THE MODELLING OF BRANCHED STRUCTURES USING A SINGLE POLYGONAL MESH † J. LLUCH, M. J. VICENT, S. FERNANDEZ, C. MONSERRAT, R.VIVO Computer Graphics Section Department of Computer Systems and Computation Valencia University of Technology (Spain) E-mail: jlluch@dsic.upv.es ABSTRACT This paper presents a method to obtain a single continuos polygonal mesh representing a branched structure taken from a tree and modelled by a L-systems-based method. A refinement process is made once the model of the tree is obtained. This process produces smooth transitions in the tree areas joining the branches. That is, the overlapping problems and geometry discontinuities are avoided. Because of this process, a continuous polygonal mesh that represents all the tree branches is generated. This mesh allows mesh simplification algorithms. Keywords. Computer Graphics, polygonal mesh, modelling of natural phenomena, modelling of vegetable species. 1. Introduction Natural environments modelled by a huge amount of geometry cause a great number of problems. So, it is necessary to use techniques capable to accelerate this kind of scene visualisation. This work introduces a method to allow the modelling of a tree, plant or any other branched form, using a single polygonal mesh. This mesh is suitable for applying simplification techniques. Vegetable species modelling is a computer graphic field studied by many authors. Initially, the main motivation for vegetable species modelling was biological. The first steps in this field were made by biologist Aristid Lindenmayer who formulated the L-system model for its application in cellular interaction. This simple model was developed later by Prusinkiewicz [1] for its application to vegetable species. The model is based on rewriting rules concepts. Starting from an initial module called axiom, the rules are applied in parallel, obtaining a chain that may be interpreted in a graphic form. Particle systems [2], fractals [3], models based on botanical principles [4], or methods based on the † This work was supported by TIC1999-0510-C02-01 parameterisation [5] of some tree characteristics obtained by observing different species have also been used to model trees in order to make the visual result noticeable. The model used in this work to generate trees is based on the parametric L-systems. The main difference is the use of random variables inside the system and the making of special modules that allows chain derivation control. There is a great variety of models for tree generation . However, none of them creates a homogeneous geometric structure to render the generated objects. The final result of the methods studied is a union of different geometric models that represent each branch or branch segment. The primitive and mostly used ones are: truncated cones, generalised cylinders and polygon meshes for each branch. Figure 1. Visibility and discontinuity problems due to using primitive unions. Using truncated cones to obtain curved branches may generate discontinuities. Problems also arise when using generalised cylinders or meshes for each branch when representing bifurcations, because the polygons belonging to different branches overlap. This produces visibility problems (see figure 1). Therefore, it is necessary to develop a solution in order to obtain a single polygon mesh representing the whole tree structure. When rendering ecosystems, a great amount of trees must be represented simultaneously [6][7]. In this kind of applications, a fast visualisation of every model is very important. Obtaining a single mesh will allow a multi-