A Rendering Method on Desert Scenes of Dunes with Wind-ripples

Transcription

1 A Rendering Method on Desert Scenes of Dunes with Wind-ripples Koichi ONOUE and Tomoyuki NISHITA LOD Level of Detail 1. [1] [2], [3] [2] [3] Graduate School of Frontier Sciences, The University of Tokyo, Hongou 7 3 1, Bunkyo-ku, Tokyo, Japan [2] ( ) LOD(Level of Detail)

2 Fig. 1 1 The saltation movement H(x, y) (1) (3) L q H n (x, y) =H n (x, y) q, (1) H n (x + L(H n (x, y)),y) = H n (x + L(H n (x, y)),y)+q, (2) L = L 0 + bh n (x, y). (3) Fig. 3 2 Fig. 2 The creep movement. 3 ( ) The creep movement shown in cross section. L 0,b n n n n +1 1 H (x, y) H n+1 (x, y) =H n (x, y)+d[ 1 H n (x, y) 6 NN + 1 H n (x, y) H n (x, y)].(4) 12 NNN D NN (x,y) NNN H(x, y) 4 Fig. 4 The saltation movement at dunes. q q = q( H n (x, y)) = q 0 +b tanh( H n (x, y)).(5) q 0 b L L = L( H n (x, y)) = L 0 b tanh( H n (x, y)).(6) 4

3 OpenGL 1 2 F a F (view frustum) F b LOD F F (1) (2) (1) (2) 5 (a) (b) (c) 3. 3 LOD Fig. 5 Bump mapping wind-ripples onto dunes. xy LOD LOD ( 6 ) LOD LOD [5] 1 LOD ( , ,64 64,32 32 ) ( ) 1

4 6 Fig. 6 Changes of resolutions according to distances from viewpoint. 7 Fig. 7 The determination of sampling points in the shadow calculation. LOD 3. 4 [6] [7] [8] [10] Z Z 8 Fig. 8 The shadow calculation in the height field. [11] P P xy ( 7 ) P 8 x i,x i+1 L P P

5 3. 5 (3. 4 ) P P [12] Heidrich [13] P (2), (3) 2 9 xy D (3) 3 P D P 10 P (x, y) x (x 1,y) 2 P PP P P 8 P 2 P (x, y) (x+1,y), (x+2,y),..., (XSIZE 1,y), (0,y), (1,y),.., (x 1,y) XSIZE x 9 Fig. 9 The calculation of horizon in the height field. 10 Fig. 10 The calculation of horizon in the height field shown in cross section. P 3. 6 ( 11 ) 3. 7

6 11 Fig. 11 An example of the sand surface texture. OpenGL x t (x t,y t,z t ) x t = x t 1 + x + αx, y t = y t 1 + αy z t = H dune (x t,y t )+ z + αz (7) x x H dune (x t,y t ) (x t,y t ) z αx, αy, αz L 0 =7.3,q =0.6,b =2.0 L 0 = 7.0,q 0 =1.5,b =2.0,b =2.0 ( [2] ) 64x LOD 64 64,32 32,16 16,8 8 [14], [15] LOD 13 LOD LOD LOD LOD 1.5 LOD 1/ ( 6.8 ) Sumner [16] CPU PentiumIII 1GHz Nvidia GeForce ( onoue/sand/)

7 12 Fig. 12 Dunes without wind-ripples. 13 Fig. 13 Dunes with wind-ripples. 14 Fig. 14 Dunes without shadows. 15 Fig. 15 Dunes with shadows. Fig Dunes with shadows (without wind-ripples shadows). 17 Fig. 17 Dunes with shadows (with wind-ripples shadows).

8 18 Fig. 18 Dunes with sand smoke and foot prints. 1 2 LOD LOD 3 LOD 4 5 [6] J. Blinn, Me and my (fake) shadow, IEEE Computer Graphics and Applications, Vol.8, No.1, pp.82-86, [7] F. Crow, Shadow algorithms for computer graphics, Computer Graphics (SIGGRAPH 77 Proceedings), Vol.11, No.2, pp , [8] L. Williams, Casting Curved Shadows on Curved Surfaces, Computer Graphics (SIGGRAPH 78 Proceedings), Vol.12, No.3, pp , August [9] W. Reeves, D. Salesin, and R. Cook, Rendering Antialiased Shadows with Depth Maps, Computer Graphics (SIGGRAPH 87 Proceedings), Vol.21, No.4, pp , July [10] M. Segal, C. Korobkin, R. Widenfelt, J. Foran, and P. Haeberli, Fast Shadows and Lighting Effects Using Texture Mapping, Computer Graphics (SIG- GRAPH 92 Proceedings), Vol.26, No.2, pp , July [11] T. Noma, K. Sumi, Shadows on Bump-Mapped Surfaces in Ray Tracing, The Visual Computer, Vol.10, No.4, pp , [12] N. Max, Horizon mapping: shadows for bumpmapped surfaces, The Visual Computer, 4(2), pp , July [13] W. Heidrich, K. Daubert, J. Kautz,, H. Seidel, Illuminating Micro Geometry Based on Precomputed Visibility, Computer Graphics (SIGGRAPH 2000 Proceedings), pp , July [14] T. Nishita, T. Shirai, K. Tadamura, and E. Nakamae, Display of The Earth Taking into Account Atmospheric Scattering, Computer Graphics (SIG- GRAPH 93 Proceedings), Vol.27, No.4, pp , August [15] Y. Dobashi, T. Nishita, K. Kaneda, and H. Yamashita, A Fast Display Method of Sky Colour Using Basis functions, The Journal of Visualization and Animation, Vol.8, pp , [16] R. Sumner, J. O Brien, J. Hodgins, Animating Sand, Mud, and Snow. Proceedings of Graphics Interface 98, June 17-21, pp [1] K. Pye and H. Tsoar, Aeolian Sand and Sand Dunes, pp , Unwin Hyman, London, [2] H. Nishimori and N. Ouchi, Formation of Ripple Patterns and Dunes by Wind-Blown Sand, Physical Review Letters, Vol.71, No.1, pp , July [3] N. Ouchi and H. Nishimori, Modeling of wind-blown sand using cellular automata, Physical Review, B 52, , [4] J. Blinn, Simulation of wrinkled surfaces, Computer Graphics (SIGGRAPH 78 Proceedings), Vol.12, No.3, pp , August [5] L. Williams, Pyramidial Parametrics, Computer Graphics, Vol.7, No.3, pp.1-11, July 1983.