Activation Force Splines

We present a method for simulating the active contraction of deformable models, usable for interactive animation of soft deformable objects. We present a novel physical principle as the governing equation for the coupling between the low dimensional 1D activation force model and the higher dimensional 2D/3D deformable model. Our activation splines are easy to set up and can be used for physics based animation of deformable models such as snake motion and locomotion of characters. Our approach generalises easily to both 2D and 3D simulations and is applicable in physics based games or animations due to its simplicity and very low computational cost. Figure 1: Cartoon man flexing the arm. Using 5 activation splines the arm is lifted, lowered and bent. 1. The Activation Spline Method Our system consists of a passive deformable model represented by a volume mesh and one or more splines, used to represent the activation forces in the deformable model. Our approach may be compared to [LST09] But our focus is interactive performance so 1-4 min/frame is not viable in our context. The simulation loop for the method is sketched out in Figure 2. Without loss of generality, in the following, we will describe our method using a single spline. We assume that an animator or modeller have created a spline with K control points and any point on the spline can be found using p(s) = K ∑ k=1 Nk(s)gk (1) where p ∈ RD with D = 2,3 and Nk : R 7→ R+ is the kth global basis function of the spline. The vector gk ∈ RD is the corresponding control point and s ∈ [0..L] is the spline parameter. The spline is assumed to be inside a volume mesh (a) (b)