基于NURBS曲面的小麦叶片三维重建

doi:10.11924/j.issn.1000-6850.casb2023-0653

摘要/Abstract

摘要：

针对小麦叶片三维可视化不易实现的问题，通过NURBS曲面算法对小麦叶片进行三维重建。实测小麦叶片长度、叶片宽度、茎叶夹角、叶鞘长度、叶鞘直径等具体数据，通过主脉控制点算法计算叶片和叶鞘的主脉控制点信息，根据叶片宽度、叶鞘直径等信息计算出全部控制点信息，在visual studio中使用OpenGL构建小麦叶片三维模型。本研究算法得出的小麦叶片模型与真实小麦叶片有较高的相似度，较好地体现了叶片的弯曲度，真实地反映了作物叶片的形态信息。基于NURBS曲面的三维重建控制灵活、使用方便、计算简单，在作物的三维建模方面有较好的应用和参考价值。

关键词: NURBS曲面算法, 小麦叶片, 实测数据, 控制点计算, 节点矢量, 三维重建, OpenGL, 形态特征

Abstract:

Aiming at the problem of three-dimensional visualization of wheat leaves which is difficult to realize, the three-dimensional reconstruction of wheat leaves was carried out by NURBS surface algorithm. Specific data such as wheat leaf length, leaf width, stem and leaf angle, leaf sheath length, and leaf sheath diameter were measured. The main vein control point information of the leaves and leaf sheaths was calculated using the main vein control point algorithm. All the control point information was calculated based on leaf width, leaf sheath diameter, and other information. The three-dimensional model of wheat leaves was constructed using OpenGL in visual studio. The wheat leaf model obtained by the research algorithm has a high similarity with real wheat leaves, which better reflects the curvature of the leaves and truly reflects the morphological information of crop leaves. The three-dimensional reconstruction based on NURBS surface has flexible control, convenient use, and simple calculation, which has good application and reference value in the three-dimensional modeling of crops.

Key words: NURBS surface algorithm, wheat leaf, measured data, control points, node vector, three-dimensional reconstruction, OpenGL, morphological characteristics

徐苗, 马娜. 基于NURBS曲面的小麦叶片三维重建[J]. 中国农学通报, 2024, 40(25): 140-146.

XU Miao, MA Na. Three-dimensional Reconstruction of Wheat Leaf Based on NURBS Surface[J]. Chinese Agricultural Science Bulletin, 2024, 40(25): 140-146.

