Recent point-based differentiable rendering techniques have achieved significant success in high-fidelity reconstruction and fast rendering. However, due to the unstructured nature of point-based representations, they are difficult to apply to modern graphics pipelines designed for structured meshes, as well as to a variety of simulation and editing algorithms that work well with structured mesh representations. To this end, we propose StructuredField, a novel representation that achieves both a structured geometric representation of the reconstructed object and a high-fidelity rendering reconstruction of the object. We employ structured tetrahedral meshes to represent the reconstructed object. We reparameterize the geometric parameters of the tetrahedral mesh into the geometric shape parameters of a 3D Gaussians, thereby achieving differentiable high-fidelity rendering of the tetrahedral mesh. We propose a novel inversion-free homeomorphism to constrain the optimization of the tetrahedral mesh, which strictly guarantees that the tetrahedral mesh is remains both inversion-free and self-intersection-free during the optimization process and the final result. Based on our proposed StructuredField, we achieve high-quality structured meshes and high-fidelity reconstruction. We also demonstrate the applicability of our representation to various applications such as physical simulation and deformation.
近年来，基于点的可微渲染技术在高保真重建和快速渲染方面取得了显著成功。然而，由于点基表示的无结构特性，它们难以应用于为结构化网格设计的现代图形管线，以及许多与结构化网格表示兼容的模拟和编辑算法。为此，我们提出了 StructuredField，一种新颖的表示方法，能够同时实现重建物体的结构化几何表示和高保真度的渲染重建。我们采用结构化四面体网格来表示重建物体，并将四面体网格的几何参数重新参数化为 3D 高斯的几何形状参数，从而实现四面体网格的可微高保真渲染。我们提出了一种新颖的无逆同胚映射，用于约束四面体网格的优化，这确保了在优化过程和最终结果中，四面体网格始终保持无逆且无自交。基于我们提出的 StructuredField，我们实现了高质量的结构化网格和高保真度的重建。我们还展示了该表示方法在物理模拟和变形等多个应用中的可行性。