Smooth Bijective Projection in a High-order Shell

We propose a new structure called a higher-order shell, which is composed of a set of triangular prisms. Each triangular prism is enveloped by three Bézier triangles (top, middle, and bottom) and three side surfaces, each of which is trimmed from a bilinear surface. Moreover, we define a continuous vector field to smoothly and bijectively transfer attributes between two surfaces inside the shell. Since the higher-order shell has several hard construction constraints, we apply an interior-point strategy to robustly and automatically construct a high-order shell for an input mesh. Specifically, the strategy starts from a valid linear shell with a small thickness. Then, the shell is optimized until the specified thickness is reached, where explicit checks ensure that the constraints are always satisfied. We extensively test our method on more than 8300 models, demonstrating its robustness and performance. Compared to state-of-the-art methods, our bijective projection is smoother, and the space between the shell and input mesh is more uniform.