A two-dimensional shape can be defmed by its boundary-polygon, which is simply a list of all coordinates ordered by a traversal of its outline. See the following figure for an example. The left...

A two-dimensional shape can be defmed by its boundary-polygon, which is simply a list of all coordinates ordered by a traversal of its outline. See the following figure for an example.

The left picture shows the original shape; the middle picture, the outline of the shape. The rightmost picture shows an abstracted boundary, using only the "most important" vertices. We can assign an importance measure to a vertex P by considering its neighbors L and R. We compute the distances LP, PR, and LR. Call these distances 11, 12, and 13. Define the importance as 11 + 12 - 13.

Write a program to read a set of coordinates that form an outline and reduce the list to the n most significant ones, where n is an input value. Draw the initial and resulting shapes. Note: This problem and the algorithm for its solution are based on the paper: L J. Latecki and R. Lakamper, "Convexity Rule for Shape Decomposition Based on Discrete Contour Evolution," Computer Vision and Image Understanding (CVIU) 73(1999): 441-454.