2.5D 1,a) 2 1 2 2.5D 2.5D 2 2 3D 2.5D 2.5D Modeling from Illustrations of Different Views Abstract: When artists design characters, they draw illustrations viewed from the front, side or slant views. In this paper, we create a 2.5D model using such illustrations. A 2.5D model is a model that is created by arranging deformable billboards in the depth direction, and it can express an appearance of the character between two viewpoints with considering depth information. Our method uses two cartoon-like illustrations and eye directions as inputs. These illustrations are consisted of contours and closed regions painted with uniform colors. Our method finds corresponding regions between two illustrations, and creates a 2.5D model by putting each matched region as a billboard in 3D space. These processes are semi-automatic. By completing regions that appear or vanish, our method can interpolate illustrations with occluded regions. 1. 3DCG 3D 3D 2.5D [1], [2] 2.5D 2D [2] 1 Kyushu University 2 University of Tsukuba a) maki.terai@gmail.com 3D 2.5D 3D 2.5D 3D 2.5D 2.5D 2.5D [3], [4], [5] 1
1 2. 3DCG Non-photorealistic rendering [6], [7] 3D View-dependent geometry [8] 3D 3D 2.5D 2D Igarashi 1 [9]1 [10], [11] [3], [4], [5] Baxter [12] Whited BetweenIT [13] [14] 2.5D Di Fiore [1] Rivers 2.5D [2] 2.5D 2.5D Yeh [15] 2.5D 2
3. 3.1 2 3D z x, y x θ y ϕ (θ, ϕ) = (0, 0) 1 ( 1(a)) 2 ( 1(b)) 3D 3D 2 ( 1(c),(d)) 2.5D 3.2 flood fill ( 1(a)) Sýkora [16] 1(c) 2 3.3 ( 1(b)) Liu [17] Liu [17] a, b s a,b (1) s a,b = J a,b e wx xa x b e wy ya y b e Sa S b (Sa+S b )/2 (1) J a,b Liu J a,b = H[T c C a,b ] (2) C a,b RGB a, b q a, q b C a,b = q a q b T c 0.3 H[n] Heaviside n 0 1 0 e wx xa x b e wy ya y b a, b (x a, y a ), (x b, y b ) x θ x x a x b y ϕ y a y b w x, w y w x θ = 0 1.0 0.5 w y ϕ e Sa S b (Sa+S b )/2 a, b S a, S b S a, S b 2 1 2 (a) (b) Liu (c) 1 3
2 Liu Liu Liu Liu 1 Liu 11 9 (0.82) 11 (1.00) 9 2 (0.22) 5 (0.56) 12 8 (0.67) 11 (0.92) 23 15 (0.65) 17 (0.74) 3.4 3D 3D p Rivers [2] Algorithm 1 Algorithm 1 Calculate a 3D billboard position. p sum (0, 0, 0), p current (0, 0, 0) N many times (e.g. 10,000) for i = 0 to N do N V the number of views for j = 0 to N V do c j the center of bounding box of region R j l j the 3D line that passes through c j and goes in the view direction of the view p j the 3D position that projected p current onto l j p sum p sum + p current end for p current p sum /N V end for p p current 3D p 2 a, b p 3D p a p b p a p b 4
3.5 3D 3 2 1(d) Baxter [18] 4. C++ Qt Library Intel Core i7-2760qm 2.40GHz CPU PC 3 ϕ = 0 θ 45 θ = 0 ϕ 45 10 50 3 5. 2 2.5D 3D 2.5D 3D 3D 3D 2D 3D 3D 25 5451 [1] Di Fiore, F., Schaeken, P., Elens, K. and Van Reeth, F.: Automatic in-betweening in computer assisted animation by exploiting 2.5D modelling techniques, Computer Animation, 2001. The Fourteenth Conference on Computer Animation. Proceedings, pp. 192 200 (2001). [2] Rivers, A., Igarashi, T. and Durand, F.: 2.5D Cartoon Models, ACM Trans. Graph., Vol. 29, No. 4, pp. 59:1 59:7 (2010). [3] Baxter, W., Barla, P. and Anjyo, K.-i.: Rigid Shape Interpolation Using Normal Equations, Proceedings of the 6th International Symposium on Non-photorealistic Animation and Rendering, NPAR 08, New York, NY, USA, ACM, pp. 59 64 (2008). [4] Sýkora, D., Dingliana, J. and Collins, S.: As-rigid-aspossible Image Registration for Hand-drawn Cartoon Animations, Proceedings of International Symposium on Non-photorealistic Animation and Rendering, pp. 25 33 (2009). [5] Wolberg, G.: Image morphing: a survey, The Visual Computer, Vol. 14, No. 8-9, pp. 360 372 (1998). [6] Decaudin, P.: Cartoon Looking Rendering of 3D Scenes, Research Report 2919, INRIA (1996). [7] Rusinkiewicz, S., DeCarlo, D. and Finkelstein, A.: Line Drawings from 3D Models, ACM SIGGRAPH 2005 Courses, SIGGRAPH 05, New York, NY, USA, ACM (2005). [8] Rademacher, P.: View-dependent Geometry, Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 99, New York, NY, USA, ACM Press/Addison-Wesley Publishing Co., pp. 439 446 (1999). [9] Igarashi, T., Moscovich, T. and Hughes, J. F.: As-rigidas-possible Shape Manipulation, ACM Trans. Graph., 5
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