Abstract: In the construction of transparent geological guarantee systems for mines, the generation of high-precision three-dimensional geological models from sparse geological data is considered a highly challenging and key research topic. Traditional implicit modeling methods are limited by the insufficient rationality of spatial interpolation and the restricted incorporation of geological rule constraints, so that geologically reasonable and topologically consistent three-dimensional geological body models cannot be constructed automatically and efficiently. To address this problem, an implicit automatic geological body modeling method based on generalized radial basis function (GRBF) interpolation is proposed. Mathematical functions based on GRBF interpolation are employed to represent geological bodies satisfying geological rule constraints. Topologically consistent geological body mesh models are obtained by defining geological body construction rules and surface reconstruction methods. In terms of spatial geometric constraints, various types of generalized interpolation constraints are constructed by using the GRBF interpolation method. In terms of geological rule constraints, multiple types of geological interface constraints and geological age constraints are formulated. In terms of geological body construction rules, lithological evaluation rules for geological body construction and their accelerated assessment strategies are analyzed. In terms of geological body surface reconstruction, the marching tetrahedra method suitable for multi-domain surface reconstruction is extended, vertex clustering algorithms are adopted to improve mesh generation quality, and surface tracking strategies are implemented to improve isosurface extraction efficiency. Based on potential field combination rules, geological modeling problems with multiple types of geological interface constraints and geological age constraints are processed automatically and efficiently, and geologically reasonable and topologically consistent three-dimensional geological body models are constructed. Since the final geological interfaces are obtained by potential field interpolation, the dynamic updating of geological models is realized through iterative adjustment of constraint rules. Three-dimensional surface reconstruction techniques are employed to verify the geological rationality of the implicit modeling results. Based on several geological datasets, multiple three-dimensional geological body models conforming to geological laws are successfully constructed, which verifies the interpolation performance of the GRBF interpolation method and the reliability of the implicit automatic geological body modeling method integrating geological rule constraints. It is demonstrated that the spatial interpolation mathematical framework and geological rule constraints are effectively integrated by the proposed modeling method, and the satisfactory applicability in geological modeling is achieved.