Abstract: In physics, mass center is defined to be the average position with regard to mass distribution, which may be located outside the object when the shape is non-convex. To overcome the disadvantage, we extend mass center to 3-manifold objects based on moments of inertia. We first replace Euclidean distance with interior distance by exploiting the discrete heat equation, and then minimize the moments by the gradient descent method. Mass center of this new type has two distinguished properties. First, it must be located inside the given object. Second, it degenerates into conventional mass center when the input shape is convex. Therefore, we call it geometric centroid in this paper. Numerous experimental results show that geometric centroid is insensitive to noise and shape deformation, and hopefully helpful for shape analysis.