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A Shape Preserving Pattern Mapping Method for Sculpture Surface Laser Marking Process
DOI: 10.12677/CSA.2021.113058, PDF, HTML, XML, 下载: 191  浏览: 272  国家自然科学基金支持

Abstract: A challenging topic of laser marking is to mark any 2D-complex pattern onto sculpture surfaces with shape preserving property, so this paper aims to provide a solution which realizes marking 2D patterns onto sculpture surfaces. A general idea of the solution is as follows: based on the data description of the 2D pattern and the sculpture surfaces presented in facet model, first flattening the facet sculpture surfaces into an abstract 2D region, then mapping the 2D pattern onto the 2D region. From the corresponding 3D line patterns on the sculpture surface, we can build tool paths to accomplish the marking of the target line patterns on the sculpture surfaces. In addition, it is verified by computer simulation that the mapping method can reduce the pattern deformation in the laser marking effectively.

1. 引言

2. 激光打标映射算法

2.1. 待打标曲面展平算法

2.1.1. 弧长法映射外缘顶点 $\left\{{y}_{j}\right\}$

Figure 1. Map exterior vertices using arc length proposition method

${{y}^{\prime }}_{j}={b}_{t}+\frac{\stackrel{^}{{y}_{j}{d}_{t}}}{{d}_{t}{d}_{t+1}}\frac{{b}_{t+1}-{b}_{t}}{|{b}_{t+1}-{b}_{t}|}$ (1)

2.1.2. 凸映射算法映射内部顶点 $\left\{{x}_{j}\right\}$

Figure 2. Map interior vertices using convex mapping

${{x}^{\prime }}_{i}=\underset{j}{\sum }{\lambda }_{ij}{x}_{j}+\underset{k}{\sum }{\lambda }_{ik}{y}_{k}$ (2)

$\underset{j}{\sum }{\lambda }_{ij}+\underset{k}{\sum }{\lambda }_{ik}=1$ (3)

Table 1. Pseudo-code mapping interior vertices

2.1.3. 采用线性插值映射三角面片

Figure 3. Map whole facet surface using linear interpolation

(4)

(5)

Figure 4. Example of shape preserving facet surface flattening

2.2. 映射图案到模型表面

Figure 5. Mapping pattern to sculpture surfaces

Figure 6. Triangular surface of the car’s frontal

Figure 7. Laser marking simulation result of the car’s frontal

3. 结束语

NOTES

*通讯作者。

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