利用最小二乘法的网壳结构点云节点中心坐标提取

doi:10.11996/JG.j.2095-302X.2024010183

图学学报 ›› 2024, Vol. 45 ›› Issue (1): 183-190.DOI: 10.11996/JG.j.2095-302X.2024010183

• 计算机图形学与虚拟现实 • 上一篇下一篇

利用最小二乘法的网壳结构点云节点中心坐标提取

王鹏(), 辛佩康(), 刘寅, 余芳强

上海建工四建集团有限公司工程研究院，上海 201103

收稿日期:2023-08-18 接受日期:2023-10-19 出版日期:2024-02-29 发布日期:2024-02-29
通讯作者:辛佩康(1993-)，男，工程师，硕士。主要研究方向为数字建造与数字测绘工程化应用。E-mail：2285037917@qq.com
第一作者:王鹏(1999-)，男，助理工程师，本科。主要研究方向为智能建造与数字测绘。E-mail：Biste.Wang@outlook.com
基金资助:
上海市国资委企业创新发展和能级提升项目(2022008)

Extracting node center coordinates of point clouds in reticulated shell structure using least squares method

WANG Peng(), XIN Peikang(), LIU Yin, YU Fangqiang

Engineering Research Institute, Shanghai Construction No.4 (Group) Co., Ltd., Shanghai 201103, China

Received:2023-08-18 Accepted:2023-10-19 Published:2024-02-29 Online:2024-02-29
First author：WANG Peng (1999-), assistant engineer, undergraduate. His main research interests cover intelligent construction and digital surveying and mapping. E-mail：Biste.Wang@outlook.com
Supported by:
Shanghai State-owned Assets Supervision and Administration Commission Enterprise Innovation Development and Upgrading Project(2022008)

摘要/Abstract

摘要：

为解决网壳结构节点坐标测量困难、处理效率低等问题，本文提出基于网壳结构扫描点云的节点中心坐标提取方法：应用三维激光扫描技术采集网壳结构点云数据并预处理；然后基于设计模型，对初始点云模型进行网壳节点局部点云分割和节点多平面拟合，判定拟合平面的属性特征并修正侧面的法向量方向；最后利用空间约束关系及最小二乘算法求取网壳结构节点的精确中心坐标。以三亚国际免税城项目为例开展应用，结果表明所提方法求取的网壳结构节点中心坐标与全站仪实测结果偏差均值为2.89 mm，效率相比传统方法提高近4倍，较大提升了网壳结构节点中心坐标的提取精度和效率，为后续网壳结构施工偏差复核、幕墙板材的深化设计与加工等工程化应用提供了准确的数据支撑。

上海建工四建集团有限公司余芳强高工团队针对网壳结构节点坐标复测困难、处理效率低等问题，提出了一种利用最小二乘法的网壳结构扫描点云节点中心坐标提取方法。该方法应用三维扫描仪采集网壳结构点云并预处理，然后基于设计模型分割初始点云模型的节点局部点云并拟合节点平面，利用空间约束关系及最小二乘法精确计算节点中心坐标，为后续网壳结构施工偏差复核、幕墙板材深化设计与加工等工程化应用提供准确的数据支撑。

关键词: 点云, 网壳结构, 最小二乘法, 节点中心坐标提取

Abstract:

To address the difficult measurement and low processing efficiency of node coordinates in the reticulated shell structure, an algorithm for extracting node center coordinates was proposed based on scanning point clouds in the reticulated shell structure. Firstly, point cloud data of the reticulated shell structure was collected using the three-dimensional laser scanning technology and was preprocessed. Subsequently, based on the design model, local point cloud segmentation and plane fitting of the shell nodes were performed on the initial model. The attributes and characteristics of the fitted planes were determined, and the normal vector directions on the sides were corrected. Finally, the accurate center coordinates of the nodes in the reticulated shell structure were determined through the utilization of spatial constraint relationships and the least squares algorithm. Taking the Sanya International Duty Free City project as an example, the results demonstrated that the proposed method yielded a mean deviation of 2.89 mm between the central coordinates obtained through this method and the Total Station measurements. Moreover, its efficiency was nearly 4 times higher than that of the traditional method. This significant advancement enhanced the accuracy and efficiency of the node center coordinate extraction in the reticulated shell structure, offering accurate data support for subsequent tasks, including structural construction deviation review, deepened design and processing of curtain wall panels.

