Add simple property tests for Vertex

.envrc

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+use nix

.gitignore

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+/genstar/doc

genstar/Main.hs

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+module Main where
+
+import Control.Monad (join)
+import Test.QuickCheck (Arbitrary (arbitrary))
+
+-- | One point of a path, consisting of its \(x\) and \(y\) coordinates.
+newtype Vertex = Point (Double, Double) deriving (Eq)
+
+instance Show Vertex where
+  show (Point (x, y)) = show x ++ " " ++ show y
+
+instance Arbitrary Vertex where
+  arbitrary = do
+    x <- arbitrary
+    y <- arbitrary
+    return (Point (x, y))
+
+-- | 'vertexDistance' @p@
+-- returns the distance of a vertex to the origin
+vertexDistance :: Vertex -> Double
+vertexDistance (Point (x, y)) = sqrt (x ** 2 + y ** 2)
+
+-- | 'fromAngle' @angle@
+-- creates a point on the unit circle at the specified angle
+-- (specified in radians).
+fromAngle angle = Point (sin angle, cos angle)
+
+-- | 'scale' @s@ @p@ scales the vector to @p@ by the factor @s@.
+scale :: Double -> Vertex -> Vertex
+scale s (Point (x, y)) = Point (s * x, s * y)
+
+-- | 'move' @p1@ @p2@ adds the coordinates of @p1@ and @p2@,
+-- effectively moving @p1@ by @p2@ (or vice-versa).
+move :: Vertex -> Vertex -> Vertex
+move (Point (x1, y1)) (Point (x2, y2)) = Point (x1 + x2, y1 + y2)
+
+-- | Points \(p_0, p_2, \dots, p_{n-1}\)
+-- that should be connected,
+-- so that \(p_{i \bmod n}\) is connected to \(p_{i+1 \bmod n}\).
+newtype PolygonPath = PolygonPath [Vertex]
+
+instance Show PolygonPath where
+  show (PolygonPath (v : vs)) = "<path d=\"M " ++ show v ++ join (map (\v -> " L " ++ show v) vs) ++ " Z\"/>\n"
+  show (PolygonPath []) = ""
+
+-- | 'regularPolygonMod' @n@ @rf@ @pos@
+-- creates a regular @n@-gon
+-- with the center at @pos@
+-- that is modified in the sense that it takes @rf@,
+-- which is used to set the radius for each individual point.
+regularPolygonMod :: Integer -> (Integer -> Double) -> Vertex -> PolygonPath
+regularPolygonMod n rf pos = PolygonPath (map (\step -> move pos $ scale (rf step) $ fromAngle (fromInteger step * 2 * pi / fromInteger n)) [0 .. (n - 1)])
+
+-- | 'regularPolygon' @n@ @r@ @pos@
+-- creates a regular polygon
+-- with the radius @r@
+-- and the center at @pos@.
+regularPolygon :: Integer -> Integer -> Vertex -> PolygonPath
+regularPolygon n r = regularPolygonMod n (const (fromInteger r))
+
+-- | 'star' @n@ @r1@ @r2@ @pos@
+-- creates a star
+-- with @n@ spikes,
+-- the inner radius @r1@,
+-- the outer radius @r2@
+-- and the center @pos@.
+star :: Integer -> Double -> Double -> Vertex -> PolygonPath
+star n r1 r2 = regularPolygonMod (n * 2) ((take (fromInteger n * 2) (cycle [r1, r2]) !!) . fromInteger)
+
+main :: IO ()
+main = putStr $ join $ map (\n -> show n ++ "-gon: " ++ show (regularPolygon n 100 (Point (100, 100)))) [5, 8, 10, 15, 18, 30]

genstar/Test.hs

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+{-# LANGUAGE TemplateHaskell #-}
+
+module Test where
+
+import Main (Vertex (Point), fromAngle, move, scale, vertexDistance)
+import Test.QuickCheck (discard, quickCheck, quickCheckAll)
+
+-- | the largest acceptable difference between two doubles so they are considered equal
+epsilon :: Double
+epsilon = 1e-10
+
+-- | checks whether the distance of a vertex constructed by 'fromAngle' to the origin is 1
+prop_VertexFromAngleDistance :: Double -> Bool
+prop_VertexFromAngleDistance angle = abs (1 - vertexDistance (fromAngle angle)) < epsilon
+
+-- | checks whether the distance of a vertex scaled by an factor is multiplied by that factor (absolute).
+prop_VertexScaleDistance :: (Vertex, Double) -> Bool
+prop_VertexScaleDistance (p, s) = abs (abs s * vertexDistance p - vertexDistance (scale s p)) < epsilon
+
+-- | checks whether moving a vertex by itself equals scaling it by 2
+prop_MoveSelfEqualsScale2 :: Vertex -> Bool
+prop_MoveSelfEqualsScale2 p = move p p == scale 2 p
+
+-- | checks whether moving a vertex by itself scaled by -1 equals the origin
+prop_MoveNegativeSelfEqualsOrigin :: Vertex -> Bool
+prop_MoveNegativeSelfEqualsOrigin p = move p (scale (-1) p) == Point (0, 0)
+
+return []
+
+check = $quickCheckAll
+
+main :: IO Bool
+main = check

shell.nix

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+{ pkgs ? import <nixpkgs> { } }:
+
+pkgs.mkShell {
+  name = "emi5";
+
+  nativeBuildInputs = with pkgs; [
+    (haskellPackages.ghcWithPackages (pkgs: with pkgs; [
+      QuickCheck
+    ]))
+  ];
+}