图/表 6

参考文献 26

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叶号	行号	控制点坐标/cm
A1	1	{0.00, 0.00, -0.15}，{0.00, 0.00, -0.075}，{0.00, 0.00, 0.00}，{0.00, 0.00, 0.075}，{0.00, 0.00, 0.15}
	2	{-0.37,1.11,-0.25}，{-0.37,1.11,-0.125}，{-0.37,1.11,0.00}，{-0.37,1.11, 0.125}，{-0.37, 1.11, 0.25}
	3	{-0.74, 2.22, -0.30}，{-0.74, 2.22, -0.15}，{-0.74, 2.22,0.00}，{-0.74, 2.22, 0.15}，{-0.74, 2.22, 0.30}
	4	{-1.48, 4.44, -0.25}，{-1.48, 4.44, -0.125}，{-1.48, 4.44, 0.00}，{-1.48, 4.44, 0.125}, {-1.48,4.44, 0.15}
	5	{-2.96,8.88, -0.15}，{-2.96, 8.88, -0.075}，{-2.96, 8.88, 0.00}，{-2.96, 8.88, 0.075}, {-2.96, 8.88, 0.15}
A2	1	{0.00, 0.00, -0.15}，{0.00, 0.00, -0.075}，{0.00, 0.00, 0.00}，{0.00, 0.00, 0.075}，{0.00, 0.00, 0.15}
	2	{0.91, 3.53, -0.20}，{0.91, 3.53, -0.10}，{0.91, 3.53, 0.00}，{0.91, 3.53, 0.10}，{0.91, 3.53, 0.20}
	3	{2.92, 6.69, -0.30}，{2.92, 6.69, -0.15}，{2.92, 6.69, 0.00}，{2.92, 6.69, 0.15}，{2.92, 6.69, 0.30}
	4	{6.73, 12.59, -0.20}，{6.73, 12.59, -0.10}，{6.73, 12.59, 0.00}，{6.73, 12.59, 0.10}，{6.73,12.59, 0.20}
	5	{14.07, 24.13, -0.15}，{14.07, 24.13, -0.075}，{14.07, 24.13, 0.00}，{14.07, 24.13, 0.075}，{14.07, 24.13, 0.15}
B1	1	{0.00, -1.00, -0.15}, {0.00, -1.00, -0.075}, {0.00, -1.00, 0.00}，{0.00, -1.00, 0.075}, {0.00, -1.00, 0.15}
	2	{-0.42, -0.03, -0.18}，{-0.42, -0.03,-0.09}，{-0.42, -0.03, 0.00}，{-0.42, -0.03, 0.09}，{-0.42, -0.03, 0.18}
	3	{-0.84, 0.94, -0.25}，{-0.84, 0.94, -0.125}，{-0.84, 0.94, 0.00}，{-0.84, 0.94, 0.125}，{-0.84, 0.94, 0.25}
	4	{-1.67, 2.88, -0.20}，{-1.67, 2.88, -0.10}，{-1.67, 2.88, 0.00}，{-1.67, 2.88, 0.10}，{-1.67, 2.88, 0.20}
	5	{-3.34,6.76, -0.15}，{-3.34, 6.76, -0.075}，{-3.34, 6.76, 0.00}，{-3.34,6.76, 0.075}，{-3.34, 6.76, 0.15}
B2	1	{0.00, 0.00, -0.15}，{0.00, 0.00, -0.075}，{0.00, 0.00, 0.00}，{0.00, 0.00, 0.075}，{0.00, 0.00, 0.15}
	2	{0.00, 0.85, -0.15}，{0.00, 0.85, -0.075}，{0.00, 0.85, 0.00}，{0.00, 0.85, 0.075}，{0.00, 0.85, 0.15}
	3	{0.00, 1.70, -0.15}，{0.00, 1.70, -0.075}，{0.00, 1.70, 0.00}，{0.00, 1.70, 0.075}，{0.00, 1.70, 0.15}
	4	{0.00, 2.55, -0.20}，{0.00, 2.55, -0.10}，{0.00, 2.55, 0.00}，{0.00, 2.55, 0.10}，{0.00, 2.55, 0.20}
	5	{0.00, 3.40, -0.15}，{0.00, 3.40, -0.075}，{0.00, 3.40, 0.00}，{0.00, 3.40, 0.075}，{0.00, 3.40, 0.15}
B3	1	{0.00, 0.00, -0.15}，{0.00, 0.00, -0.075}，{0.00, 0.00, 0.00}，{0.00, 0.00, 0.075}，{0.00, 0.00, 0.15}
	2	{0.96, 2.87, -0.20}，{0.96, 2.87, -0.10}，{0.96, 2.87, 0.00}，{0.96, 2.87, 0.10}，{0.96, 2.87, 0.20}
	3	{1.91, 5.74, -0.25}，{1.91, 5.74, -0.125}，{1.91, 5.74, 0.00}，{1.91, 5.74, 0.125}，{1.91, 5.74, 0.25}
	4	{2.87, 8.61, -0.20}，{2.87, 8.61, -0.10}，{2.87, 8.61, 0.00}，{2.87, 8.61, 0.10}，{2.87, 8.61, 0.20}
	5	{9.00, 15.80, -0.15}，{9.00, 15.80, -0.075}，{9.00, 15.80, 0.00}，{9.00, 15.80, 0.075}，{9.00, 15.80, 0.15}

