AP-Assignment0 - Look at Those Curves

The objective of this assignment is to gain hands-on programming experience with Haskell.

The goal is to implement a library, Curves, for working with piecewise linear curves in the plane (based on an idea by Hansen and Rischel, who in turn got the idea from Maarten M. Fokkinga).

SYNOPSIS

Example of usage:

toFile  (hilbert $ hilbert $ hilbert $ hilbert $ curve (point (0,0)) []) "hilbert.svg"

DESCRIPTION

The sections below describe the most important points of the assignment.

Point and Curve data types

data Point = Point { x :: Double, y :: Double} deriving (Show)
type Curve = [Point]

Basically a Curve is a list of Points

Comparing 2 points

We can use (==) for comparing 2 points because we declared Point as an instance of Eq

The function reflect

We used map for reflecting all of the points to a given Axis

reflect :: Curve -> Axis -> Double -> Curve
reflect points axis axisValue
	= map (reflectPoint axis axisValue) points

Calculating the bounding box

To compute the lower left and the upper right corner of the bounding box we need to compare the smallest (x,y) coordinate and the biggest (x,y) coordinate from all the points in the list. We do this buy applying foldl on the Curve so that on every step we find the min/max values.

bbox :: Curve -> (Point, Point)
bbox [] = error "no items in the list"
bbox (aPoint:[]) = (aPoint, aPoint)
bbox points = 
		let (minPoint, maxPoint) = (
				Point {x = (min (x (head points)) (x (head (tail points)))) , y = (min (y (head points)) (y (head (tail points))))}, 
				Point {x = (max (x (head points)) (x (head (tail points)))) , y = (max (y (head points)) (y (head (tail points))))})
		in foldl findMinMaxValues (minPoint, maxPoint) (tail (tail points))

Printing the SVG

We do a basic string concat using (++) for example:

toSVG :: Curve -> String
toSVG points = 
	"<svg xmlns=\"http://www.w3.org/2000/svg\" width=\""
	 ++ (show (ceiling (width points))) ++ "px\" height=\""
	 ++ (show (ceiling (height points))) ++ "px\" version=\"1.1\"><g>" 
	 ++ printPoints points

RESULT

A nice figure using Hilbert curves