In the study, it is proposed that a coordinate-parametric matrix model is performed to a square-conjoint pattern of cross woven (SCPCW) in the bamboo mat. The patterns of SCPCW are firstly detected according to the perspective of configuration, which is divided into the basic-monomer shape and the basic combination shape. Secondly, the compositions of design patterns in SCPCW are analyzed to attain the trend of curve shape. Based on the coordinate-parametric matrix model, the specimens of SCPCW are subsequently accomplished to elaborate the woven logic of bamboo mats. The digital innovation of SCPCW, defined by a mathematical resolution, is implemented by the software of Grasshopper (GH), which plays a crucial role in capturing image information by the Image Sampler component. Successively, the weaving logic of coordinated matrix is referred to apply in the computing component of Grasshopper software. Finally, the computer simulation could demonstrate that the coordinate-parametric matrix model of SCPCW would be realized to analyze the micro-weaving structure and overall weaving effect in the bamboo mat.

In the Asia-Pacific region, some conventional bamboo products are abundant [

Many brands have popularized the design elements of woven bamboo due to their natural material texture, woven patterns, color matching, and other aesthetic values [

There are a lot of digitized and visualized means to help designers preview partial woven structures and holistic aesthetic effects [

In this study, the dogtooth pattern and the fish-style pattern of SCPCW will be investigated by the coordinate-parametric matrix model, configurated by the basic-monomer shape and basic-combination shape, respectively. It could be reinterpreted woven logic of SCPCW through the coordinate sequences of the bamboo mat. Compared to bamboo weaving and jacquard fabric, the image information is likewise digitalized to realize the freely desired effects. Namely, the matrix coordinate of the bamboo mat pattern is similar to the digital weaving software of the jacquard fabric [

A basic shape is the unit of pattern in a bamboo mat, which can be divided into two forms, namely monomeric and duplex-style shapes. The primary skeletal framework of basic shape is made up of visible and invisible lines or geometric shapes. The skeleton-framework joints are seamless and can be continuously stretched toward four directions-top of the woven bamboo mat [

In

From different viewpoints, the continuous patterns of SCPCW are regarded as varied apperceptions [

The longitudinal strips picked and pressed in the cross-woven bamboo mat are known as warp strips, while the horizontal strips weaved in sequence are known as weft strips [

In

In the practical performance, the minimum width and thickness of the strip in the weaving bamboo mats are 1.5 and 0.1 mm, respectively. In the study, the design of the weaving model is conducted with bamboo strips of 1.5 mm width and 0.1 mm thickness. It is explored that the uneven surface of the bamboo mat would emerge if a weft strip is sequentially weaved in 7 warp strips (

The coordinate array

where _{w} represents the variable of the warp strips of woven bamboo, _{h} represents the variable of the weft strips of woven bamboo, _{1}, _{2}, ..., _{w} and in the horizontal direction from bottom to top as _{1}, _{2}, ..., _{h}.

Based on

where _{h} represents the variable of the weft strips of woven bamboo, _{s} is the starting warp variable, and subscript _{h} matrix take values in the range of _{s}_{s+a}.

According to _{DT} _{1}_{4}, _{1}_{5}

_{DT} is the coordinate matrix of positive shapes of the dogtooth pattern,

In the same way, the coordinate array of negative shapes in the dogtooth pattern is reflected in

where _{DT} is the coordinate matrix of negative shapes of the dogtooth pattern,

According to

where _{DT} is the coordinate combination of positive and negative shapes of the dogtooth pattern,

In the dogtooth pattern (_{1} _{1}_{4}, _{1}_{2} _{2}_{4}, _{2}_{1} _{1}, _{2}_{2} _{1}_{2}, _{3}

According to _{FS} _{1}_{9}, _{1}_{6}

in the coordinate matrix, where _{FS} is the positive shape of the fish-style pattern,

In the same way, the coordinate array of negative shapes in the fish-style pattern is reflected in

in the coordinate matrix, where _{FS} is the negative shapes of the fish-style pattern,

In _{1}, _{2.2}, _{3.2}, _{4}, _{5.2}, and _{6}, respectively. After that, it forms multiple sets of symmetric matrices with the coordinates of the central axis. In the fish-style pattern,

in the fish-style pattern, where _{FS} is the coordinate combination of positive and negative shapes,

Especially, the weaving logic of the coordinated matrix is referred to apply in the computing component of GH software, which is realized to predict the micro-weaving structure and weaving effect in the bamboo mat. First, the bamboo-mat pattern is segmented to the binary image, similar to when a jacquard fabric’s pattern matrix [

In _{DT} _{16} _{20} and _{FS} _{21} _{21}, which realize the matrix space of the bamboo mats pattern (

Arithmetic logic | Structural components | Variable components |
---|---|---|

Build woven surface 2D grid framework; Pattern information collection | Spuare/Polygon Center/Image Sampler | Number slider |

Build warp and woven nodes | Deconstruct/Construct Domain/Remap Numbers/Construct Point/Flip Matrix | Number slider |

Build warp and woven interpolation curve | Interpolate | – |

Build warp and woven surface | Perp Frame/Rectangle/Construct Domain/ Negative/Extrude Along | Number slider |

Secondly, the Z-axis value mapped for the image acquisition is input into the Image Sampler component to generate upward and downward altitudes floating on the 2D matrix lattices. Hence, the wave-like variation (

Successively, the interpolation lines are pointed into after connecting some woven nodes along the warp direction, and the weft direction, respectively (

In order to realize the digitization of bamboo mats, a mathematical resolution has been substantially elaborated by extracting the configuration form and composition form of SCPCW in the traditional bamboo mat. In the future, parametric technology in bamboo mats will not only attain some diverse landscape designs but also efficiently fabricate beautiful bamboo decoration. In the project, some analyses have been presented as follows:

The image configuration of the cross woven in the bamboo mat could be explicitly defined as follows, the basic-monomer shape and the basic combination shape. At the same time, the compositions of design patterns in the bamboo mat of SCPCW are analyzed to attain the trend of curve shape.

The coordinate-parametric matrix model has been executed to inspire a digital analysis of the cross-woven delineation in a bamboo mat.

A computer simulation carried out by GH software could confirm that the coordinate-parametric matrix model of SCPCW in the bamboo mat would be effective.

This work acknowledges the financial support from the Hunan Provincial Key Research and Development Program (2020WK2018); the Arts Crafts Industrial Design Center of Hunan Province (No. 2022GYMSZ2); and the Scientific Innovation Fund for Post-Graduates of Central South University of Forestry and Technology (No. 2022CX02079).

Conceived and designed the experiments: Ye Fu, Jinbo Hu; performed the experiment: Ye Fu, Liwen Deng, Ting Li; supervised the work: Jinbo Hu, Shanshan Chang; wrote the paper: Ye Fu, Liwen Deng, Jinbo Hu; revised the paper: Jinbo Hu, Shanshan Chang.

Data generated or analyzed during this study were included in this published article and its supplementary information files.

The authors declare that they have no conflicts of interest to report regarding the present study.