Particle Image Velocimetry (PIV) often utilizes a cross-correlation method to determine how far particles have moved between two captured images. The most common methods for vector estimation use computationally exhaustive cross-correlation functions across the interrogation window and an exhaustive search to find the maximum correlation position. This paper proposes a novel method to vector generation in which a preprocessing blur is applied to the two image before performing a cross-correlation for only nine points. These nine points are used to approximate the original cross-correlation surface as a second-order polynomial surface that can be solved analytically to find the optima point. Three iterations of the process are used for each location converging to a precise optimum. This method is very accurate on computer-generated PIV images and solves the entire vector field faster than the original basic method at any image size. However, the success is limited to in silico PIV data and cannot produce coherent vector fields when applied to experimental data captured on a supra-aortic bypass PIV experiment. This method may find applications in other domains where the input data is closer to the perfect computer-generated particle data.