叶号	行号	控制点坐标/cm
A1	1	{0.00, 0.00, -0.15}，{0.00, 0.00, -0.075}，{0.00, 0.00, 0.00}，{0.00, 0.00, 0.075}，{0.00, 0.00, 0.15}
	2	{-0.37,1.11,-0.25}，{-0.37,1.11,-0.125}，{-0.37,1.11,0.00}，{-0.37,1.11, 0.125}，{-0.37, 1.11, 0.25}
	3	{-0.74, 2.22, -0.30}，{-0.74, 2.22, -0.15}，{-0.74, 2.22,0.00}，{-0.74, 2.22, 0.15}，{-0.74, 2.22, 0.30}
	4	{-1.48, 4.44, -0.25}，{-1.48, 4.44, -0.125}，{-1.48, 4.44, 0.00}，{-1.48, 4.44, 0.125}, {-1.48,4.44, 0.15}
	5	{-2.96,8.88, -0.15}，{-2.96, 8.88, -0.075}，{-2.96, 8.88, 0.00}，{-2.96, 8.88, 0.075}, {-2.96, 8.88, 0.15}
A2	1	{0.00, 0.00, -0.15}，{0.00, 0.00, -0.075}，{0.00, 0.00, 0.00}，{0.00, 0.00, 0.075}，{0.00, 0.00, 0.15}
	2	{0.91, 3.53, -0.20}，{0.91, 3.53, -0.10}，{0.91, 3.53, 0.00}，{0.91, 3.53, 0.10}，{0.91, 3.53, 0.20}
	3	{2.92, 6.69, -0.30}，{2.92, 6.69, -0.15}，{2.92, 6.69, 0.00}，{2.92, 6.69, 0.15}，{2.92, 6.69, 0.30}
	4	{6.73, 12.59, -0.20}，{6.73, 12.59, -0.10}，{6.73, 12.59, 0.00}，{6.73, 12.59, 0.10}，{6.73,12.59, 0.20}
	5	{14.07, 24.13, -0.15}，{14.07, 24.13, -0.075}，{14.07, 24.13, 0.00}，{14.07, 24.13, 0.075}，{14.07, 24.13, 0.15}
B1	1	{0.00, -1.00, -0.15}, {0.00, -1.00, -0.075}, {0.00, -1.00, 0.00}，{0.00, -1.00, 0.075}, {0.00, -1.00, 0.15}
	2	{-0.42, -0.03, -0.18}，{-0.42, -0.03,-0.09}，{-0.42, -0.03, 0.00}，{-0.42, -0.03, 0.09}，{-0.42, -0.03, 0.18}
	3	{-0.84, 0.94, -0.25}，{-0.84, 0.94, -0.125}，{-0.84, 0.94, 0.00}，{-0.84, 0.94, 0.125}，{-0.84, 0.94, 0.25}
	4	{-1.67, 2.88, -0.20}，{-1.67, 2.88, -0.10}，{-1.67, 2.88, 0.00}，{-1.67, 2.88, 0.10}，{-1.67, 2.88, 0.20}
	5	{-3.34,6.76, -0.15}，{-3.34, 6.76, -0.075}，{-3.34, 6.76, 0.00}，{-3.34,6.76, 0.075}，{-3.34, 6.76, 0.15}
B2	1	{0.00, 0.00, -0.15}，{0.00, 0.00, -0.075}，{0.00, 0.00, 0.00}，{0.00, 0.00, 0.075}，{0.00, 0.00, 0.15}
	2	{0.00, 0.85, -0.15}，{0.00, 0.85, -0.075}，{0.00, 0.85, 0.00}，{0.00, 0.85, 0.075}，{0.00, 0.85, 0.15}
	3	{0.00, 1.70, -0.15}，{0.00, 1.70, -0.075}，{0.00, 1.70, 0.00}，{0.00, 1.70, 0.075}，{0.00, 1.70, 0.15}
	4	{0.00, 2.55, -0.20}，{0.00, 2.55, -0.10}，{0.00, 2.55, 0.00}，{0.00, 2.55, 0.10}，{0.00, 2.55, 0.20}
	5	{0.00, 3.40, -0.15}，{0.00, 3.40, -0.075}，{0.00, 3.40, 0.00}，{0.00, 3.40, 0.075}，{0.00, 3.40, 0.15}
B3	1	{0.00, 0.00, -0.15}，{0.00, 0.00, -0.075}，{0.00, 0.00, 0.00}，{0.00, 0.00, 0.075}，{0.00, 0.00, 0.15}
	2	{0.96, 2.87, -0.20}，{0.96, 2.87, -0.10}，{0.96, 2.87, 0.00}，{0.96, 2.87, 0.10}，{0.96, 2.87, 0.20}
	3	{1.91, 5.74, -0.25}，{1.91, 5.74, -0.125}，{1.91, 5.74, 0.00}，{1.91, 5.74, 0.125}，{1.91, 5.74, 0.25}
	4	{2.87, 8.61, -0.20}，{2.87, 8.61, -0.10}，{2.87, 8.61, 0.00}，{2.87, 8.61, 0.10}，{2.87, 8.61, 0.20}
	5	{9.00, 15.80, -0.15}，{9.00, 15.80, -0.075}，{9.00, 15.80, 0.00}，{9.00, 15.80, 0.075}，{9.00, 15.80, 0.15}

