Obtaining intersection-freeness or global injectivity is important in computer graphics. However, it is challenging, especially for the non-oriented deformation primitives. Most methods often rely on an intersection-free initialization and track the continuous trajectory to keep the legitimacy and cannot be used for the task without such an initialization. For the latter one in 3D space, we introduce a novel second-order differentiable energy defined from the 3D triangle-triangle intersection testing, and a GPU-based inexact Newton optimization route. We show that intersection can be efficiently resolved integrated with our method, requiring no user interaction, history information or a valid initialization.

翻译：在计算机图形学中，实现无交叉性或全局单射性至关重要，但这一目标尤为困难，尤其是针对非定向变形基元。现有方法通常依赖无交叉初始化并追踪连续轨迹以保持合法性，而无法应用于缺乏此类初始化的任务。针对三维空间中的后者，我们提出一种基于三维三角形-三角形交叉检测的新型二阶可微能量，并设计了一种基于GPU的非精确牛顿优化路径。实验表明，结合我们的方法能够高效解决交叉问题，无需用户交互、历史信息或有效初始化。