3DCG 1,a) 2 2 2 2 3 On rigid body animation taking into account the 3D computer graphics camera viewpoint Abstract: In using computer graphics for making games or motion pictures, physics simulation is an important tool to generate realistic animation. In general, it is necessary to fine-tune a number of physical parameters in order to reflect the user intention on the results of physics simulation. Thus the reflection of user intention is practically very difficult. We focus on the rigid body simulation and address the problem to reflect an intention on the movements of spattering rigid fragments broken by a simulated explosion. This paper describes how to control the undesired movements of fragments flying toward the camera. We propose a rigid body animation control method to get the fragments to avoid the camera as unobserved as possible. Keywords: rigid body simulation, user control, explosion 1. 3 3DCG 1 Graduate School, Tokyo University of Technology 2 Tokyo University of Technology a) g311102589@st.teu.ac.jp c 2012 Information Processing Society of Japan 1
Twigg [3] Popović, [2] [7] [8] Chenney [1] Twigg [4] [6] [5] 2. 1 1 Fig. 1 A case that some exploded fragments hit the camera (blue box) 2 Fig. 2 A case that a fragment hits the near clipping plane, causing an unnatural rendering result 1 2 2 3 3 3 4 c 2012 Information Processing Society of Japan 2
Fig. 5 5 An ideal fragment trajectory in the proposed method Fig. 3 3 A case that a transparent wall is placed in front of the camera 5 3. 3.1 V cam t = 0 t p P p (t) (x p (t), y p (t)) V p (t) (V x p (t), V y p (t)) p 4 Fig. 4 A trajectory of a fragment which goes around the frame 3 ( 1 ) ( 2 ) ( 3 ) x p (t) =x p (0) + V x p (0)t y p (t) =y p (0) + V y p (0)t 1 2 gt2. (1) g p t G p (1) y = 0 t R(t) R(t) = V cam (t G p t) (2) t P cam (t) (x cam (t), y cam (t)) t = 0 t P cam (t) P cam (0) 2 = R(0) 2. (3) (1) (3) t 4 t [0, t G p ] p t = 0 t t C p t = 0 c 2012 Information Processing Society of Japan 3
6 Fig. 6 Collision prospect computation 6 p t = 0 t = 0 (1) V p (0) t = 0 t > 0 n t = t n > 0 t = 0 (1) (3) t = 0 t = t n 7 3.2 5 Fig. 7 Fig. 8 7 The relationship between time steps and collision candidates 8 The direction of the force to add to a collision candidate 8 p F p p D p p t C p F p = k t C p t D p (4) k t 4. PhysX c 2012 Information Processing Society of Japan 4
11 Fig. 11 Trajectories of fragments viewed from the camera position 9 10 9 Fig. 9 Fragment spattering without our method 11 11 11 10 5. 10 Fig. 10 Fragment spattering with our method 512 9 9 10 [1] Chenney, S. and Forsyth, D. A.: Sampling Plausible Solutions to Multi-body Constraint Problems, Proc. SIG- GRAPH 2000, pp. 219-228 (2000) [2] Popović, J., Seitz, S.M., Erdmann, M., Popovic, Z. and Witkin, A.: Interactive manipulation of rigid body simulations, ACM Transactions on Graphics, Vol. 26, No. 3 (Proc. SIGGRAPH 2000), pp.209-217 (2000) [3] Twigg, C.D. and James, D.L.:, Many-worlds browsing for control of multibody dynamics, ACM Transactions on Graphics, Vol. 26, No. 3 (Proc. SIGGRAPH 2007), c 2012 Information Processing Society of Japan 5
Article 14(2007) [4] Twigg, C.D. and James, D.L.: Backward Steps in Rigid Body Simulation, AMC Transactions on Graphics, Vol. 27, No. 3 (Proc. SIGGRAPH 2008), Article 25 (2008) [5], Vol. 38, No. 6, pp. 449-458 (2009) [6], Visual Computing CAD, No.20 (2011) [7] :, Visual Computing CAD, pp. 5-10 (2006) [8], :, In Proc. Workshop on Interactive Systems and Software, pp. 25-28 (2008) c 2012 Information Processing Society of Japan 6