叶鞘	行号	控制点坐标/cm
A 叶鞘	1	{-0.16, -6.00, 0.00}，{-0.16,-6.00,-0.16}，{0.16,-6.00,-0.16}，{0.16, -6.00, 0.00}，{0.16, -6.00, 0.16}，{-0.16, -6.00, 0.16}，{-0.16, -6.00, 0.00}
	2	{-0.16, -5.00, 0.00}，{-0.16, -5.00, -0.16}，{0.16, -5.00, -0.16}，{0.16, -5.00, 0.00}，{0.16, -5.00, 0.16}，{-0.16, 5.00, 0.16}，{-0.16, -5.00, 0.00}
	3	{-0.16, -4.00,0.00}，{-0.16, -4.00, -0.16}，{0.16, -4.00, -0.16}，{0.16, -4.00, 0.00}，{0.16, -4.00, 0.16}，{-0.16, -4.00, 0.16}，{-0.16, -4.00, 0.00}
	4	{-0.16,-3.00,0.00}，{-0.16,-3.00,-0.16}，{0.16,-3.00,-0.16}，{0.16,-3.00,0.00}，{0.16, -3.00, 0.16}，{-0.16, -3.00, 0.16}，{-0.16, -3.00, 0.00}
	5	{-0.16,-2.00, 0.00}，{-0.16,-2.00,-0.16}，{0.16, -2.00, -0.16}，{0.16, -2.00, 0.00}，{0.16, -2.00, 0.16}，{-0.16, -2.00, 0.16}，{-0.16, -2.00, 0.00}
	6	{-0.16, -1.00, 0.00}，{-0.16, -1.00, -0.16}，{0.16, -1.00, -0.16}，{0.16, -1.00, 0.00}，{0.16, -1.00, 0.16}，{-0.16, -1.00, 0.16}，{-0.16,-1.00, 0.00}
	7	{-0.16,0.00,-0.16}，{-0.16, 0.00,-0.16}，{0.16,0.00,-0.16}，{0.16, 0.00, 0.00}，{0.16, 0.00, 0.16}，{-0.16, 0.00, 0.16}，{-0.16, 0.00, 0.16}
B 叶鞘	1	{-0.06, -4.00, 0.00}，{-0.06, -4.00, -0.06}，{0.06, -4.00, -0.06}，{0.06, -4.00, 0.00}，{0.06, -4.00, 0.06}，{-0.06, -4.00, 0.06}，{-0.06, -4.00, 0.00}
	2	{-0.06, -3.33, 0.00}，{-0.06, -3.33, -0.06}，{0.06, 3.33, -0.06}，{0.06, 3.33, 0.00}，{0.06, -3.33, 0.06}，{-0.06, 3.33, 0.06}，{-0.06, 3.33, 0.00}
	3	{-0.06, 2.67, 0.00}，{-0.06, 2.67, -0.06}，{0.06, 2.67 -0.06}，{0.06, 2.67, 0.00}，{0.06, 2.67, 0.06}，{-0.06, 2.67, 0.06}，{-0.06, 2.67, 0.00}
	4	{-0.06, -2.00, 0.00}，{-0.06, -2.00, -0.06}，{0.06, -2.00, -0.06}，{0.06, -2.00, 0.00}，{0.06, -2.00, 0.06}，{-0.06, -2.00, 0.06}，{-0.06, -2.00, 0.00}
	5	{-0.06, -1.33, 0.00}，{-0.06, -1.33, -0.06}，{0.06, -1.33, -0.06}，{0.06, -1.33, 0.00}，{0.06, -1.33, 0.06}，{-0.06, -1.33 0.06}，{-0.06, -1.33, 0.00}
	6	{-0.06, -0.67, 0.00}，{-0.06, -0.67, -0.06}，{0.06, -0.67 -0.06}，{0.06, -0.67, 0.00}，{0.06, -0.67, 0.06}，{-0.06, -0.67, 0.06}，{-0.06, -0.67, 0.00}
	7	{-0.06, -4.00, 0.00}，{-0.06, -4.00, -0.06}，{0.06, -4.00, -0.06}，{0.06, -4.00, 0.00}，{0.06, -0.67, 0.06}，{-0.06, -0.67, 0.06}，{-0.06, -0.67, 0.00}

