Shape Machine: shape embedding and rewriting in visual design
Hong, Tzu-Chieh Kurt
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Shape 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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