{-
http://mathworld.wolfram.com/ConvexPolygon.html
|a x b| = |a| * |b| * sin(theta)
a . b = |a| * |b| * cos(theta)
aL . b = |a| * |b| * sin(theta) — perp dot product
Since all vectors have Z’s scalar equals zero (all in x-y plane),
we can easily to determine convex polygon in this case by
testing all cross products’ Z scalar; they must have the same sign.
-}
type Vector = (Float, Float)
convex :: Shape -> Bool
convex (Polygon vs) = all (>=0) zScalars || all (<=0) zScalars
where
toPair :: [a] -> [(a,a)]
toPair ns = zip ns (tail (cycle ns))
vector :: (Vertex, Vertex) -> Vector
vector ((x1, y1), (x2, y2)) = (x2-x1, y2-y1)
vectors = map vector (toPair vs)
crossProductZscalar :: (Vector, Vector) -> Float
crossProductZscalar ((x1, y1), (x2, y2)) = x1 * y2 - x2 * y1
zScalars = map crossProductZscalar (toPair vectors)
convex _ = True
{-
Notes:
1. This calculates all cross product vectors’ z scale and checking their sign.
We can speed up by recursion; once find different sign than
returns Flase immediately without calculate them all.
2. The type Vector only uses inside "convex" function.
I would like to definie it only "inside" the "convex" function.
(example, under "where" of "convex")
But this seems not allowed. (syntax error) 
-}
data Shape
= Rectangle Side Side
| Ellipse Radius Radius
| RtTriangle Side Side
| Polygon [Vertex]
deriving Show
type Radius = Float
type Side = Float
type Vertex = (Float, Float)
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on Saturday, May 19th, 2007 at 11:56 am and is filed under Haskell - SOE.
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