To address the problems of low accuracy and numerical errors in the current intersection methods for 3D geological models, this paper proposes a precise intersection algorithm for geological bodies based on the triangulated irregular network (TIN) and integrating floating-point arithmeticwith exact arithmetic. The specific process is as follows: First, a oriented bounding box (OBB) hierarchy for the TIN is constructed, and a set of effectively intersecting triangle pairs is identified through fast collision detection, thereby greatly reducing the scope of subsequent calculations. Second, the intersecting triangle pairs are decomposed into edge-triangle intersection tests, and an intersection positional-relationship data structure is established. This structure includes the spatial position states of intersections (atVertex: at a vertex, onEdge: on an edge, inTriangle: inside the face) and the IDs of corresponding entities (points, edges, faces). It not only eliminates redundant computations of intersection coordinates but also accurately identifies duplicate intersections by matching positional states with entity IDs (e.g., matching vertex IDs in the atVertex state and edge IDs in the onEdge state). Finally, the precision mode is selected dynamically according to the requirements of topological correctness: if floating-point precision can maintain topological correctness, projection-based constrained delaunay triangulation (CDT) is used to perform retriangulation; if deviations such as intersection position offsets (e.g., an inTriangle point projected outside the edge), point coincidence, or spurious intersections between intersection segments occur, the algorithm switches to exact precision represented by rational numbers. Retriangulation is carried out through constrained point insertion (an inTriangle point splits a triangle into three new triangles, and an onEdge point splits adjacent triangles into four new triangles) and constrained line-segment insertion (processing intersecting line segments and implementing edge-swap rules: Direct edge swapping for convex quadrilaterals and queued edge swapping for concave quadrilaterals), thereby ensuring the topological consistency of the reconstructed results. Experimental results show that the proposed algorithm effectively supports intersection operation on triangular networks, requires infrequent conversions to exact precision, and exhibits good computational efficiency and high robustness. The average runtime is lower than that of GOCAD, and the method meets the intersection requirements of most complex geological models based on triangulated irregular networks.