Smooth Bijective Projection in a Highorder Shell
Shibo Liu Yang Ji JiaPeng Guo Ligang Liu XiaoMing Fu  
University of Science and Technology of China 
ACM Transactions on Graphics (Proc. SIGGRAPH), 43(4), 2024.
Teaser: Highorder shell and application. Given a lowquality triangular mesh (a), we construct a highorder shell (b). Then, we remesh the lowquality mesh within the highorder shell to generate a new mesh, which is further tetrahedrized (c). We deform the mesh in (c) to generate a deformed mesh (d) using the settings in (a). Finally, the displacement field of the deformation is bijectively transferred back to the input to produce a deformation of the input mesh (e). 

Abstract 

Keywords 
highorder shell, attribute transfer, smooth projection, bijective 
Motivation 

Methods 
Figure 2: The definition of highorder shell. (a) The continuous vector field. (b) The triangular prism envelopes by three Bezier triangles and three side bilinear surfaces. (c) The generation of the bezier triangles such that the boundaries of thr Bezier triangle conform to the bilinear patch. To efficiently construct sparse and highquality highorder shells, we start with a linear shell of minimal initial thickness and continuously perform local operations to optimize the shell structure until the target thickness is reached. During the optimization process, we use an interiorpoint method strategy. After each local operation, we perform conditional fitting of the Bezier triangles and reject any local operations that would cause the shell space to lose its bijective properties.
Figure 3: Workflow of our method. Given an input mesh, our algorithm is initialized with a dense linear shell, where the vector field is defined to align with the image of the side bilinear surfaces' parametric lines in one direction. Then, we iteratively perform local remeshing operations to optimize and simplify the shell until the specified thickness is reached. In each operation, we place the control points based on the placement condition and check whether any constraint is violated. If there is a violation, we reject the operation.
Specifically, the operations include collapse, flip, zoom and optimize.
We terminate the algorithm when no local operations can be further conducted.

Paper 

Ack 

BibTex 
@article {liu2024curveshell, title = {Smooth Bijective Projection in a Highorder Shell}, author = {Liu, Shibo and Ji, Yang and Guo, JiaPeng and Liu, Ligang and Fu, XiaoMing} journal = {ACM Transactions on Graphics}, volume={43}, number={4}, pages={113}, year = {2024} } 
Copyright and disclaimer: 