# 07.29.07

## Exercise 8.4

Posted in Uncategorized at 11:49 pm by admin

The simplest way to allow vertices in clockwise or anticlockwise order is to define isRightOf analogously to isLeftOf, and combine them with a boolean expression.

```isLeftOf :: Coordinate -> Ray -> Bool (px,py) `isLeftOf` ((ax,ay), (bx,by)) = let (s,t) = (px-ax, py-ay) (u,v) = (px-bx, py-by) in s * v >= t * u   isRightOf :: Coordinate -> Ray -> Bool (px,py) `isRightOf` ((ax,ay), (bx,by)) = let (s,t) = (px-ax, py-ay) (u,v) = (px-bx, py-by) in s * v <= t * u   (Polygon pts) `containsS` p = let leftOfList = map isLeftOfp (zip pts (tail pts ++ [head pts])) isLeftOfp p' = isLeftOf p p' rightOfList = map isRightOfp (zip pts (tail pts ++ [head pts])) isRightOfp p' = isRightOf p p' in and leftOfList || and rightOfList```

1. August 3, 2007 at 10:29 pm

[…] our updated definition of `containsS` for polygons from Exercise 8.4. To prove the second fact is […]

2. August 5, 2007 at 9:30 pm

[…] Exercise 8.4 for definitions of isLeftOf and […]

3. Wieslaw Poszewiecki said,

April 16, 2008 at 8:31 am

Seems this also works:

(Polygon pts) `containsS` p
= let leftOfList = map (isLeftOf p)
(zip pts (tail pts ++ [head pts]))
in and leftOfList || not (or leftOfList)

4. Wieslaw Poszewiecki said,

April 16, 2008 at 8:39 am

Can anyone advise me how to forbid this control

>(Polygon pts) `containsS` p
> = let leftOfList = map (isLeftOf p) (zip pts (tail pts ++ [head pts]))
> in and leftOfList || not (or leftOfList)

5. Wieslaw Poszewiecki said,

April 16, 2008 at 8:47 am

Sorry,
I noticed that my previous solution does not work
if some points are on sides.

6. Wieslaw Poszewiecki said,

April 16, 2008 at 9:03 am

This one seems to work also for sides

>(px,py) `isLeftOf` ((ax,ay),(bx,by))
> = let (s,t) = (px-ax, py-ay)
> (u,v) = (px-bx, py-by)
> in s*v – t*u

>(Polygon pts) `containsS` p
> = let leftOfList = map (isLeftOf p) (zip pts (tail pts ++ [head pts]))
> in and (map (>=0) leftOfList) || and (map (<=0) leftOfList)

April 17, 2008 at 9:38 pm

To preserve code formatting, use <pre> tags around it.

8. fero said,

July 22, 2008 at 10:15 am

This is my solution and works even with [] because of and function:

(Polygon pts) `containsS` p = let leftOfList = map (isLeftOf p)
(zip pts (tail pts ++ [head pts]))
in and (map (==head leftOfList) leftOfList)

9. Ricky Liu said,

March 4, 2014 at 7:15 am

@fero, your solution is similar to the first one given by Wieslaw. As Wieslaw already said it did not work when p lies on one of the edges of the polygon.