Computer Aided Drafting, Design and Manufacturing Volume 26, Number 1, March 2016, Page 1

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1 Computer Aided Drafting, Design and Manufacturing Volume 26, Number 1, March 2016, Page 1 CADDM Clustering and merging for real-time forest rendering Ouyang Taoxu 1,3, Lai Shunnan 2, Li Sheng 2,3,4 1. Peking University Shenzhen Graduate School, Shenzhen , China; 2. School of EECS, Peking University, Beijing , China; 3. Beijing Engineering Technology Research Center of Virtual Simulation and Visualization (Peking University), Beijing , China. 4. Peking University Information Technology Institute (Tianjin Binhai), Tianjin , China. Abstract: Rendering of large-scale forest scenes is a challenging task, whose highly geometric complexity will put heavy burden on current graphics hardware. When navigating the scene, the overall visual result is generally considered as the core concern. A new method is proposed in this paper for large-scale forest rendering using clustering and merging strategies. Our method improves the rendering effect by clustering polygons according to the point information with relation to neighbours. A fast forest rendering system is developed accordingly. The relative techniques in the system can improve the visual quality on demand of different applications. Key words: cluster analysis; polygon merging; texture merging; large-scale rendering 1 Introduction It is very important to render trees in outdoor scene. In recent years, the state-of-art of trees rendering has been improved with the development of hardware. However, it is still a challenge to render large-scale forest. For instance, a forest scene consisting of trees, each with only a single polygon, will amount to polygons, which can bring a heavy burden on rendering system. In fact, the number of polygons to represent a tree will be far beyond one polygon. Without the forest, the outdoor scene will be unrealistic, while rendering of them will bring a lot of computational cost to the whole rendering system. We propose a new approach to accelerate the rendering of forest, which deals tree position with point spirit. According to point attributes, we can classify them to some more sparse positions by means of clustering. When rendering the scene in real time, we can draw large trees through few polygons taking advantage of the clustering result. So that we can reduce large resource of rendering trees without loss of visual quality in the scene. Our paper is organized as the followings. Sec.2 will present a survey of plant rendering. In Sec. 3, we will introduce how to realize hierarchical clustering on the point spirit. Sec. 4 describes how to merge polygons using the clustering result. We also developed a fast rendering system accordingly. The details of our system are discussed. Finally, we demonstrate that the system can achieve interactive frame rates for a very complex outdoor scene including millions of trees. We also discuss the future work. 2 Related work Tree modeling and rendering have been intensively investigated with many successful methodologies. Lindenmayer-system [1] is a well-known vegetation modeling approach for plant growth modeling. A lot of commercial products such as SpeedTree [2], AMAP Genesis [3], XFrog [4], natfx [5] are available to generate realistic tree models efficiently. However, the tree models are usually too complex to render in a large-scale scene. From the large-scale rendering point of view, various techniques have been used to speedup rendering. These can be classified into four categories: polygon-based rendering, point-based rendering, volume rendering and image-based rendering. 2.1 Polygon-based rendering Polygon is the primitive to represent the model of a Project item: Supported by National Natural Science Foundation of China ( , ) and National Key Technology R&D Program of China (2015BAK01B06). Corresponding author: Lai Shunnan, Female, Master, Engineer, snlai@pku.edu.cn.

