Kempthorne Daryl M, Turner Ian W, Belward John A, McCue Scott W, Barry Mark, Young Joseph, Dorr Gary J, Hanan Jim, Zabkiewicz Jerzy A
Mathematical Sciences School, Queensland University of Technology, Brisbane, Qld 4001, Australia.
High Performance Computing and Research Support, Queensland University of Technology, Brisbane, Qld 4001, Australia.
Funct Plant Biol. 2015 May;42(5):444-451. doi: 10.1071/FP14058.
Realistic virtual models of leaf surfaces are important for several applications in the plant sciences, such as modelling agrichemical spray droplet movement and spreading on the surface. In this context, the virtual surfaces are required to be smooth enough to facilitate the use of the mathematical equations that govern the motion of the droplet. Although an effective approach is to apply discrete smoothing D2-spline algorithms to reconstruct the leaf surfaces from three-dimensional scanned data, difficulties arise when dealing with wheat (Triticum aestivum L.) leaves, which tend to twist and bend. To overcome this topological difficulty, we develop a parameterisation technique that rotates and translates the original data, allowing the surface to be fitted using the discrete smoothing D2-spline methods in the new parameter space. Our algorithm uses finite element methods to represent the surface as a linear combination of compactly supported shape functions. Numerical results confirm that the parameterisation, along with the use of discrete smoothing D2-spline techniques, produces realistic virtual representations of wheat leaves.
逼真的叶片表面虚拟模型对于植物科学中的多种应用都很重要，例如模拟农用化学品喷雾液滴在叶片表面的运动和扩散。在这种情况下，虚拟表面需要足够光滑，以便于使用控制液滴运动的数学方程。虽然一种有效的方法是应用离散平滑D2样条算法从三维扫描数据重建叶片表面，但在处理容易扭曲和弯曲的小麦（Triticum aestivum L.）叶片时会出现困难。为了克服这种拓扑困难，我们开发了一种参数化技术，对原始数据进行旋转和平移，使得可以在新的参数空间中使用离散平滑D2样条方法拟合表面。我们的算法使用有限元方法将表面表示为紧支形状函数的线性组合。数值结果证实，这种参数化方法与离散平滑D2样条技术的使用相结合，能够生成逼真的小麦叶片虚拟模型。
