The intersection of two surfaces, approximating curves, has been seen one of problematic issue in geometrics, computer graphics & engineering. With the rising interest in computing design field, surface intersection specifically turned into focal point of several studies. Its significant application in these fields makes it yet fascinating topic for research. This paper targets to lessening time and error needs for computation cycle of surface intersection. For this purpose, a robust algorithm for approximating parametric-parametric, explicit-explicit, explicit-implicit surface intersection curves is proposed in this study. The proposed process begins with the identification of "turning & boundary" points from an array of surface intersection points, and then uses an iterative optimization technique called Genetic Algorithm (GA) with a quadratic spline to approximate these locations. It has been used to determine the best fit curve by determining the optimum shape parameter values specified in the quadratic spline description. The suggested approach is advantageous since it does not include any unnecessary data points for the intended objectives. Experiments show that this strategy is successful and a superior option for locating solutions to surface intersection issues with the least amount of error.