Key words: point cloud, reticulated shell structure, least squares method, node center coordinate extraction

中图分类号:

TU741.3

王鹏, 辛佩康, 刘寅, 余芳强. 利用最小二乘法的网壳结构点云节点中心坐标提取[J]. 图学学报, 2024, 45(1): 183-190.

WANG Peng, XIN Peikang, LIU Yin, YU Fangqiang. Extracting node center coordinates of point clouds in reticulated shell structure using least squares method[J]. Journal of Graphics, 2024, 45(1): 183-190.

图/表 17

参考文献 25

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节点编号	本文方法计算坐标结果/m			全站仪复核坐标结果/m			位置偏差/ mm	节点编号	本文方法计算坐标结果/m			全站仪复核坐标结果/m			位置偏差/ mm
节点编号	X	Y	Z	X	Y	Z	位置偏差/ mm	节点编号	X	Y	Z	X	Y	Z	位置偏差/ mm
1	−84.254	64.232	20.920	−84.252	64.235	20.920	3.61	21	−74.016	63.968	20.967	−74.015	63.970	20.966	3.32
2	−82.167	64.322	20.966	−82.167	64.321	20.967	1.41	22	−62.632	59.292	21.827	−62.631	59.290	21.827	2.24
3	−80.867	62.515	22.140	−80.866	62.516	22.139	1.73	23	−53.748	54.942	20.948	−53.747	54.940	20.947	2.45
4	−78.736	62.574	22.163	−78.738	62.573	22.163	2.24	24	−44.794	46.622	20.971	−44.794	46.622	20.970	1.00
5	−77.281	60.654	23.197	−77.280	60.650	23.200	5.10	25	−35.036	42.087	20.830	−35.035	42.088	20.830	1.41
6	−67.997	62.617	20.965	−66.998	62.615	20.964	2.45	26	−30.997	40.764	21.221	−30.998	40.762	21.220	2.45
7	−71.404	58.947	23.687	−71.400	58.945	23.688	4.58	27	−25.237	39.024	21.301	−25.240	39.025	21.300	3.32
8	−56.182	53.738	22.395	−56.180	53.736	22.395	2.83	28	−19.314	39.568	21.578	−19.315	39.570	21.575	3.74
9	−48.681	37.692	23.189	−48.685	37.690	23.185	6.00	29	−15.591	37.668	22.395	−15.590	37.668	22.395	1.00
10	−37.482	40.874	21.387	−37.482	40.874	21.387	0.00	30	−9.474	40.393	21.819	−9.475	40.392	21.820	1.73
11	−21.574	36.957	22.145	−21.575	36.958	22.145	1.41	31	−1.713	42.471	21.072	−1.715	42.471	21.075	3.61
12	−13.290	41.456	21.026	−13.290	41.450	21.027	6.08	32	5.447	42.301	21.065	5.447	42.300	21.065	1.00
13	−5.562	42.298	21.070	−5.566	42.297	21.068	4.58	33	13.464	38.590	22.238	13.465	38.590	22.236	2.24
14	9.450	40.388	21.839	9.453	40.382	21.940	6.78	34	20.998	40.350	20.944	21.000	40.350	20.945	2.24
15	17.244	40.207	21.239	17.248	40.207	21.236	5.00	35	26.997	40.351	20.877	26.998	40.350	20.879	2.45
16	31.022	40.810	20.926	31.025	40.810	20.925	3.16	36	40.967	44.594	20.902	40.965	44.592	20.901	3.00
17	48.042	48.028	21.448	48.042	48.027	21.448	1.00	37	51.338	50.088	21.892	51.342	50.085	21.891	5.10
18	60.424	53.535	23.734	60.428	53.535	23.735	4.12	38	63.299	57.342	22.950	63.300	57.342	22.950	1.00
19	82.912	62.362	21.969	82.915	62.362	21.970	3.16	39	78.715	62.585	22.013	78.715	62.584	22.015	2.24
20	91.013	45.253	23.219	91.015	45.253	23.220	2.24	40	86.317	64.027	20.906	86.315	64.028	20.905	2.45

