diff --git a/app/Main.hs b/app/Main.hs
--- a/app/Main.hs
+++ b/app/Main.hs
@@ -2,6 +2,7 @@
 
 import           Codec.Picture
 import           Codec.Picture.Drawing
+import           Codec.Picture.Geometry
 
 main :: IO ()
 main = do
@@ -24,15 +25,14 @@
         -- A dark green filled triangle
         fillTriangle m 50 200 250 300 70 350 (PixelRGB8 0 150 50)
 
-        -- A blue pentagon
-        drawPolygon m
+        -- A blue filled pentagon
+        fillPolygon m ((closed . clockwise)
             [ (340, 80)
             , (245, 149)
             , (281, 261)
             , (399, 261)
             , (435, 149)
-            , (340, 80)
-            ]
+            ])
             (PixelRGB8 0 0 255)
 
     writePng "example.png" img
diff --git a/juicy-draw.cabal b/juicy-draw.cabal
--- a/juicy-draw.cabal
+++ b/juicy-draw.cabal
@@ -1,7 +1,7 @@
 name:                   juicy-draw
-version:                0.1.0.0
-synopsis:               Functions for drawing and filling lines, rectangles and polygons directly onto a mutable image
-description:            This package provides 2D primitives for drawing/fill simple 2D shapes
+version:                0.2.0.0
+synopsis:               Draw and fill lines, rectangles and polygons
+description:            This package provides 2D primitives for drawing/filling simple 2D shapes directly onto a JuicyPixels mutable image
 homepage:               https://github.com/rcook/juicy-draw#readme
 license:                MIT
 license-file:           LICENSE
@@ -24,8 +24,11 @@
   build-depends:
       JuicyPixels
     , base >= 4.7 && < 5
+    , numeric-extras
     , primitive
-  exposed-modules:      Codec.Picture.Drawing
+  exposed-modules:
+      Codec.Picture.Drawing
+    , Codec.Picture.Geometry
 
 executable juicy-draw-demo
   default-language:     Haskell2010
diff --git a/src/Codec/Picture/Drawing.hs b/src/Codec/Picture/Drawing.hs
--- a/src/Codec/Picture/Drawing.hs
+++ b/src/Codec/Picture/Drawing.hs
@@ -14,12 +14,14 @@
     ( drawLine
     , drawPolygon
     , drawRectangle
+    , fillPolygon
     , fillRectangle
     , fillTriangle
     , withDefaultMutableImage
     , withMutableImage
     ) where
 
+import           Codec.Picture.Geometry (Point2D)
 import           Codec.Picture.Types
                     ( Image
                     , MutableImage(..)
@@ -82,7 +84,7 @@
 -- | Draw a polygon in the specified colour
 drawPolygon :: (Pixel px, PrimMonad m) =>
     MutableImage (PrimState m) px   -- ^ mutable image
-    -> [(Int, Int)]                 -- ^ sequence of vertices
+    -> [Point2D]                    -- ^ sequence of vertices
     -> px                           -- ^ colour
     -> m ()                         -- ^ action
 drawPolygon _ [] _ = pure ()
@@ -139,6 +141,18 @@
                 w2 = orient2D v1x v1y v2x v2y x y
             when (w0 >= 0 && w1 >= 0 && w2 >= 0) $ writePixel m x y px
 
+-- | Fill a polygon as a series of triangles with the specified colour
+fillPolygon :: (Pixel px, PrimMonad m) =>
+    MutableImage (PrimState m) px   -- ^ mutable image
+    -> [Point2D]                    -- ^ sequence of vertices
+    -> px                           -- ^ colour
+    -> m ()                         -- ^ action
+fillPolygon m ((x1, y1) : vs) px =
+    let temp = zip vs (drop 1 vs)
+    in for_ temp $ \((x2, y2), (x3, y3)) ->
+        fillTriangle m x1 y1 x2 y2 x3 y3 px
+fillPolygon _ _ _ = pure ()
+
 orient2D :: Int -> Int -> Int -> Int -> Int -> Int -> Int
 orient2D ax ay bx by cx cy = (bx - ax) * (cy - ay) - (by - ay) * (cx - ax)
 
@@ -152,5 +166,5 @@
     | a > b = max a c
     | otherwise = max b c
 
-minMax3 :: Int -> Int -> Int -> (Int, Int)
+minMax3 :: Int -> Int -> Int -> Point2D
 minMax3 a b c = (min3 a b c, max3 a b c)
diff --git a/src/Codec/Picture/Geometry.hs b/src/Codec/Picture/Geometry.hs
new file mode 100644
--- /dev/null
+++ b/src/Codec/Picture/Geometry.hs
@@ -0,0 +1,64 @@
+{-|
+Module      : Codec.Picture.Geometry
+Description : Essential geometry for 2D shapes
+Copyright   : (C) Richard Cook, 2018
+Licence     : MIT
+Maintainer  : rcook@rcook.org
+Stability   : stable
+Portability : portable
+
+Essential geometric functions to generate 2D shapes and paths
+-}
+
+module Codec.Picture.Geometry
+    ( FPoint2D
+    , Point2D
+    , centroid
+    , clockwise
+    , closed
+    ) where
+
+import           Data.Foldable (foldl')
+import           Data.List (sortBy)
+import           Numeric.Extras (fmod)
+
+-- | 2D coordinate
+type Point2D = (Int, Int)
+
+-- | 2D coordinate
+type FPoint2D = (Double, Double)
+
+-- | Compute the centroid of a polygon
+centroid ::
+    [Point2D]           -- ^ sequence of vertices
+    -> Maybe FPoint2D   -- ^ centroid
+centroid [] = Nothing
+centroid ps =
+    let (totalX, totalY, n') = foldl' (\(accX, accY, n) (x, y) -> (accX + x, accY + y, n + 1)) (0, 0, 0 :: Int) ps
+        n'' = fromIntegral n'
+    in Just (fromIntegral totalX / n'', fromIntegral totalY / n'')
+
+-- | Closed sequence of vertices
+closed ::
+    [Point2D]       -- ^ sequence of vertices
+    -> [Point2D]    -- ^ sequence of vertices
+closed [] = []
+closed ps@(p : _ ) = ps ++ [p]
+
+-- | Sequence of vertices in clockwise order relative to its centroid
+clockwise ::
+    [Point2D]       -- ^ sequence of vertices
+    -> [Point2D]    -- ^ sequence of vertices
+clockwise ps =
+    case centroid ps of
+        Just (cx, cy) -> sortBy (\(ax, ay) (bx, by) ->
+            let a1 = angle (fromIntegral ax) (fromIntegral ay) cx cy
+                a2 = angle (fromIntegral bx) (fromIntegral by) cx cy
+            in compare a2 a1) ps
+        Nothing -> []
+
+angle :: Double -> Double -> Double -> Double -> Double
+angle x y cx cy = fmod (degrees (atan2 (x - cx) (y - cy)) + 360) 360
+
+degrees :: Double -> Double
+degrees rad = rad * pi / 180