Fast Three-Dimensional Printing for Terrain Models Based on Improved K-Dimensional Tree Spatial Segmentation
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摘要:
针对当前3D打印的物理地形模型制作方法效率低、成本高的问题，提出一种改进KD树（K-dimensional tree）空间分割的地形模型快速打印方法，以提升打印效率、节约材料. 首先，通过分析数字地形模型特征与3D打印参数间的关联，构建空间分割约束规则集，进而建立融合维度自适应与尺寸约束的改进KD树模型，突破传统分割中位置与维度固化的局限，实现对地形模型的精细化分割与地下部分的有效剔除；在此基础上，设计融入贪心策略的快速空间分割算法，通过局部最优分割最大化底座镂空体积，并借助区域聚类整合微小地形区域，优化子块划分结果；针对分块后的各地形单元，提出基于分块并行与倒置打印的快速成型方法，通过在四角设置细支撑结构避免模型畸变，同时实现底座大幅镂空，从而减少材料消耗与打印时间；最后，搭建实验环境并开展案例实验分析，选取地震、林火、洪水、滑坡和泥石流5种典型灾害地形数据，在不同分辨率与空间范围条件下进行打印验证. 研究结果表明：所提方法有效克服了传统分割的固化限制与熔融堆积打印中的模型下垂畸变问题；在5种灾害类型实例中，3D打印时间平均可减少17.69%，节省打印材料28.98%，实现物理地形模型快速、低成本打印，并展现出良好的多种地形适用性.
Abstract:In view of the problems of low efficiency and high cost associated with current three-dimensional (3D) printing methods for fabricating physical terrain models, a rapid printing method for terrain models based on improved K-dimensional (KD) tree spatial segmentation was proposed, aiming to enhance printing efficiency and reduce material consumption. First, the correlation between digital terrain model features and 3D printing parameters was analyzed to establish a rule set of spatial segmentation constraints. Subsequently, an improved KD tree model integrating dimension adaptation and size constraints was constructed, overcoming the rigid limitations of positions and dimensions in traditional segmentation and achieving refined segmentation for the terrain model and effective removal of underground sections. Building upon this foundation, a rapid spatial segmentation algorithm incorporating a greedy strategy was designed. This algorithm maximized the hollowed-out volume of the base by pursuing locally optimal segments. Micro terrain areas were integrated by means of regional clustering to optimize the sub-block segmentation results. For each terrain unit after segmentation, a rapid prototyping method based on block-based parallel and inverted printing was proposed. Fine support structures at four corners prevented model distortion while enabling substantial base hollowing and reducing material consumption and printing time. Finally, an experimental environment was established; case experiments and analysis were carried out; five typical disaster terrain data, including earthquakes, wildfires, floods, landslides, and debris flows, were selected for printing validation under conditions of varying resolutions and spatial scales. Research results demonstrate that the proposed method effectively overcomes the rigid limitations of traditional segmentation and the problem of model sagging distortion in fused deposition modeling. Across cases of the five disaster types, the approach achieves an average reduction of 17.69% in 3D printing time and 28.98% in material consumption. This facilitates rapid and low-cost physical terrain model printing with high applicability across diverse terrains.
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Key words:
- terrain model /
- fast 3D printing /
- improved KD tree /
- spatial segmentation /
- block-based parallel
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图 6 打印时间和材料减少效率分析
Figure 6. Analysis of printing time and material reduction efficiency
图 7 不同空间分割策略下的分割结果
Figure 7. Segmentation results under different spatial segmentation strategies
图 8 规则格网、四叉树与改进KD树分割的效率分析
Figure 8. Segmentation efficiency analysis of regular grids, quadtrees, and improved KD tree
图 9 用于增强现实可视化的积石山地震物理模型
Figure 9. Physical model of Jishishan Earthquake for augmented reality visualization
表 1 案例数据参数
Table 1. Parameters for case data
案例编号 灾害类型 像元数量 高程/m 分辨率/m 比例尺 dem1 地震 3614 ×2974 1680 ～4575 12.5 1∶ 50000 dem2 林火 2910 ×2608 1623 ～4395 12.5 1∶ 50000 dem3 洪水 3734 ×3339 341～ 4026 30.0 1∶ 250000 dem4 滑坡 3737 ×3280 125～ 3471 30.0 1∶ 250000 dem5 泥石流 3796 ×3347 564～ 6052 30.0 1∶ 250000 
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表 2 地形3D打印参数
Table 2. Parameters for terrain 3D printing
类别 参数项 参数值 打印参数 层高/mm 0.15 填充密度/% 20 打印温度/℃ 200 打印平台温度/℃ 60 打印速度/（mm·s−1） 50 设备和材料参数 平台深度/mm 225 平台宽度/mm 300 喷嘴直径/mm 0.4 灯丝厚度/mm 0.3
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表 3 不同案例数据效率统计
Table 3. Efficiency statistics of different case data
案例编号 打印尺寸（长、宽、高）/mm 打印时间/h 分块数/个 时间减少率/% 材料减少率/% dem1 90.35、74.35、72.30 1.60 100 19.95 29.80 dem2 72.75、65.20、69.30 1.68 101 17.80 27.90 dem3 44.81、40.07、44.22 1.75 100 16.32 25.84 dem4 44.84、39.36、40.15 1.66 101 16.88 27.87 dem5 45.55、40.16、65.86 1.54 102 17.51 33.48
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