<p>Surface curvature, a fundamental characteristic of a surface, is directly related to its local shape. Despite their potential for controlling local geometry in implicit modeling, surface curvature constraints have received limited attention, leading to challenges in managing local shape variability, especially in scenarios with sparse modeling constraints. In this paper, we present a mean curvature-controllable Hermite radial basis function approach, termed curvRBF, to enhance shape manipulation in implicit geological modeling. This approach builds on the Hermite radial basis function method, incorporating novel mean curvature constraints alongside the original position and normal constraints. Although the mean curvature operator is analytically nonlinear, we linearize it by treating the implicit function’s gradient as a fixed, known vector instead of differentiating it. Specifically, we devise an optimization method to estimate the gradient, enabling it to adapt to the shape of the implicit surface. The resulting mean curvature constraints can be applied either directly on the surface (on-contact) or at nearby points in the surrounding field (off-contact), enabling flexible manipulation of shape geometry by adjusting the mean curvature at the constraint positions. We validate the effectiveness of this approach through a series of modeling cases, demonstrating that it effectively and flexibly controls the geometry and topology of implicit surfaces. We also demonstrate that mean curvature information enhances reconstruction accuracy in scenarios with sparse constraints.</p>