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ItemShape Machine: shape embedding and rewriting in visual design(Georgia Institute of Technology, 2021-07-27) Hong, Tzu-Chieh KurtShape grammar interpreters have been studied for more than forty years addressing several areas of design research including architectural, engineering, and product design. At the core of all these implementations, the operation of embedding – the ability of a shape grammar interpreter to search for subshapes in a geometry model even if they are not explicitly encoded in the database of the system – resists a general solution. It is suggested here that beyond a seemingly long list of technological hurdles, the implementation of shape embedding, that is, the implementation of the mathematical concept of the “part relation” between two shapes, or equivalently, between two drawings, or between a shape and a design, is the single major obstacle to take on. This research identifies five challenges underlying the implementation of shape embedding and shape grammar interpreters at large: 1) complex entanglement of the calculations required for shape embedding and a shape grammar interpreter at large, with those required by a CAD system for modeling and modifying geometry; 2) accumulated errors caused by the modeling processes of CAD systems; 3) accumulated errors caused by the complex calculations required for the derivation of affine, and mostly, perspectival transformations; 4) limited support for indeterminate shape embedding; 5) low performance of the current shape embedding algorithms for models consisting of a large number of shapes. The dissertation aims to provide a comprehensive engineering solution to all these five challenges above. More specifically, the five contributions of the dissertation are: 1) a new architecture to separate the calculations required for the shape embedding and replacement (appropriately called here Shape Machine) vs. the calculations required by a CAD system for the selection, instantiation, transformation, and combination of shapes in CAD modeling; 2) a new modeling calibration system to ensure the effective translation of geometrical types of shapes to their maximal representations without cumulative calculating errors; 3) a new dual-mode system of the derivation of transformations for shape embedding, including a geometric approach next to the known algebraic one, to implement the shape embedding relation under the full spectrum of linear transformations without the accumulated errors caused by the current algorithms; 4) a new multi-step mechanism that resolves all cases of indeterminate embeddings for shapes having fewer registration points than those required for a shape embedding under a particular type of transformation; and 5) a new data representation for hyperplane intersections, the registration point signature, to allow for the effective calculation of shape embeddings for complex drawings consisting of a large number of shapes. All modules are integrated into a common computational framework to test the model for a particular type of shapes – the shapes consisting of lines in the Euclidean plane in the algebra U12.
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ItemThe Portman Variations: A Critical Approach to Entelechy I Mediated by Shape Machine(Georgia Institute of Technology, 2020-10-20) Ligler, Heather MichelleJohn Portman’s work is perplexing and polarizing. Characterized by his atria that captivate the popular imagination and his hybrid practice as architect-developer that redefined skylines throughout the world, but also ambivalently caricatured and dismissed for these same moves, the question of his impact remains blurry. This tension in Portman’s assessment has been described as paradoxical and in fact, a closer look at the scholarship on his work reinforces this as an ongoing condition – one that highlights the challenges of interpreting the work. Yet, Portman’s own imaginative account of his practice emphasizes another perspective. In reflections throughout his life, he referenced his 1964 house, Entelechy I, as the generator informing his entire corpus and the key design to understanding his architectural principles across all scales and programs. The research here takes on the productive myth of Entelechy I – and its presumed adaptable and repetitive logic – as the impetus to develop a shape grammar on the plan of the house. This grammar is then the basis for generating variations that address the transformation of spatial relationships in the house revisited for other design contexts. Significantly, this two-stage procedure is mechanically (and automatically) implemented in Shape Machine for Rhino, a new shape grammar interpreter developed at the Shape Computation Lab (SCL) in the School of Architecture, Georgia Institute of Technology. Subsequently, the implementation of the Entelechy grammar reproduces the design of the original house and a series of new designs too – here proposed as Portm-Inoes to systematically recontextualize the house as a postmodern reinvention of Corbusier’s Dom-Ino. In addition, the corresponding adaptation of parts of the grammar under different predicates yields transformation grammars that generate a series of plans at various scales to interpret Portman’s broader corpus of interior, hospitality, urban, and residential designs. The contributions of the dissertation are: a) a critical compilation of perspectives on John Portman encompassing various interpretations that have remained so far distinct including connections to the Aristotelian and Emersonian philosophical underpinnings of the work; b) a formal approach to interpret Entelechy I in an automated shape grammar; c) a series of implemented transformation grammars that further redescribe Portman’s architectural language in interior, hospitality, urban, and residential designs; d) an assessment of Portman’s work derived by correlating the predicates, transformations, and shape rules in the grammars with fundamental aspects of design including the use of Platonic geometries, self-similarity, figure-ground reversal, boundary ornamentation, offset forms, and their combinations; and e) the setup of a constructive cycle of design propositions and evaluations achieved in Shape Machine to mechanically execute line drawings in an automated environment.
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ItemThe venation lattice(Georgia Institute of Technology, 2020-08-06) Ferro, EmanuelNature offers an inexhaustible source of inspiration for design. Among the various lenses deployed to look at nature, symmetry continues to play one of the most profound ones that have continuously used in the description and interpretation of the study of natural form. This study takes on the five fundamental translational structures of the Euclidean plane, the five Dirichlet domains, and correlates them with motifs extracted front the vein architecture of leaf growth patterns, to propose: a) a particular class of designs characterized by planar translational structure; b) a formal specification of these designs in terms of a shape grammar, the venation lattice grammar; c) an automated implementation of the venation lattice grammar in the Shape Machine – the first general purpose shape grammar interpreter that can carry visually shape computations; and d) a series of digital fabrications of designs in the language. Implications pertain to the visual study of shape, the immediacy of working directly with shapes as opposed to a symbolic or discursive representation of shape in a programming language, and its automated computation in a visual interpreter are discussed throughout the work.