2 2 Computer Aided Drafting, Design and Manufacturing (CADDM), Vol.26, No.1, Mar tree. There are many geometric simplification methods to eliminate geometric details [6-7]. Multiresolution modeling and levels of detail(lod) algorithms are two basic methods to address polygon decimation and geometry compression. These methods cannot be applied to deal with trees without changing the overall appearance of the scene due to topological complexity of trees. Deng et al. [8] proposed a new approach based on LOD for coniferous leaves with two types of representations for both near and far trees respectively. However, the number of trees by polygon-based rendering will reach its upper limit even if a tree is expressed by minimal polygons. 2.2 Point-based rendering Point models for tree rendering are first proposed by Reeves and Blau [9]. They combined points with small polygons to construct hybrid models for trees. Due to the missing of some details, Point-based rendering will become visually unacceptable when to mix trees with other 3D objects of the scene. 2.3 Volume rendering A 3D shape with volume textures, usually a bounding box that contains one or more instances of the object to be rendered are tiled over the ground. Textures are generated by synthesizing a series of images into parallel slides. Decaudin and Neyret [10] utilized aperiodic tiles of textures to render large forests. When the viewpoint is changing, volume can be rendered correctly with appropriate transformation. But unfortunately, walking into the volume of forest is impossible. 2.4 Image-based rendering Image-based rendering(ibr) has been used for many years [11]. Billboards are the simplest form, which is quadrilaterals covered with a semi-transparent texture. It allows not only efficient rendering of complex natural scenes, but also is considered to be the best choice in recent industrial simulators. Several kinds of billboards are designed including single billboard that is always facing to the camera to represent the model [12], fixing crossed quadrilaterals of two billboards to produce a more three-dimensional appearance [13]. Billboard Clouds, proposed by Decoret et al. [14] is a means of extreme simplification. It generates a set of arbitrarily oriented billboards to represent the geometry of a tree. Image-based rendering, is the most efficient approach for rendering of large-scale forest. In this work, we mainly adopt the method of image-based rendering, coupled with volume/polygon-based rendering. It is feasible to use such scheme to realize a rendering system with large-scale and realistic forest. 3 Clustering algorithm Strategies for hierarchical clustering mainly fall into two types: agglomerative which is a bottom-up approach and divisive which is a top-down approach. The agglomerative method starts with each singleton in its own cluster. Then pairs of clusters are merged along with moving up to the upper hierarchy. Until all of singletons are in one cluster, or meet a termination condition. We use the bottom-up strategy. In order to determine which clusters should be combined, a measure of dissimilarity between sets of observations is required. In most methods of hierarchical clustering, there are five commonly used linkage criteria. Single-linkage(minimum) clustering: min{ d a, b : aa, b B} Complete-linkage(maximum) clustering: max{ d a, b : aa, b B} Centroid linkage clustering: d c c i Average(mean) linkage clustering: 1 AB j a Ab B dab (, ) Minimum energy clustering: nm, n m ai bj 2 ai aj 2 bi bj i, j1 i, j1 i, j nm n m where d is the chosen metric, c i and c j are the centroids of clusters A and B, n and m are the number of the objects in clusters A and B. The process is as follows: (1) Precompute point data. Make each observation in its own cluster. (2) Compute the minimum (maximum) distance between every two clusters. (3) Merge clusters which have the least distance. (4) Repeat the above two steps (2,3) until the termination. Fig. 1 demonstrates the result of clustering. When the cluster process has been finished, there are connectivities among these observations. To deal with the result, we get a dendrogram. The root node

3 Ouyang Taoxu et al., Clustering and merging for real-time forest rendering 3 represents a cluster that contains all the trees while each leaf shows a single object related to a tree. We gather all leaf nodes from the bottom converging successively to the root, then split from the top. Starting from the root, we recursively search the tree by defining a metric(it will be introduced in Sec. 4). By the similarity comparison between clusters, we can decide whether to stop or not. Finally, we cut the dendrogram at a specified level and get a suitable dendrogram for rendering. (a) Fig. 1 Hierarchical Clustering, Single-linkage. 42 original trees. Points with different grey-scale represent the second-largest clusters individually. The 4 farthest points with black color show some single nodes which have no connection to others. (a) Original tree position. (b) Cluster result. (b) 4 Merging approach The result of clustering is a dendrogram that can represent the relationship among the attributes of tree position. We need to merge point spirits using the dendrogram we have got. Meanwhile, the viewpoint also has great influence on rendering efficiency. We can adjust the way that points gathering together using the information of viewpoint. After the merging of polygons and textures, the whole scene can be made up by fewer point positions and textures attributes which can be rendered with much less resources. 4.1 Metric Metric mainly constraints the searching depth on the dendrogram. The most commonly used metrics include Euclidean distance. Squared Euclidean distance, Manhattan distance, Mahalanobis distance, depth distance, etc. They can make the metric optional. More complex the metric, smaller the threshold, deeper the searching, it may also need more resource for rendering, making the clustering faster with less resource for computing (please see the Fig.2). Fig. 2 Cluster and divide by Eulidean distance metric, Single-linkage. 6 original trees. (up) Tree position cluster. (down) Dendrogram divide.

4 4 Computer Aided Drafting, Design and Manufacturing (CADDM), Vol.26, No.1, Mar Texture merging When dendrogram dividing finished, we can combine textures in accordance with the polygons. If the polygons are merged directly, textures can be merged directly too. If the polygons are merged as a bounding box, textures should be projected toward the viewer, and then be merged into a whole. Once the cluster is very large, the scale of texture will become large too. So it will slow down the overall time. Considered that clustering is so big to distinguish a single tree, we can merge some textures using the common appearance (line, row) in advance. In real-time rendering, we use the preprocessed textures instead of merging the textures, therefore the resources to be process will be reduced. The results of textures merging can be seen in Fig. 3. The whole procedure of the algorithm is shown in Fig. 4. (a) (b) (c) Fig. 3 Textures merging. (a) Original tree texture. (b) Preprocessed tree texture. (c) Texture merging result. Fig. 4 Algorithm procedure. 5 Experiments and results We test our method on a PC with Core i at 3.20 GHz, NVIDIA GeForce GT 640 graphic card, 4 GB of memory and a PC with Core i at 3.30 GHz, NVIDIA GeForce GTX 970 graphic card 8 GB memory. We fix Level of Detail distance to near clipping plane so that all of the points will be clustered and merged. We use point spirit to represent all the trees. We render a scene containing trees. Clustering and merging are performed on while point spirits rendered on. Fig. 5 Forest scene with small parallax (algorithm apllied, ). Fig. 5 and Fig. 6 show the results of a forest scene with small parallax. The terrain is covered almost by trees. We compare the results with or without our algorithm. Table 1 and Table 2 show the time statistics. Table 1 Small parallax scene (GT 640, pixels) Fig. 6 Forest scene with small parallax ( ).

