From 8e353802f75521d523fa526974792e569fec6758 Mon Sep 17 00:00:00 2001
From: Jan Sucan <jan@jansucan.com>
Date: Sun, 12 Mar 2023 11:44:22 +0100
Subject: 3_b_10: Add solution

---
 ch03/3_b_9.hs | 31 +++++++++++++++++++++++++++----
 1 file changed, 27 insertions(+), 4 deletions(-)

(limited to 'ch03/3_b_9.hs')

diff --git a/ch03/3_b_9.hs b/ch03/3_b_9.hs
index c6595de..d276c7b 100644
--- a/ch03/3_b_9.hs
+++ b/ch03/3_b_9.hs
@@ -1,9 +1,32 @@
--- Consider three two-dimensional points a, b, and c. If we look at the angle
--- formed by the line segment from a to b and the line segment from b to c, it
--- either turns left, turns right, or forms a straight line. Define a Direction
--- data type that lets you represent these possibilities.
+-- 1. Consider three two-dimensional points a, b, and c. If we look at the angle
+--    formed by the line segment from a to b and the line segment from b to c,
+--    it either turns left, turns right, or forms a straight line. Define a
+--    Direction data type that lets you represent these possibilities.
+--
+-- 2. Write a function that calculates the turn made by three 2D points and
+--    returns a Direction.
 
 data Direction = DLeft
                | DRight
                | DStraight
                deriving (Show)
+
+type Point = (Int, Int)
+
+-- The algorithm for computing the direction is taken from
+-- https://en.wikipedia.org/wiki/Graham_scan
+direction :: Point -> Point -> Point -> Direction
+direction (x1, y1) (x2, y2) (x3, y3)
+  | cross_product_z > 0 = DLeft
+  | cross_product_z < 0 = DRight
+  | otherwise = DStraight
+  where cross_product_z = (x2 - x1) * (y3 - y1) - (y2 - y1) * (x3 - x1)
+
+-- [1 of 1] Compiling Main             ( 3_b_9.hs, interpreted )
+-- Ok, one module loaded.
+-- ghci> direction (1,1) (2,2) (3,3)
+-- DStraight
+-- ghci> direction (1,1) (2,2) (3,4)
+-- DLeft
+-- ghci> direction (1,1) (2,2) (3,2)
+-- DRight
-- 
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