Abstract
This paper shows an approximate solution to restricted Weber problems with Weighted Regions. By measuring the shortest-path distances of a random Delaunay Network, we provide the method to convert Weber problems under complex situations into simple and practical problems of shortest-path finding on weighted networks. And, we verify that the weighted shortest-path of a Delaunay network approximately obeys both the rule of Snell's Law which describes the refraction of light and the one of Lensmaker's equation, as the exact shortest-path through weighted regions obeys theoretically. Moreover, we solved a sample Weber problem with free-shaped and weighted regions.
