A curvature-adaptive implicit surface reconstruction for noisy and irregularly spaced points in 3D is introduced. The reconstructed surface traces the zero crossings of a signed field obtained from the sum of first-derivative anisotropic Gaussians centered at the points. The standard deviations of the anisotropic Gaussians are adapted to surface curvatures estimated from local data. A key characteristic of the formulation is its ability to smooth more along edges than across them, thereby preserving shape details while smoothing noise. The behavior of the proposed method under various density and organization of points is investigated and surface reconstruction results are compared with those obtained by well-known methods in the literature.