叶鞘	行号	控制点坐标/cm
A 叶鞘	1	{-0.16, -6.00, 0.00}，{-0.16,-6.00,-0.16}，{0.16,-6.00,-0.16}，{0.16, -6.00, 0.00}，{0.16, -6.00, 0.16}，{-0.16, -6.00, 0.16}，{-0.16, -6.00, 0.00}
	2	{-0.16, -5.00, 0.00}，{-0.16, -5.00, -0.16}，{0.16, -5.00, -0.16}，{0.16, -5.00, 0.00}，{0.16, -5.00, 0.16}，{-0.16, 5.00, 0.16}，{-0.16, -5.00, 0.00}
	3	{-0.16, -4.00,0.00}，{-0.16, -4.00, -0.16}，{0.16, -4.00, -0.16}，{0.16, -4.00, 0.00}，{0.16, -4.00, 0.16}，{-0.16, -4.00, 0.16}，{-0.16, -4.00, 0.00}
	4	{-0.16,-3.00,0.00}，{-0.16,-3.00,-0.16}，{0.16,-3.00,-0.16}，{0.16,-3.00,0.00}，{0.16, -3.00, 0.16}，{-0.16, -3.00, 0.16}，{-0.16, -3.00, 0.00}
	5	{-0.16,-2.00, 0.00}，{-0.16,-2.00,-0.16}，{0.16, -2.00, -0.16}，{0.16, -2.00, 0.00}，{0.16, -2.00, 0.16}，{-0.16, -2.00, 0.16}，{-0.16, -2.00, 0.00}
	6	{-0.16, -1.00, 0.00}，{-0.16, -1.00, -0.16}，{0.16, -1.00, -0.16}，{0.16, -1.00, 0.00}，{0.16, -1.00, 0.16}，{-0.16, -1.00, 0.16}，{-0.16,-1.00, 0.00}
	7	{-0.16,0.00,-0.16}，{-0.16, 0.00,-0.16}，{0.16,0.00,-0.16}，{0.16, 0.00, 0.00}，{0.16, 0.00, 0.16}，{-0.16, 0.00, 0.16}，{-0.16, 0.00, 0.16}
B 叶鞘	1	{-0.06, -4.00, 0.00}，{-0.06, -4.00, -0.06}，{0.06, -4.00, -0.06}，{0.06, -4.00, 0.00}，{0.06, -4.00, 0.06}，{-0.06, -4.00, 0.06}，{-0.06, -4.00, 0.00}
	2	{-0.06, -3.33, 0.00}，{-0.06, -3.33, -0.06}，{0.06, 3.33, -0.06}，{0.06, 3.33, 0.00}，{0.06, -3.33, 0.06}，{-0.06, 3.33, 0.06}，{-0.06, 3.33, 0.00}
	3	{-0.06, 2.67, 0.00}，{-0.06, 2.67, -0.06}，{0.06, 2.67 -0.06}，{0.06, 2.67, 0.00}，{0.06, 2.67, 0.06}，{-0.06, 2.67, 0.06}，{-0.06, 2.67, 0.00}
	4	{-0.06, -2.00, 0.00}，{-0.06, -2.00, -0.06}，{0.06, -2.00, -0.06}，{0.06, -2.00, 0.00}，{0.06, -2.00, 0.06}，{-0.06, -2.00, 0.06}，{-0.06, -2.00, 0.00}
	5	{-0.06, -1.33, 0.00}，{-0.06, -1.33, -0.06}，{0.06, -1.33, -0.06}，{0.06, -1.33, 0.00}，{0.06, -1.33, 0.06}，{-0.06, -1.33 0.06}，{-0.06, -1.33, 0.00}
	6	{-0.06, -0.67, 0.00}，{-0.06, -0.67, -0.06}，{0.06, -0.67 -0.06}，{0.06, -0.67, 0.00}，{0.06, -0.67, 0.06}，{-0.06, -0.67, 0.06}，{-0.06, -0.67, 0.00}
	7	{-0.06, -4.00, 0.00}，{-0.06, -4.00, -0.06}，{0.06, -4.00, -0.06}，{0.06, -4.00, 0.00}，{0.06, -0.67, 0.06}，{-0.06, -0.67, 0.06}，{-0.06, -0.67, 0.00}