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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.

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