Assuming that we have access to i.i.d. samples in \(\mathbb{R}^n \)obtained from an underlying d-dimensional shape S endowed with a possibly non uniform density θ, we propose and analyse an estimator of the varifold structure associated to S. The shape S is assumed to be piecewise \(C^{1,a}\) in a sense that allows for a singular set whose small enlargements are of small d-dimensional measure. The estimators are kernel-based both for infering the density and the tangent spaces and the convergence result holds for the bounded Lipschitz distance between varifolds, in expectation and in a noiseless model. The mean convergence rate involves the dimension d of S, its regularity through \(a\in(0,1]\) and the regularity of the density θ.