Shadow | Topcoder Archive

Problem Statement

We are going to plant a tree on level ground near a streetlight, and we want to know how big a shadow it will cast. We will model the tree as a (possibly degenerate) rectangular solid, and treat the streetlight as casting rays from a single point. We will use an x,y,z coordinate system that is aligned with the rectangular solid and in which y is the distance above ground level.

int[] tree contains exactly 6 elements, namely the x,y,z coordinates of one corner of the rectangular solid followed by the coordinates of the diagonally opposite corner. int[] light contains exactly 3 elements, the x,y,z coordinates of the streetlight. Given tree and light, return the area of the shadow, or return -1 to indicate that the shadow has an infinite area. If the shadow is an infinitely long line, return 0 as its area.

Definition

Class:: Shadow
Method:: area
Parameters:: int[], int[]
Returns:: double
Method signature:: double area(int[] tree, int[] light)
(be sure your method is public)

Notes

A return value with either an absolute or relative error of less than 1.0E-9 is considered correct.

Constraints

tree will contain exactly 6 elements.
light will contain exactly 3 elements.
Each element of tree and of light will be between 1 and 10, inclusive.
The coordinates of the light will not lie on the boundary of the tree.

Examples

```
{1,1,1, 10,1,1}
```
```
{5,5,5}
```
```
Returns: 0.0
```
This tree is just a line so its shadow has no area.
```
{1,3,1, 10,1,1}
```
```
{2,2,2}
```
```
Returns: -1.0
```
This tree is just a rectangle. Its shadow covers an infinite rectangular area on the ground.
```
{1,1,1, 2,2,2}
```
```
{3,3,3}
```
```
Returns: 15.75
```
This is a unit cube one unit above the ground. The shadowed area is a six-sided polygon.
```
 {1,1,1, 3,3,3} 
```
```
{2,2,2}
```
```
Returns: -1.0
```
When the light is inside the tree the shadow extends everywhere.

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