No abstract

No abstract

Embedding parts is a key problem in computing when dealing with continuous matter such as shapes rather than discrete matter such as symbols. For computing part relations such as embedding, a technical framework that uses weighted shapes is introduced and implemented. In the proposed framework, for any given two-dimensional shape, the entire canvas is defined as a weighted shape and serves as a registration mark in detecting embedded parts. The approach treats shapes as perceived wholes rather than composed and eliminates the technical distinction between shape categories such as line, curve, or plane. The implementation is shown for two-dimensional shapes but is extendable to three dimensions. As demonstrated on a Seljuk geometric pattern, the framework allows for embedding multiple and various perceived wholes, thus exploring emerging shapes and shape relations to be used for analysis and synthesis in design.

ResearchV Vi i i Vis su ua al al l S Sc ch he em ma as s: : P Pr ra ag gm ma at ti ic cs s o of f D De es si ig gn n L Le ea ar rn ni in ng g i in n F Fo ou un nd da at ti io on ns s S St tu ud di io os s A Ab bs st tr ra ac ct t. . Visual schemas are prequels to shape rules in formalizing the pedagogical discussions in foundational design studios.

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.