Path planning in 3D environment is a fundamental research area for robots and autonomous vehicles. Based on the principle ``the shortest path consists of tangents'', RimJump* is proposed as a tangent-based path planning method suitable for finding the shortest path (both off-ground and on-ground) in 3D space (e.g., octomap and point cloud) for mobile platform to follow. RimJump* searches the tangent graph in the form of a path tree and considers the geometrical properties of the locally shortest path. Therefore, the method can provide all of the locally shortest paths that connect the starting point and the target, including the globally shortest path. And the time cost of RimJump* is insensitive to map scale increases in comparison to methods that search the whole passable space rather than the surface of the obstacle, e.g., Dijkstra and A*. In the Results, RimJump* is compared with other methods in terms of path length and time cost.