In this paper, we propose a numerical method to solve isotropic elliptic equations on
point cloud by generalizing the point integral method. The idea of the point integral method is to
approximate the differential operators by integral operators and discretize the corresponding integral
equation on point cloud. The key step is to get the integral approximation. In this paper, with proper
kernel function, we get an integral approximation for the elliptic operators with isotropic coefficients.
Moreover, the integral approximation has been proved to keep the coercivity of the original elliptic
operator. The convergence of the point integral method is also proved.