# Exercise 8.7

One way to do this is to handle each constructor for a Region (and a Shape for those cases) and reflect those in the x-axis, i.e.

```flipX :: Region -> Region
flipX (Translate (a,b) r) = Translate (a,-b) (flipX r)
flipX (Scale (a,b) r) = Scale (a,-b) (flipX r)
flipX (Complement r) = Complement (flipX r)
flipX (r1 `Union` r2) = (flipX r1) `Union` (flipX r2)
flipX (r1 `Intersect` r2) = (flipX r1) `Intersect` (flipX r2)
flipX (HalfPlane (x1,y1) (x2,y2)) = HalfPlane (x2,-y2) (x1,-y1)
flipX Empty = Empty
flipX (Shape s) = Shape (flipXShape s)
where flipXShape (RtTriangle a b) = RtTriangle a (-b)
flipXShape (Polygon vs) = Polygon (map ((x,y) -> (x,-y)) vs)
flipXShape s = s```

And similarly (negating the x-coordinate) for flipY. Note that the order of points must change in HalfPlane, and should also be reversed in flipping a Polygon if we had the clockwise ordering constraint. Another way to solve this exercise is to use the Scale constructor on a Region:

```flipX :: Region -> Region
flipX r = Scale (1, -1) r

flipY :: Region -> Region
flipY r = Scale (-1, 1) r```

### 2 responses to “Exercise 8.7”

1. fero says:

Wow, that Scale solution is really good one.

2. Joe says:

2 minor errors in the first solution:
> flipX (Scale (a,b) r) = Scale (a,-b) (flipX r)
flipX (Scale (a,b) r) = Scale (a,b) (flipX r)
> flipXShape (Polygon vs) = Polygon (map ((x,y) -> (x,-y)) vs)
flipXShape (Polygon vs) = Polygon (map (\ (x,y) -> (x,-y)) vs)