Computational morphology of debris and alluvial fans on irregular terrain using the visibility polygon

Abstract

A computational method is proposed to simulate the morphology of debris and alluvial fans formed on irregular terrain, where they may abut or bend around steeper valley sides or obstacles. Fan elevation and slope are assumed to depend only on the distance from the apex, measured along straight or winding paths. When there are no obstacles, the resulting fan morphologies are simply surfaces of revolution, with a straight (for constant slope fans) or curved generatrix (for concave fans). When obstacles are present, however, fan surfaces of great variety can be produced. To capture the resulting morphology, we exploit a powerful tool of computational geometry: the visibility polygon algorithm. Starting from one or more initial fan apexes, the proposed algorithm iteratively generates fan sectors with new apexes along their margins, until the fan complex has attained its maximal extent. To validate the method, we first apply it to several cases with analytical solutions, such as single fans on faceted topography, and multiple coalescing fans with weld lines. We then apply the method to real valleys, and check that it can reproduce observed fan morphologies even in complex cases involving diffluences and confluences.