Abstract: We present hierarchical algorithms for visibilit culling of spline models. This includes back-patch culling, a generalization of back-face culling for polygons to splines. These algorithms are extended to trimmed surfaces as well. We propose different spatial approximations for enclosing the normals of spline surface and compare them for efficiency and effectiveness on different graphics systems. We extend the culling algorithms using hierarchical techniques to collection of surface patches and combine them with view-frustum culling to formulate a ONE (Object-Normal Exclusion)-tree for a given model. The algorithm traverses the ONE-tree at run time and culls away portions of the model not visible from the current viewpoint. These algorithms have been implemented and applied to a number of large models. In practice, we are able to speed-up the overall spline rendering algorithms by about 20 - 30% based on back-patch culling only and by more than 50% using ONE-trees.