A New Algorithm for Finding Convex Hull Based on Coiling with a Minimum Lever Pitch in Double Domains and Single Direction
双域单向水平倾角最小化圈绕凸壳新算法

According to the isomorphic fundamental theorem of the convex hull construction, a more efficient new algorithm to find a convex hull based on coiling with a minimum lever pitch in double domain and single direction is advanced. It has realized the improvement of the Gift Wrapping convex hull algorithm and Coiling with a Minimum Lever Pitch in Single Domain and Single Direction Convex Hull Algorithm. This new algorithm isomorphism characteristic is: 1)"the generation of initial vertex and double domain": find out the hottommost point and the highest point on the convex hull S as the initial vertex of the con- vex hull, which has the minimum or the maximum coordinate value of the Y axis among all the points in given 2D point set (if the bottommost point is not only one, the bottommost and leftmost or the highest rightmost point should be selected). The line which take the two initial vertexes as end points divide the 2D point set into two absolute point set S_(right), S_(left). 2)in the 2D point set S_(left), do the process of seeking the newest apex with single direction: A. in S_(right), passing the last new regressive vertex,make the vertex's half line paralleled by X axis along positive direction, and find out the current vertexes with a minimum pitch to its vertex's regressive half line(as the initial line) to be the newest vertex in coiling; B. A. in S_(left),passing the last new regressive vertex,make the vertex's half line paralleled by X axis along negative direction, and find out the current vertexes with a mini- mum pitch to its vertex's regressive half line(as the final line) to be the newest vertex in coiling; 3)Deletes the sub-convex hull's inner points. And loop from"2)"to coil with double direction side by side continuingly while the reminded point set is not empty.