A PDE method for patchwise approximation of large polygon meshes
Three-dimensional (3D) representations of complex geometric shapes, especially when they are reconstructed from magnetic resonance imaging (MRI) and computed tomography (CT) data, often result in large polygon meshes which require substantial storage for their handling, and normally have only one fixed level of detail (LOD). This can often be an obstacle for efficient data exchange and interactive work with such objects. We propose to replace such large polygon meshes with a relatively small set of coefficients of the patchwise partial differential equation (PDE) function representation. With this model, the approximations of the original shapes can be rendered with any desired resolution at interactive rates. Our approach can directly work with any common 3D reconstruction pipeline, which we demonstrate by applying it to a large reconstructed medical data set with irregular geometry.
partial differential equations 3d reconstruction surface modeling surface approximation