节点编号	本文方法计算坐标结果/m			全站仪复核坐标结果/m			位置偏差/ mm	节点编号	本文方法计算坐标结果/m			全站仪复核坐标结果/m			位置偏差/ mm
节点编号	X	Y	Z	X	Y	Z	位置偏差/ mm	节点编号	X	Y	Z	X	Y	Z	位置偏差/ mm
1	−84.254	64.232	20.920	−84.252	64.235	20.920	3.61	21	−74.016	63.968	20.967	−74.015	63.970	20.966	3.32
2	−82.167	64.322	20.966	−82.167	64.321	20.967	1.41	22	−62.632	59.292	21.827	−62.631	59.290	21.827	2.24
3	−80.867	62.515	22.140	−80.866	62.516	22.139	1.73	23	−53.748	54.942	20.948	−53.747	54.940	20.947	2.45
4	−78.736	62.574	22.163	−78.738	62.573	22.163	2.24	24	−44.794	46.622	20.971	−44.794	46.622	20.970	1.00
5	−77.281	60.654	23.197	−77.280	60.650	23.200	5.10	25	−35.036	42.087	20.830	−35.035	42.088	20.830	1.41
6	−67.997	62.617	20.965	−66.998	62.615	20.964	2.45	26	−30.997	40.764	21.221	−30.998	40.762	21.220	2.45
7	−71.404	58.947	23.687	−71.400	58.945	23.688	4.58	27	−25.237	39.024	21.301	−25.240	39.025	21.300	3.32
8	−56.182	53.738	22.395	−56.180	53.736	22.395	2.83	28	−19.314	39.568	21.578	−19.315	39.570	21.575	3.74
9	−48.681	37.692	23.189	−48.685	37.690	23.185	6.00	29	−15.591	37.668	22.395	−15.590	37.668	22.395	1.00
10	−37.482	40.874	21.387	−37.482	40.874	21.387	0.00	30	−9.474	40.393	21.819	−9.475	40.392	21.820	1.73
11	−21.574	36.957	22.145	−21.575	36.958	22.145	1.41	31	−1.713	42.471	21.072	−1.715	42.471	21.075	3.61
12	−13.290	41.456	21.026	−13.290	41.450	21.027	6.08	32	5.447	42.301	21.065	5.447	42.300	21.065	1.00
13	−5.562	42.298	21.070	−5.566	42.297	21.068	4.58	33	13.464	38.590	22.238	13.465	38.590	22.236	2.24
14	9.450	40.388	21.839	9.453	40.382	21.940	6.78	34	20.998	40.350	20.944	21.000	40.350	20.945	2.24
15	17.244	40.207	21.239	17.248	40.207	21.236	5.00	35	26.997	40.351	20.877	26.998	40.350	20.879	2.45
16	31.022	40.810	20.926	31.025	40.810	20.925	3.16	36	40.967	44.594	20.902	40.965	44.592	20.901	3.00
17	48.042	48.028	21.448	48.042	48.027	21.448	1.00	37	51.338	50.088	21.892	51.342	50.085	21.891	5.10
18	60.424	53.535	23.734	60.428	53.535	23.735	4.12	38	63.299	57.342	22.950	63.300	57.342	22.950	1.00
19	82.912	62.362	21.969	82.915	62.362	21.970	3.16	39	78.715	62.585	22.013	78.715	62.584	22.015	2.24
20	91.013	45.253	23.219	91.015	45.253	23.220	2.24	40	86.317	64.027	20.906	86.315	64.028	20.905	2.45

测量方法	外业工作量	内业工作量	总工作量
皮尺测量	12.5	5.0	17.5
全站仪测量	8.0	1.0	9.0
三维扫描+人工拾取	2.0	3.0	5.0
三维扫描+算法提取(本文)	2.0	0.5	2.5

测量方法	外业工作量	内业工作量	总工作量
皮尺测量	12.5	5.0	17.5
全站仪测量	8.0	1.0	9.0
三维扫描+人工拾取	2.0	3.0	5.0
三维扫描+算法提取(本文)	2.0	0.5	2.5

利用最小二乘法的网壳结构点云节点中心坐标提取

Extracting node center coordinates of point clouds in reticulated shell structure using least squares method

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