Citation: Wang, X.; Wu, C.; Bai, C.
Generating the Regular Axis from
Irregular Column Grids through
Genetic Algorithm. Appl. Sci. 2022,
12, 2109. https://doi.org/10.3390/
app12042109
Academic Editors: Zhihan Lv, Kai Xu
and Zhigeng Pan
Received: 29 December 2021
Accepted: 14 February 2022
Published: 17 February 2022
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Article
Generating the Regular Axis from Irregular Column Grids
through Genetic Algorithm
Xi Wang
1,
* , Cong Wu
1,
* and Chengjun Bai
2
1
School of Architecture, Tianjin University, No. 92 Weijin Road, Nankai District, Tianjin 30072, China
2
School of Civil Engineering, Tianjin University, No. 92 Weijin Road, Nankai District, Tianjin 30072, China;
babybcj@sina.com
* Correspondence: wangxi88love@tju.edu.cn (X.W.); wucong@tju.edu.cn (C.W.)
Featured Application: This study proposes an auto-generation method of the regular axis, ap-
plied in digital documentation of cultural heritage. The procedure is repeatable, the results show
the displacement of columns with visual expression and numerical analysis.
Abstract:
Historic building information modeling (HBIM) provides an index frame for digital docu-
mentation of the cultural heritage, as a continuous process of reverse engineering. The index frame
should be a regular model, with a clear comprehension of each component; consequently, associated
knowledge could be live-updated with the investigation progress. Therefore, the method of data
registration stresses its importance. The axis is fundamental for Chinese traditional architecture as
the basis for positioning all components in wooden structures. However, displacement often happens.
To correct the displacement while modeling, the hypothetical axis should be determined first. This
paper thus proposes a method of generating the regular axis from irregular column grids and aims to
develop an automatic solution that is repeatable and transplantable. The finite element modeling
(FEM) abstracts the actual problem to enable numerical calculation. Starting from a candidate solu-
tion, the genetic algorithm calculates a solution closest to the expectation from the possible solutions
in several minutes. The standard deviation is used to measure the amount of displacement based on
the hypothetical axis, which is expected to be minimum. This method is compatible with most kinds
of input data, e.g., point cloud, excel data, 2D drawing, mesh model, etc., and applied to a World
Heritage Site in Qufu (Shandong, China). The results show the displacement of columns with visual
expression and numerical analysis and prove that the proposed method is repeatable and traceable
and can easily be applied to different projects by changing input parameters.
Keywords:
HBIM; reverse engineering; grid system; column displacement; regularized rebuild; FEM;
algorithm generation; heritage documentation
1. Introduction
1.1. Review of Related Works
During the digital documentation of cultural heritage, displacements are usually
found in wooden structures [1–4], resulting in difficulty of positioning while modeling.
Different from modern architecture, in Chinese traditional architecture, the axis is
designed for locating column heads, rather than column feet. Because eave columns are
inclined and raised in an arithmetic sequence, from center to corner, the plane projection of
centroids connection line of eave column heads is rectangular, while the eave column feet
are not.
This manufacturing method is documented in “Ying Zao Fa Shi” [
5
–
9
] (which states
building regulations of Song Dynasty, A.D. 1103), and it can be seen in many heritage
sites in East Asia nowadays. However, this method is difficult to verify, as all the wooden
structures have lost their original positions.
Appl. Sci. 2022, 12, 2109. https://doi.org/10.3390/app12042109 https://www.mdpi.com/journal/applsci
