Grasl and Economou (2013) that supports emergent shape detection and parametric rule applications.…”

Analysis of shape grammar application as a tool for urban design

“…Generally speaking, the problem of recognition of embedded shapes represents one of the key challenges for practical shape grammar computer implementation, and this remains a current topic. Some of the more recent approaches to this problem can be seen in the works of Keles et al (2010;2012) and Jowers et al (2010). These approaches abandon the concept that shapes should be predefined as compositions of geometry such as points, lines, curves, or planes.…”

From topologies to shapes: parametric shape grammars implemented by graphs

“…Heisserman (1991;1994) uses boundary graphs to guarantee well-formed solids during the execution of his boundary solid grammars. Keles et al (2010) present the overcomplete graph as a tool to search for embedded shapes. Further, Grasl (2012) presented Grappa, an implementation of the Palladian grammar (Stiny and Mitchell, 1978) based on graph grammars.…”