Fast Computation Of Single Scattering In Participating Media

With the development of film industry and theoretical research,the scenes and materials to be processed in rendering are becoming more and more complex,meanwhile the demand for various realistic rendering effects like simulating light scattering has attracted wide attention.The simulation of single scattering of participating media(such as jade,milk,skin,etc.)with complex physical phenomena is one of the problems that industry and academia urgently want to solve.In the single scattering of the participating media with refractive boundary,the internal refracted ray is also prone to local high-frequency regions and even caustics that is difficult to simulate,besides,we should consider the influence of the phase function on its distribution of scattering.In addition,although the hardware has been greatly improved,the complexity of calculations about material leads to limited efficiency,which is also a problem need to solve.There are some algorithms for solving such problems now,such as a point-based rendering in the participating media with refractive boundary.In the preprocessing stage,the point samples are generated at the boundary and inside of the medium,and the sampling information is collected into the spatial hierarchy as a point cloud.In the rendering stage,camera samples are generated by the camera light at the interior of the medium,then single scattering,second scattering and multiple scattering are separately calculated with the energy contribution of each samples to the camera sample and final irradiance.This method has good convergence in speed and can obtain images without noise,but it still has a large disadvantage in dealing with local high frequency events,because the samples cannot construct an energy distribution that matches the frequency of the light transport.In order to balance the energy loss,the algorithm increases the redundancy of the memory overhead and the extra computation at the cost of increasing the number of point samples.In order to solve the local frequency computation of single scattering in participating media with refractive boundaries,this paper introduces the frequency analysis technology under global illumination into the rendering process of the participating media,and proposes a point-based rendering method in participating media based on frequency analysis.The method is roughly as follows:in the preprocessing stage,a local illumination field of 4D space and direction distribution is constructed for the light source,and the spectrum information in time domain is transformed into the frequency domain by Fourier transform,to obtain the local light field with a series of illumination operations,such as light transport,occlusion,reparameterization,refraction and other microscopic changes in the transmission process.This paper gives the formulas and approximation methods for parameterization of these linear transformations using covariance matrix.The value of the frequency factor is thus expressed using the Jacobian determinant of covariance matrix at each point sample.In the rendering stage,the function of mapping model is constructed by frequency factors at each point sample to dynamically adjust its energy distribution and spatial density,which enables the camera sample to effectively distinguish point samples about different frequency content and obtain the final radiance.This algorithm can track the frequency information of the light transport effectively,and the extra computation of matrix is negligible.The algorithm proposed in this paper has great advantages in speed and quality by tested through multiple sets of scene tests and compared against some other algorithms:based on the total rendering speed increased by 2 times and above,the memory occupation cost is 20%of other algorithms.The improvement of efficiency gave an expression in two aspects:the use of frequency analysis in the preprocessing stage can reduce the number of sample points in the body without degrading the quality,which leads to acceleration;a smaller number of sample points in the rendering stage make the fast traversal of the spatial hierarchy.This paper also verifies the robustness of the algorithm by adjusting the number of samples.Based on theoretical proof and various experimental data analysis,this method can achieve faster convergence and more realistic effects.In this paper,the method of point-based rendering in participating media is improved and extended.And the efficient physical rendering method is applied to the complex material of the participating media.The combination of signal processing and physically-based rendering is providing great help for theoretical research.