floating horizon algorithm 1 DEM [ 01] [Luebke01] LDI Layered Depth Image [Shade98] DEM Digital Elevation Model Height field

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1 Introduction to Point-based Graphics Tadahiro FUJIMOTO Kouichi KONNO Norishige CHIBA Faculty of Engineering, Iwate University Point-based Graphics Eurographics [ ] LOD Level of Detail 8

2 floating horizon algorithm 1 DEM [ 01] [Luebke01] LDI Layered Depth Image [Shade98] DEM Digital Elevation Model Height field

3 2 (a) (b) (c) (b) LDI LDC Layered Depth Cube [Lischinski98] (a) (b) (a) ( ) 3 (a) (b) (a) (c) (b) ( ) 2 10

4 (a) (b) 3 [Piegl02] 4 5 (Ray-Casting) Splatting Shear-Warp Texture Mapping 6 (a) (b) 4 11

5 5 [Ito03] (a) (b) 6 7 [ 02] [Amenta98] 8 12

6 [ 02] [ 03] [Dobashi00] [ 03 Dobashi00] [ 01] 9 [ 02 Takeshita03] primitive [Levoy85] (a) (b) 13

7 backward mapping forward mapping [Westover90] footprint footprint splat footprint kernel splatting [Westover90] 10 reconstruction kernel 10 14

8 Image-based Rendering warping LDI Layered Depth Image [Shade98] LDI 11 LDI LDI LDI LDI LDI LDI incremental warping algorithm LDI ( x, y, z) ( x, y, z) McMillan s ordering algorithm [McMillan95a McMillan95b] 11 LDI 15

9 LDI LDI LDI LDC Layered Depth Cube [Lischinski98] LDI LDI LDI LDI tree [Chang99] LDI LDI tree LDI tree LDI surfel surface element [Pfister00] LDC LDC tree LDC tree LDC tree 12 LDI LDI-1 LDI-2 LDI LDC tree LDI LDC 0 LDC 12 (a) LDI 12 (a) LDI-1 LDI-2 0 LDC LDI 1/2 (1/2) n n = 1, 2, 3, LDC 12 (b) (c) b LDC b b 2 LDI LDC 12 b = 4 (a) (b) (c) n 1/8 LDC tree LDC LDI 3-to-1 reduction LDI LDC tree 16

10 EWA Elliptical Weighted Average filter [Heckbert89] surfel mipmap LDC tree LDC tree view-frustum culling backface culling LDC tree visibility splatting LDC tree 17

11 EWA EWA source space EWA filter EWA screen space EWA filter surface splatting [Zwicker01] P k u r k w k u f c x u f c (u) EWA x r k x resampling kernel ρ k ρ k w k x g' c x g' c ( x) u EWA EWA Q Q QSplat [Rusinkiewicz00] bounding sphere hierarchy normal cone 18

12 LOD [ 01] CAD No pp [ 02] Visual Computing 2002 [ 02] CAD No pp [ 03] CAD No pp [ 01] DEM GIS 9 1 pp [Luebke01] D. Luebke, Developer s Survey of Polygonal Simplification Algorithms, CG&A, Vol.21, No.3, pp.24 35, [Shade98] J. Shade, S. J. Gortler, L. He, and R. Szeliski, Layered Depth Images, SIGGRAPH 98, pp , [Lischinski98] D. Lischinski and A. Rappoport, Image-Based Rendering for Non-Diffuse Synthetic Scenes, Rendering 19

13 Techniques 98, pp , [Piegl02] L. A. Piegl and W. Tiller, Algorithm for finding all k nearest neighbors, Computer Aided Design, Vol.34, No.2, pp , [Ito03] T. Ito, T. Fujimoto, K. Muraoka, and N. Chiba, Modeling Rocky Scenery Taking into Account Joints, CGI2003, pp , [ 02] [Amenta98] N. Amenta, M. Bern, and M. Kamvysselis, A New Voronoi-Based Surface Reconstruction Algorithm, SIGGRAPH 98, pp , [ 01] Vol.42 No.5 pp [ 02] NICOGRAPH pp [ 03] OpenGL 3D 3D NICOGRAPH pp [Dobashi00] Y. Dobashi, K. Kaneda, H. Yamashita, T. Okita, and T. Nishita, A Simple, Efficient Method for Realistic Animation of Clouds, SIGGRAPH 2000, pp.19 28, [ 02] 18 NICOGRAPH pp [Takeshita03] D. Takeshita, S. Ota, M. Tamura, T. Fujimoto, K. Muraoka, and N. Chiba, Particle-Based Visual Simulation of Explosive Flames, Pacific Graphics 2003, pp , [Levoy85] M. Levoy and T. Whitted, The Use of Points as Display Primitives, Technical Report TR , University of North Carolina, [Westover90] L. Westover, Footprint Evaluation for Volume Rendering, SIGGRAPH 90, pp , [McMillan95a] L. McMillan, Computing Visibility Without Depth, Technical Report , University of North Carolina, [McMillan95b] L. McMillan, A List-Priority Rendering Algorithm for Redisplaying Projected Surfaces, Technical Report , University of North Carolina, [Chang99] C. F. Chang, G. Bishop, and A. Lastra, LDI Tree: A Hierarchical Representation for Image-Based Rendering, SIGGRAPH 99, pp , [Pfister00] H. Pfister, M. Zwicker, J. van Baar, and M. Gross, Surfels: Surface Elements as Rendering Primitives, SIGGRAPH 2000, pp , [Heckbert89] P. Heckbert, Fundamentals of Texture Mapping and Image Warping, Master s thesis, University of California at Berkeley, Department of Electrical Engineering and Computer Science, [ 99] 20

14 Vol.28 No.2 pp [Zwicker01] M. Zwicker, H. Pfister, J. van Baar, and M. Gross, Surface Splatting, SIGGRAPH 2001, pp , [Rusinkiewicz00] S. Rusinkiewicz and M. Levoy, QSplat: A Multiresolution Point Rendering System for Large Meshes, SIGGRAPH 2000, pp ,

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