In this paper, we present a novel method for surface sampling and remeshing with good blue‐noise properties. Our approach is based on the farthest point optimization (FPO), a relaxation technique that generates high quality blue‐noise point sets in 2D. We propose two important generalizations of the original FPO framework: adaptive sampling and sampling on surfaces. A simple and efficient algorithm for accelerating the FPO framework is also proposed. Experimental results show that the generalized FPO generates point sets with excellent blue‐noise properties for adaptive and surface sampling. Furthermore, we demonstrate that our remeshing quality is superior to the current state‐of‐theߚart approaches.