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：可展性是指从二维平面创建曲面而不发生撕裂或剪切的过程，在制造工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，这意味着一个或两个主曲率为零。本文提出了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一个作用于神经隐式二阶导数的正则化项，有效促进高斯曲率为零。隐式曲面具有无限分辨率下更平滑变形的优势，克服了当前使用离散表示的最先进方法所面临的高多边形约束限制。我们从曲面曲率特性中汲取灵感，采用源自压缩感知的秩极小化技术。在可展曲面和不可展曲面（包括受噪声影响的曲面）上的实验结果验证了本文方法的泛化能力。