geometric matching of two dimensional objects

The system to be implemented will be a user-based system using graphical user interfaces(java). Given an object A and its set of coordinate points, can we find another object that is exactly the same as object A or somewhat similar. A user will specify the source object to be used in the matching process. The attributes and properties of geometric object to be used in the matching process will be captured, stored, and used. The first step in the matching process to be performed will entail considering the source and the target object's coordinate point information. If the source and the target object have the same coordinate points, then we could say that the two objects match perfectly. When a point-wise comparison is done, the results can range from an exact match to objects being somewhat similar or objects not having a match. Depending on the result the matching process yields, equivalence can be further analyzed. If the point-wise comparison showed that the source and target objects were somewhat similar, say about 96% similar or 4% margin of error, then, we could perform other matching techniques to find out whether we accept the object or reject the object. One of these techniques is to apply Voronoi and Delaunay triangulation to the defined set points. The Voronoi diagram is created from a set of point by dividing the plane into regions, where each region consists of the area closest to one of the points. Voronoi diagrams allow us to perform additional computations on the geometric objects and give us the difference between the points in the source and target objects. Given this information, we could then figure out whether we accept or reject the object. If the Voronoi diagramming information proved to produce results that still could not determine whether a match exist or not, because of the closeness of the source and the target object, we would further our analysis by using Delaunay triangulation techniques. Delaunay triangulation is the geometric dual of the Voronoi diagrams, (i.e. the go hand-in-hand). This technique gives the user a visual perspective of the object's structure. If the user recognizes a significant difference, then he/she could reject the object. If the objects are so similar that the user cannot tell whether the objects are the same, the user can specify computations on the angles that exist within the object. We could then determine whether we accept or reject the object. ## Deliverables Also these are for 2d objects , example Source object x y axis (2,1, 3,3, 8,6) target object x y axis (2,2, 3,3, 5,6) etc... Find the difference in the coordinate points i.e point-wise comparison, giving a 10% margin of error. If within that limit and not an exact match do further analysis, voronoi and delaunay triangulation to see if we could consider the source and target somewhat equivalent. Complete and fully-functional working program(s) in executable form as well as complete source code of all work done. ## Deadline information phase 1, point-wise comparison within 2 weeks from the day bid accepted. phase 2, voronoi analysis within 2 weeks of completion of phase one. phase 3, delaunay triangulation analysis within 2 weeks of completion of phase 2. phase 4, entire system integrated, 1 week after completion of phase 3