Beyond Catmull-Clark? A Survey of Advances in Subdivision Surface Methods

Subdivision surfaces allow smooth free-form surface modelling without topological constraints. They have become a fundamental representation for smooth geometry, particularly in the animation and entertainment industries. This survey summarizes research on subdivision surfaces over the last 15 years in three major strands: analysis, integration into existing systems and the development of new schemes. We also examine the reason for the low adoption of new schemes with theoretical advantages, explain why CatmullClark surfaces have become a de facto standard in geometric modelling, and conclude by identifying directions for future research.