We propose a new algorithm for a classical problem in the planer computational geometry: computing a shortest path between two points in the presence of circular obstacles. Proposed algorithm actually computes a path tree that encodes a shortest path between given two points. Types of path are defined as a tangent line segment between circles, between point and circle, or as an arc. Using circle set voronoi diagram, geometric information that is very useful to search circles is obtained. The key of proposed algorithm is the reduction of the number of circles to need for constructing path tree. The main advantages of our algorithm are its robustness, speed, and the simplicity in implementation.

Presented in this paper is an algorithm to compute a Voronoi diagram of circles in a circle, where circles are located in a large circle. Given circles in a large circle, the region in the plane is divided into regions associated with the given circles. The proposed algorithm uses point Voronoi diagram, and then some topological remedies are applied so that we obtain proper initial topology including enclosing circle. From this initial topology, we can obtain the correct topology by a series of edge-flip operations. After getting the correct topology, the equations of edges are computed and represented in a rational quadratic Bézier curve form.

In this study, an accelerated carbonation process was applied to stabilize hazardous heavy metals of industrial solid waste incineration (ISWI) bottom ash and fly ash, and to reduce CO2 emissions. The most commonly used method to stabilize heavy metals is accelerated carbonation using a high water-to-solid ratio including oxidation and carbonation reactions as well as neutralization of the pH, dissolution, and precipitation and sorption. This process has been recognized as having a significant effect on the leaching of heavy metals in alkaline materials such as ISWI ash. The accelerated carbonation process with CO2 absorption was investigated to confirm the leaching behavior of heavy metals contained in ISWI ash including fly and bottom ash. Only the temperature of the chamber at atmospheric pressure was varied and the CO2 concentration was kept constant at 99% while the water-to-solid ratio (L/S) was set at 0.3 and 3.0 dm3/kg. In the result, the concentration of leached heavy metals and pH value decreased with increasing carbonation reaction time whereas the bottom ash showed no effect. The mechanism of heavy metal stabilization is supported by two findings during the carbonation reaction. First, the carbonation reaction is sufficient to decrease the pH and to form an insoluble heavy metal-material that contributes to a reduction of the leaching. Second, the adsorbent compound in the bottom ash controls the leaching of heavy metals; the calcite formed by the carbonation reaction has high affinity of heavy metals. In addition, approximately 5 kg/ton and 27 kg/ton CO2 were sequestrated in ISWI bottom ash and fly ash after the carbonation reaction, respectively.