PhD Defense by Tzu-Chieh Kurt Hong

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  • Date/Time:
    • Wednesday June 30, 2021
      10:00 am - 12:00 pm
  • Location: Atlanta, GA; REMOTE
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  • URL: Bluejeans
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Summary Sentence: Shape Machine: Shape Embedding and Rewriting in Visual Design

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College of Design – School of Architecture - PhD Final Dissertation Defense – Tzu-Chieh Kurt  Hong


Defense date and time: 6/30/2021 Wednesday, 10:00 am - 12:00 pm


Defense link:


Dissertation Title: Shape Machine: Shape Embedding and Rewriting in Visual Design


Dissertation Committee:


Dr. Athanassios Economou, Advisor

School of Architecture

Georgia Institute of Technology


Dr. Ramesh Krishnamurti

School of Architecture

Carnegie Mellon University


Dr. Dennis Shelden

School of Architecture

Rensselaer Polytechnic Institute/Georgia Institute of Technology


Dr. Josephine Yu

School of Mathematics

Georgia Institute of Technology


Dr. Kristina Shea

Dep. of Mechanical and Process Eng.

ETH Zürich



Dissertation Abstract:


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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Phd Defense
  • Created By: Tatianna Richardson
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  • Created On: Jun 15, 2021 - 2:27pm
  • Last Updated: Jun 15, 2021 - 2:27pm