An efficient approach for computing distance between two quadratic surfaces

In computer-aided design systems and virtual reality, the computation of distance between two objects is required. The problem of distance computation has been well studied for polyhedral objects in the past years. However, the curve surfaces of objects are often approximated by polyhedral, suffering from accuracy problem due to approximation errors. In order to improve the accuracy, the surfaces of objects are approximated by piecewise quadratic surfaces, and the conditional relative extremum is calculated with Lagrange multiplier, which results in solving a system of two bivariate polynomials with high degree. In this paper, an efficient approach is presented, yielding a system of two bivariate polynomial with degree 6. Compared with the other bivariate polynomials arising from distance computation for two quadratic surfaces, the degree of polynomials from our approach is the lowest and the computation amount is the least so far. Hence, the new approach can meet the requirement for real-time computation in the virtual reality.