Java：凸多边形的周长

Question

I have an ArrayList of some Point -s. It's guaranteed that the Points are part of a convex polygon.

How can I calculate the perimeter of this convex polygon?

Update: The Points in the ArrayList are out of any order

Update 2: All the points are part of the convex polygon's edge

Answer 1

Are the points in order? If so, you just need to sum up the distance from each vertex to the next

Answer 2

对每两个连续点之间的距离求和。

Answer 3

If the points are not ordered, its impossible without determining the correct order. Thats because if there are more than 3 points there is more than one polygon they could form.

I'm not entirely sure the constraint that the points are forming a convex polygon is sufficient to determine a canonic shape from the point cloud.

My guess is that by taking a random point from the list, and then looking for the nearest remaining point you can build a canonic order. From there its just summing up the length of the lines formed by consecutive points.

Edit: On second thought, scratch that idea. It won't work for all cases. That leaves you with permuting the points and checking if the formed polygon is indeed convex.

The question on how to check if a polygon is convex has been asked and answered here: How do determine if a polygon is complex/convex/nonconvex?