Developability refers to the process of creating a surface without any tearing or shearing from a two-dimensional plane. It finds practical applications in the fabrication industry. An essential characteristic of a developable 3D surface is its zero Gaussian curvature, which means that either one or both of the principal curvatures are zero. This paper introduces a method for reconstructing an approximate developable surface from a neural implicit surface. The central idea of our method involves incorporating a regularization term that operates on the second-order derivatives of the neural implicits, effectively promoting zero Gaussian curvature. Implicit surfaces offer the advantage of smoother deformation with infinite resolution, overcoming the high polygonal constraints of state-of-the-art methods using discrete representations. We draw inspiration from the properties of surface curvature and employ rank minimization techniques derived from compressed sensing. Experimental results on both developable and non-developable surfaces, including those affected by noise, validate the generalizability of our method.

翻译：可展性是指将二维平面通过无撕裂或剪切的方式创建曲面的过程，在制造业中具有实际应用价值。可展三维曲面的本质特征是其高斯曲率为零，这意味着主曲率中至少有一个为零。本文提出一种从神经隐式曲面重建近似可展曲面的方法。该方法的核心思想是引入作用在神经隐式函数二阶导数上的正则化项，从而有效促进高斯曲率为零的特性。隐式曲面具有无限分辨率的平滑变形优势，突破了现有基于离散表示的方法在高多边形约束下的限制。我们从曲面曲率性质中汲取灵感，并采用源自压缩感知的秩极小化技术。在包括含噪声可展曲面与不可展曲面上的实验结果，验证了本方法的泛化能力。