Compressed Irregular Triangulation Network for Level_of_Detail Visualization

It is of vital importance to generate multi-resolution TIN model dynamically and efficiently in 3D visualization, virtual reality and GIS, due to the reason that multi-scale and large data volume to be processed. This paper proposes a method for compressing TIN model to create multi-resolution TIN model (LOD) dynamically. Here, multi-resolution TIN model means different level of details TIN model that can be transformed dynamically by the proposed solution, specifically based on TIN edge collapse and vertex split among different levels of TIN models. First, edge collapse and vertex split is determined according to the minimum distance to an average plane. An edge fulfill this requirement will be collapsed, in the same time, the angle between two triangles is used as an additional criterion for this judgment. Secondly, the vertex tree model is proposed to manage and store the vertex relationship between different level of TIN models. The corresponding encoding method is proposed based on the bracketing method (Donaghey, 1980) -each vertex is represented only with 0 or 1 to encode the position relationship in a tree. Thirdly, two new regulations for edge collapse and vertex split are defined to prevent the problem of surface foldovers during running time. In the validity judgment of the edge collapse and vertex split, we extended the assessment to (a) time, (b) quality. The elevation RMS and triangle shape quality were proposed to evaluate the quality of a generated multi-resolution TIN model. In the proposed method, we do not store vertex dependency relationships explicitly, this is great helpful in reducing data volume. The experiments demonstrate that the proposed method can acquire reasonable balance between model quality and running time. 1.Introduction Triangulated Irregular Network (TIN) is a popular representation for surface models in GIS, computer graphics and virtual reality (VR) because it has a simple data structure and can easily be rendered by common graphics hardware. High resolution representations of TIN can lead to huge data volumes and long computation times for rendering. Therefore, TIN representation should maintain a good trade-off between computation time, rendering speed and data storage where visualization is a key issue. Level_of_Detail (LOD) models provide an s much research has investigated models and algorithms for 3D compression, terrain visualization, model simplification, multi-resolution analysis, progressive transmission, and so on, for example hierarchy triangle (De Floriani 1989), progressive model (Hoppe 1996), triangle decimation (Schroeder 1992), edge collapse/split (Garland et al 1998). In these approaches many methods were proposed based on edge collapse/split for constructing LOD of a TIN (Xia et al 1997, EI-Sana et al 1999). The main difference between them is the encoding of the vertex dependency relationship when visualizing the model. The encoding of the vertex dependency relationship has a big impact on the rendering speed, data storage because it is the preconditions to judge the validity of edge collapse/split, Xia (1997) stores the explicit relationship of the vertex dependencies and EI-Sana (1999) improved the relationship by storing them implicitly. In fact, this approach has unnecessary restrictions (De Floriani et al 2001), and can prevent the further simplification of the original model. The method in this paper extends the method in EI-Sana (EI-Sana et al 1999), and adopts a new method to encode the relationship, which can reduce the data storage and running time. The main contribution in this paper is to develop an efficient algorithm to encode the vertex dependency relationship dynamically during the procedure of LOD construction based on edge collapse/split. The method presented in this paper intends to extend the edge collapse and vertex split algorithm by using a new method to encode the topological relationships in TIN model. The solution further improves the vertex dependency relationships without storing vertex dependency relationship explicitly. The core of this development is on an efficient algorithm to encode the vertex dependency relationships dynamically for a multi-resolution TIN model construction based on edge collapse and vertex split. Following an introduction of this section, the following sections are arranged as the following. The principle and concept of the approach and the algorithm of constructing vertex tree are proposed in Section 2. The data structure and implementation of the approach are thus presented in Section 3. This is followed by several experimental studies for testing the performance of the approach and evaluating the quality of the multi-resolution model in Section 4. 2. The Concept and Principles of the Proposed Method The method proposed in this paper is derived based on the basic concept of edge collapse and vertex split algorithm, which is illustrated in figure 1. According to the principles of edge collapse and vertex split, four key issues will be resolved in order to propose an efficient solution for multiresolution TIN model generation in this study. These are (a) to select candidate edges for collapse; (b) to judge the validity of edge collapse and vertex split; (c) to store and encode the vertex relationships, and (d) to evaluate the model quality. Figure 1. The concept of edge collapse and vertex split Within the above four issues, the first three are related to the validity of the surfaces in the multiresolution model and the performance of the model. The forth issue is related to the quality of multiresolution model. In constructing a multi-resolution model, edge collapse and vertex split operation are very essential. For example, these will control whether an operation proceeds can be controlled according to the model accuracy or the triangle numbers in a multi-resolution model, such as the root mean square error RMS of elevations or the maximum error of point elevation in a terrain model. The collapse