Abstract: Sampling various geometries have been the subject of intensive research in computer graphics community. A popular application is for realistic image synthesis where geometries represented as different light sources are sampled before applying Monte Carlo methods to solve the global illumination problem. In this paper, we present a novel stratified sampling algorithm (SSA) for the helical canal surface to extend the coverage of the light sources. To our knowledge, no similar stratified sampling approaches for this surface have ever been addressed in the literature. Initially, we define the mathematical expression for the helical canal surface. We then present the SSA in detail, which is developed from the inverse function of the integration for the areas of the helical canal surface. Furthermore, we develop a Hierarchical Allocation Strategy (HAS) to abate the restriction of SSA so that it becomes feasible to generate arbitrary sample number but still maintain sample stratification. Besides, we present an acceleration algorithm, Faster SSA (FSSA), to meliorate the computation efficiency, significantly reducing the time required to generate stratified samples with negligible expenses. We also propose a parabolic interpolation approach to reduce the average error occurred for using FSSA. We have implemented these algorithms and collected some experimental results. Results show that SSA together with HAS make possible to generate stratified samples with arbitrary numbers. Comparing to SSA, FSSA expedites the sample generation process considerably to real-time sampling. The parabolic interpolation reduces the average error to merely half of the magnitude of using linear interpolation. Finally, FSSA requires less than 20K bytes memory to perform the computing, and the memory requirement does not grow with the desired sample numbers. In conclusion, the proposed sampling approach is novel, efficient and feasible for the helical canal surface.