Leaves play a vital role in the development of a plant, as they are major resource collectors. Adequate models of leaves are therefore required for the modelling of plants. Such models may be used for visualisation purposes only, or they may incorporate leaf function such as photosynthesis. While the modelling of plant architecture has been researched extensively over the last decades, models of leaf surfaces have mostly not been generated with great accuracy or level of detail, and have often been handcrafted. This thesis aims to provide techniques for the creation of detailed, accurate models of leaf surfaces for the plant modelling community; models that may be used as parts of virtual plants for applications in fields as diverse as the arts, agriculture or computer games. These techniques are mathematical methods of surface fitting based on data that has been sampled from real leaves.
First, leaf data needs to be collected. The digitising of leaf surfaces is described in detail in this thesis, and issues arising for three data collection techniques are discussed. The laser scanner is selected to sample data from leaf surfaces of four example leaf types. The two surface fitting methods which are applied to the data are finite element interpolation approaches. Since the size of a laser scanned data set can be enormous, an incremental algorithm is used to identify significant points that result in a surface fit that approximates all remaining data points to a specified accuracy. Interpretation of the positions of these points leads to the formulation of guidelines that describe the locations of significant points on a leaf surface. These are the points that should be digitised with a single-point device such as a sonic or magnetic digitiser, possibly the only digitising technique available to a plant scientist.
Triangle-based finite element methods lead to surface models with piecewise linear boundaries in the triangulation reference plane. This may not be an issue for applications where the boundary of a model is not important. Leaf surfaces, however, possess a specific boundary. To generate a visually realistic model of a leaf surface the boundary needs to be captured; a method is introduced that improves the boundary of a triangle-based interpolant. A new boundary curve is specified that passes through all boundary points, and the surface is extended so that it matches the new curve. Visual criteria are listed for the acceptance or rejection of the boundary, and a preliminary discussion is made of numerical criteria.
The research presented in this thesis is the first to model detailed and accurate leaf surfaces based on data points. It delivers a basis for further research both into the application of detailed models as well as into extensions of the presented model.