PolygonRotation | Topcoder Archive

Problem Statement

We have a convex polygon in the XY plane. The vertices of the polygon are the points (x[0], y[0]), (x[1], y[1]), ... in clockwise order. You are given the int[]s x and y.
In order to make the implementation simpler the polygon and its representation satisfy some additional constraints. Please read the Constraints section carefully.
A three-dimensional solid is obtained by rotating this polygon around the Y axis. Compute and return the volume of the resulting solid.

Definition

Class:: PolygonRotation
Method:: getVolume
Parameters:: int[], int[]
Returns:: double
Method signature:: double getVolume(int[] x, int[] y)
(be sure your method is public)

Notes

The returned value must have an absolute or relative error less than 1e-9.

Constraints

x will contain between 3 and 50 elements, inclusive.
y will contain the same number of elements as x.
Each element of x and y will be between -100 and 100, inclusive.
The polygon will be convex.
All vertices of the polygon will be distinct.
The polygon will have exactly two vertices on the Y axis. Let's denote them (0, Ymin) and (0, Ymax) with Ymin < Ymax.
The vertices will be listed in clockwise order, starting with (0, Ymax).
The y-coordinates of all vertices will be between Ymin and Ymax, inclusive.
No three points will lie on the same line.

Examples

```
{0, 1, 1, 0}
```
```
{1, 1, 0, 0}
```
```
Returns: 3.141592653589793
```
The polygon is a square with sides parallel to the coordinate axes. One of the sides of the square belongs to the Y axis. The resulting solid of revolution is a right cylinder of height 1 and radius 1.
```
{0, 1, 0, -1}
```
```
{2, 1, 0, 1}
```
```
Returns: 2.0943951023931953
```
This polygon is also a square. Each of its sides is angled at 45 degrees to the coordinate axes. The resulting solid of revolution is the union of two cones, each with base radius 1 and height 1.

{0, 3, 0, -2, -2}

{2, 0, -3, -1, 1}

Returns: 49.91641660703782

{0, 3, 3, 0, -1, -1}

{2, 2, -2, -2, -1, 1}

Returns: 113.09733552923255

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