A point-wise approach that can be used efficiently in the numerical solution of Electric Field Integral Equations is introduced. The algorithm is based on the so-called magic distance concept, which defines exactly the point-to-point equivalent of a four-dimensional integral. Magic distance values are rigorously obtained in the electrostatic case and their usefulness is demonstrated. The concept is generalized to the electrodynamic case, resulting in a family of very simple magic-distance inspired algorithms that maintain the overall accuracy of Galerkin formulations without appreciable deterioration in the overall accuracy. (c) 2013 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2013.