GPU-based Deformation Of Subdivision Surfaces

Subdivision surfaces and mesh deformation have been paid much attention in the past decade and have been widely applied in many applications, such as mechanical manufacture, digital movie, video game.Subdivision surfaces build a bridge between C~1 continuous mesh and smooth surfaces with high-order continuity. Constructing subdivision surfaces elegantly addresses many issues that computer graphics practitioners are confronted with, such as arbitrary topology, uniformity of representation and numerical stability. It is useful for not only modeling piecewise smooth surfaces, but also for representing surfaces associated with displacement map or geometry texture. On the other hand, surface deformation techniques allow users to interactively change the surface shape, which avoids generate individual model for every frame and plays an important role in computer animation.Motivated by this, we propose a novel algorithm for deforming subdivision surfaces, including traditional subdivision surfaces, displaced subdivision surfaces and subdivision surfaces with geometry textures. Our system lets user directly manipulate the surface using freely-selected surface points as handles. During deformation, the control mesh vertices are automatically adjusted so that the deforming surface satisfies the handle position constraints while preserving the original surface shape and details. To best preserve surface details, we incorporate the handle position constraints and detail preserving constraints into the deformation energy. For displaced subdivision surfaces and surfaces with geometric textures, the deformation energy is highly nonlinear and cannot be handled with existing iterative solvers. Accordingly, we introduce a new solver, which replaces numerical unstable iteration step with two stable deformation operations.Because our deformation algorithm employs only local operations, it is suitable for GPU implementation. This results in a real-time deformation system running orders of magnitude faster than the state-of-the-art multigrid deformation algorithm. Experimental results demonstrate that our algorithm is suitable for all kinds of subdivision surfaces and produces visually pleasing character animations in real-time by driving a subdivision surface with motion capture data.