A novel heterogeneous deformable surface model based on elasticity

Abstract

The thin membranes and shells in nature are heterogeneous. They are widely used in surgical simulation, biological techniques, and computer animation. The corresponding surface deformable models can implement dynamic simulations of thin membranes and shells in nature, while most surface deformable models are isotropic and cannot represent thin membranes and shells in nature accurately. Therefore, we propose a novel physically-based heterogeneous deformable surface model. By utilizing the same B-spline basis functions or the parameter space of surfaces' geometric representations, we implement material modeling and propose the representations of surfaces with material variations with composite or continuous material functions. Then, we propose a novel physically-based elastic deformable surface model that constructs infinitesimal elements in the parameter space and employs elasticity to analyze their deformation. The corresponding elastic potential energy function is only related to surfaces' continuous representations, and our model avoids the computation error caused by meshes' quality and large rotation of points' frames. We employ isogeometric analysis to solve the dynamic equations derived from our surface model. To demonstrate the validity and reality of our model, several comparison experiments are designed. The corresponding results are in line with expectations and consistent with physical laws.