Abstract: Implicit surface has a simple expression,and meets the smoothness requirements naturally.However,rendering implicit surface is computationally complex and inefficient.More importantly,it is difficult to control and adjust the shape of the implicit surface.Therefore,the modeling technology of implicit surface is far from being practical.To overcome these deficiencies,this paper presents an interval analysis method for rendering and polygonizing implicit surfaces based on GPU parallel computing architecture,which greatly improves the computational efficiency and rendering speed.The method first divides the rendering-space into voxels with a given resolution.Then,taking full advantage of GPU's parallel computing ability,the algorithm uses an interval analysis method to compute the range of implicit function in every voxel in parallel to find the feature-voxels which contain the zero-isosurface of the implicit function.Next,we extract the outer surface of feature-voxels,and handle it with topology-correction operations to ensure that the mesh is two-dimensional manifold;at last,using Laplace operation to smooth the mesh,we get the mesh representation of the implicit surface.A large number of experiments have been done,and the results show that the time of the implicit surface rendering and mesh smoothing are usually in millisecond magnitude which achieves the real-time level.