Abstract: The Fermat location problem consists of searching for a point on a plane，such that the sum of distances from the feature point to each point in the given set is minimized．On-line Fermat location problem arises when points are allowed to be inserted or deleted arbitrarily in the given point set．The problem is tackled using contour line extracting technique in scientific visualization，and an on-line performance is obtained．The presented method can be considered as a generic one for solving a series of problems where some specific location is searched in a plane and other related issues．Three examples： on-line largest empty circle，on-line smallest enclosing circle，and on-line range search，are shown here．Case studies show that the given method has wide field of applications．