This paper describes a 3D surface segmentation method that uses morphological watersheds. The use of watersheds is common in image segmentation, and in this paper we describe a generalization of that concept to the task of segmenting three-dimensional surface meshes. While the image-segmentation algorithms operate on the gradient magnitude or some related edge measure, the surface-mesh algorithm uses surface curvature. The algorithm segments the surface into patches, where each patch has a relatively consistent curvature throughout and is bounded by areas of higher, or significantly different, curvature.