Real-time Rendering of Dynamic Scenes under All-frequency Lighting using Integral Spherical Gaussian

We propose an efficient rendering method for dynamic scenes under all-frequency environmental lighting. To render the surfaces of objects illuminated by distant environmental lighting, the triple product of the lighting, the visibility function and the BRDF is integrated at each shading point on the surfaces. Our method represents the environmental lighting and the BRDF with a linear combination of spherical Gaussians, replacing the integral of the triple product with the sum of the integrals of spherical Gaussians over the visible region of the hemisphere. We propose a new form of spherical Gaussian, the integral spherical Gaussian, that enables the fast and accurate integration of spherical Gaussians with various sharpness over the visible region on the hemisphere. The integral spherical Gaussian simplifies the integration to a sum of four pre-integrated values, which are easily evaluated on-the-fly. With a combination of a set of spheres to approximate object geometries and the integral spherical Gaussian, our method can render object surfaces very efficiently. Our GPU implementation demonstrates realtime rendering of dynamic scenes with dynamic viewpoints, lighting, and BRDFs.