5 Ouyang Taoxu et al., Clustering and merging for real-time forest rendering Table 2 Small parallax scene (GTX 970, pixels) Fig. 7 and Fig. 8 show a forest scene with large parallax. Table 3 and Table 4 show the time statistics. polygon number to extremely small brings a lot burden on process while only a little improvement on which will be suitable for high-polygon scene where there are a lot of render resource. Clustering, merging and searching are calculated on. Point spirit rendering is processed on. Optimistically, it can render mass of data points because they are already merged together. However, clustering is too slow to process in real time. So we need to precompute the data. When rendering, we just deal with the big clusters that have been already clustered by small clusters to reduce the calculation on. 6 Fig. 7 Forest scene with large parallax (Algorithm applied, ). Fig. 8 Forest scene with large parallax ( ). Table 3 Large parallax scene (GT 640, pixels) Table 4 Large parallax scene (GTX 970, pixels). Conclusion In this paper, we proposed a new approach for rendering of large-scale forest using clustering and merging strategy. We mainly utilize the image-based rendering, merging multiply textures into a few polygon. Meanwhile, we adopt the idea of volume rendering to optimize the visual quality of the outdoor terrain. A fast rendering system has also been realized. We greatly reduce the polygons while ensuring the render efficiency. It is necessary to trade off between merging and rendering in implementation, rely to the characteristic of the scene. An appropriate approach is to precompute more necessary data, create more clusters off-line while perform less clustering on-line. Consider that there are many objects in the scene other than trees, and the trees can t be presented only by point spirit. We can nearly avoid re-clustering. Using visual bias, we can merging larger-scale forest by larger parts instead of single tree. More repeating, less computing. A better result can be achieved if we take the information of the terrain into consideration. We can get tree position and other GIS information from terrain. On the one hand we use terrain hierarchic block diving trees, on the other hand textures can be merged easily. It will greatly improve the represent of point spirit. A better algorithm will be developed in the future. References [1] From the table above, we can see that time is reduced obviously when rendering the scene using our approach, while time increases a little both in the scenes with and trees. Reducing 5 [2] [3] [4] Prusinkiewicz P, Lindenmayer A. The algorithmic beauty of plants [M]. Springer Verlag: New-York, 1990: Interactive Data Visualization Inc [EB/OL]. [ ]. Reffye de P, Edelin C, Francon J, et al. Plant models faithful to botanical structure and development [C]//ACM SIGGRAPH, Atlanta: ACM Publisher, 1988, 22: Greenworks Software [EB/OL]. [ ].

6 6 Computer Aided Drafting, Design and Manufacturing (CADDM), Vol.26, No.1, Mar [5] Bionatics tree modeling Software [EB/OL]. [ ]. [6] Hechbert P, Garland M. Survey of polygonal surface simplification algorithms [EB/OL]. [ ] [7] Cignoni P, Montani C, Scopigno R. A comparison of mesh simplification algorithms [J]. Computer Graphics, 1988, 22(1): [8] Deng Q, Zhang X, Gay S, et al. Continuous lod model of coniferous foliage [J]. International Journal of Virtual Reality, 2007, 6(4): [9] Reeves W, Blau R. Approximate and probabilistic algorithms for shading and rendering structured particle systems [C]//ACM SIGGRAPH Computer Graphics. San Francisco: ACM Publisher, 1985, 19(3): [10] Decaudin P, Neyret F. Rendering forest scenes in real-time [C]//Eurographics Symposium on Rendering. Geneve: Eurographics Assocaition, 2004: [11] Rohlf J, Helman J. IRIS performer: A high performance multiprocessing toolkit for real-time 3D graphics [C]// SIGGRAPH 1994 Conf. San Francisco: ACM Publisher, 1994: [12] Whatley D. Toward photorealism in virtual botany. gems 2 [M]. New Jersey: Addison-Wesley, 2005: [13] Pelzer K. Rendering countless blades of waving grass. gems [M]. New Jersey: Addison-Wesley, 2004: [14] Decoret X, Durand F, Sillion F X, et al. Billboard clouds for extreme model simplification [J]. ACM Transactions on Graphics, 2003, 22(3): Ouyang Taoxu received his Master degree from the Graphics & Interactive Technology Laboratory, Peking University in His current research interests include computer graphics, plant modeling. He can be reached by ouyangtx1@pku.edu.cn. Lai Shunnan is currently an engineer in School of Electronics Engineering and Computer Science, Peking University. Her current research interests include virtual simulation, sensor technology. She can be reached at snlai@pku.edu.cn. Li Sheng is currently an associate professor in School of Electronics Engineering and Computer Science, Peking University. His current research interests include virtual reality, real-time graphics, photorealistic rendering, physical simulation and parallel computing on. He is member of China Computer Federation (CCF), ACM, IEEE. He can be reached at lisheng@pku.edu.cn.