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D Gaussian scene based on the material configuration. Further, we align the scene to the eulerian frame with xx–yy–zz axes and perform internal particle filling in designated regions, which is initialized as Ω0,t=0\Omega_{0},t=0, with each Gaussian kernel denoted pp. For particle-to-grid transfers, our shape function wIpw_{Ip} leverages the most common separable cubic B-spline function: wIp=N(xI−xph)N(yI−yph)N(zI−zph),\!w_{Ip}\!=\!N\!\left(\frac{x_{I}-x_{p}}{h}\right)N\!\left(\frac{y_{I}-y_{p}}{h}\right)\!N\!\left(\frac{z_{I}-z_{p}}{h}\right), (6) where (xp,yp,zp)(x_{p},y_{p},z_{p}) is the position of particle pp, (xI,yI,zI)(x_{I},y_{I},z_{I}) is the coordinate of grid node II, hh is the grid spacing, and N(⋅)N(\cdot) denotes the
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Forget finicky time steps: i-PhysGaussian uses implicit integration with 3D Gaussian Splatting to simulate physics with 20x greater stability.
