Research And Implementation On The Algorithm For Computing The Area Of Union Of Circles

The computing of the area covered by N circles placed randomly on a plane iscalled the computing of the area of the union of circles, it is not only a a basic algorithmin computational geometry,CAD/CAM and computer graphics, but also has strongapplication background. The computing of area of the union of circular arcs as onemethod to calulate the area of the union of circles, refers to the entire area divied intothe area with circular arc and the area without circular arc. As a calculating of complexshape collection area, it has important practical significance in the studing with thealgorirhm of computing the area of union of circles, needing to search for effectivesegmentation and accurately numerical methods.By studying a variety of algorithms to calculate the area of a circle, and especiallyagainst to the repeat counting problem in the area calculation algorithm of the union ofcircular arcs, this article proposes an improved algorithm for it. In the improvedalgorithm, the problem of judging constraint arcs’ direction vaguely and merging withconstraint arcs wrongly have been solved by quantitative process with constraints arcs,and the area double counting has been avoided thought the deletion process of circlewhose constraint arc is a full arc. Though a concret example verifies the correctness ofimprobed alogorithm, the the results show that the improved algorithm can effectivelysolve those problems of the original algorithm in calculating the area of union of circles,and the time complexity of the algorithm is not increased.Finally, Qt implementsdesktop application and HTML5implements network visualization, making a goodcombination between grapgics and computer technology.