A predictor-corrector method for graphing level curves

Present techniques used in graphing level curves mainly involve time-consuming numerical methods which are repeated until the desired accuracy is reached. A predictor-corrector method is developed to determine points on a level curve given the partial derivatives of a function. While this method is proven for level curves of constant curvature, it is demonstrated to be useful for all continuous curves which have uniform curvature within a small neighborhood of any point on that curve.Conceptually, this method uses the gradient of the function to determine two points close to the level curve that passes through a starting point. A third point lying on the level curve is geometrically determined. This point is then used as a new starting point, thereby tracing a series of segments of a level curve.This technique is demonstrated with a Pascal program which graphs level curves of various functions and a second Pascal program fragment which graphs equipotential lines of electric fields.