Abstract
Visualization plays an important role to understand complicated phenomena. Joinery is complicated combination of woods. The mechanism of joinery, in particular the difference between the tenon-mortise and lap joints, is analyzed using homotopy theory. Then, designing a simple house is visually described using the incrementally modular abstraction hierarchy that starts from the homotopy level and ends at the physical level. At the cellular structured level that plays an important role in design, the frame represented by a fundamental group of homotopy theory is transformed into CW-complex consisting of cells, where the concept model is transferred to the physical model. Visualization of designing joinery is realized at each level of the abstraction hierarchy to help a designer understand joinery intuitively.
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Ohmori, K., Kunii, T.L. (2012). Visualization of Joinery Using Homotopy Theory and Attaching Maps. In: Gavrilova, M.L., Tan, C.J.K. (eds) Transactions on Computational Science XVI. Lecture Notes in Computer Science, vol 7380. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32663-9_6
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DOI: https://doi.org/10.1007/978-3-642-32663-9_6
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