Abstract: A major problem of the existing curvilinear grid Line Integral Convolution (LIC) algorithm is that the resulting LIC textures may be distorted after being mapped onto the parametric surfaces, since a curvilinear grid usually consists of cells of different sizes. This paper proposes a way for solving the problem through using multi-granularity noise as the input image for LIC. A stochastic sampling technique called Poisson ellipse sampling is employed to resample the computational space of a curvilinear grid into a set of randomly distributed points. From this set of points, we are able to reconstruct a noise image with its local noise granularity being adapted to the physical space cell size of the grid.