The S-rule and 1-d representation for the traversal of a planar graph in AEC industry
Based on two trivial observations of the AEC industry, this paper proposes a traversal method ("S-rule") and expression ("1-dimensional-graph") transformed from DFS. This traversal method conforms to the original cognitive logic of the AEC industry, and the 1-d expression has cle...
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Zusammenfassung: | Based on two trivial observations of the AEC industry, this paper proposes a
traversal method ("S-rule") and expression ("1-dimensional-graph") transformed
from DFS. This traversal method conforms to the original cognitive logic of the
AEC industry, and the 1-d expression has clear language characteristics while
completely retaining the topological relationship of the planar graph : a
sequence of finite symbols (vocabularies) under definite rules. Moreover, the
language can be restored to a standard 2-d form that is isomorphic to the
original planar graph, thus ensuring its visualization characteristics.
Fragments of the 1-d language can be used as planar units for free combination
and weighting, and as the data foundation to support advanced calculations
including FEM and isomorphic matching. And after the 2-d graph is reduced to
1-d, any 3-d or higher-dimensional graphs can also be reduced to 1 or 2
dimensions. The first half of this paper (Chapter 1) takes the 4X4 standard
grid as an example to introduce the prototype of S-rule and 1-d expression, and
gives the mapping rule from 1-d expression to its editable text form. In the
second half of this paper, the rule and expression are gradually extended to
non-embedded planar graphs (Chapter 2) and embedded planar graphs (Chapter 3),
and the "grammar" is finally summarized (Chapter 4). |
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DOI: | 10.48550/arxiv.2308.06446 |