Morph | Topcoder Archive

Problem Statement

Some interesting visual effects can be created by "morphing" one shape into another. It is necessary to be able to calculate where a point in the original shape ends up in the new shape. The simplest case is when the objects are both two dimensional triangle shapes. In this case, the morphing can be done by gradually translating, rotating, reflecting, and scaling the original until it has become the morphed version.

Create a class Morph that contains method coordSum that is given the 3 vertices of an original triangle, the 3 vertices of the morphed triangle, and a point P in the original triangle (possibly on its boundary) and that calculates where P ends up in the morphed triangle. It returns the sum of the x and y coordinates of P's final location.

The parameters are int[]s x and y giving the 3 vertices of the original triangle, int[]s newx and newy giving the 3 vertices of the morphed triangle, and ints px and py giving the coordinates of a point in the original triangle. The i-th element of x and y is to be morphed into the i-th element of newx and newy.

Definition

Class:: Morph
Method:: coordSum
Parameters:: int[], int[], int[], int[], int, int
Returns:: double
Method signature:: double coordSum(int[] x, int[] y, int[] newx, int[] newy, int px, int py)
(be sure your method is public)

Notes

If the return has either a relative or absolute error less than 1.0E-9 it is acceptable.

Constraints

x, y, newx, and newy will each contain exactly 3 elements.
All values (px, py, and each element of x, y, newx, and newy) will be between -1000 and 1000 inclusive.
The points given by x,y will not be colinear.
The points given by newx,newy will not be colinear.
px,py will be contained in the (closed) triangle given by x and y.

Examples

```
{0,0,4}
```
```
{0,3,0}
```
```
{3,3,7}
```
```
{1,4,1}
```
```
2
```
```
0
```
```
Returns: 6.0
```
The first triangle is morphed onto the second by translation of 3 in the x direction and 1 in the y direction. So 2,0 ends up at 5,1 and the returned value is 5+1 = 6.
```
{0,0,4}
```
```
{0,3,0}
```
```
{3,7,3}
```
```
{1,1,4}
```
```
2
```
```
0
```
```
Returns: 5.5
```
These are the same triangles as in the preceding example, but the vertices are mapped differently. The point 2,0 ends up at 3,2.5
```
{0,0,4}
```
```
{0,3,0}
```
```
{3,7,3}
```
```
{1,1,4}
```
```
4
```
```
0
```
```
Returns: 7.0
```
The point 4,0 is the third vertex of the original triangle, so it is morphed to the third vertex of the new triangle which is 3,4.

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