✎ fp:lab07 [books]

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====== 7. Working with matrices and images using higher-order functions ======

===== 7.1. Bitmaps as matrices =====

We can represent images as matrices of pixels. In our example a pixel will be represented as a ''Char'', which can take the values: '*' (signifying that the respective pixel is //on//) and ' ' (the pixel is off). 

<code haskell> type Image = [String] </code>

For instance, a rectangle could be represented as:
<code>
********
*      *
********
</code>

more precisely, as the string: 
<code haskell>
m = "********\n*      *\n********\n"
</code>

7.1.1. Implement an image-displaying function. Use the image from the Appendix as a test.
<code haskell>
toStringImg :: Image -> String
toStringImg = 

</code>

Add the following function in order to view images in a nicer format:
<code haskell>
displayImg = putStrLn . toStringImg
</code>

7.1.2. Implement a function which flips an image horizontally:
<code haskell>
flipH :: Image -> Image 
flipH = 
</code>

7.1.3. Implement a function which flips an image vertically:
<code haskell>
flipV :: Image -> Image
flipV = 
</code>

7.1.4. Implement a function which rotates an image 90grd clockwise
<code haskell>
rotate90r :: Image -> Image
rotate90r =
</code>

7.1.5. Implement a function which rotates an image -90grd clockwise
<code haskell>
rotate90l :: Image -> Image
rotate90l = 
</code>

7.1.6. Implement a function which inverts an image: ' ' becomes * and * becomes ' ':
<code haskell>
invert :: Image -> Image
invert = 
</code>

===== 7.2. Combining images =====

7.2.1. Implement a function ''maskKeep'' which takes a mask and some image and only keeps the part of image which overlays the mask. Use the mask and the logo from Appendix to test it.
<code haskell>
maskKeep :: Image -> Image -> Image
maskKeep = 
</code>
$math[ maskKeep \left(\begin{array}{ccc}  &  & * \\  &  & * \\  &  & * \\ \end{array}\right) \left(\begin{array}{ccc} * &  & * \\ * &  &  \\ * &  & * \\ \end{array}\right) = \left(\begin{array}{ccc}  &  & * \\  &  &  \\  &  & * \\ \end{array}\right) ]

7.2.2. Implement a function ''maskDiscard'' which takes a mask and some image and discards the part of the mask which overlays the image.

$math[ maskDiscard\left(\begin{array}{ccc}  &  & * \\  &  & * \\  &  & * \\ \end{array}\right) \left(\begin{array}{ccc} * &  & * \\ * &  &  \\ * &  & * \\ \end{array}\right) = \left(\begin{array}{ccc}  &  &  \\  &  & * \\  &  &  \\ \end{array}\right) ]

7.2.3. Implement the ''union''' of two images.
<code haskell>
unionp :: Image -> Image -> Image
unionp = 
</code>
$math[ union \left(\begin{array}{ccc}  &  & * \\  &  & * \\  &  & * \\ \end{array}\right) \left(\begin{array}{ccc} * &  & * \\ * &  &  \\ * &  & * \\ \end{array}\right) = \left(\begin{array}{ccc} * &  & * \\ * &  & * \\ * &  & * \\ \end{array}\right) ]

7.2.4. Implement a function which takes a list of transformations and an image and applies all those transformations.
<code haskell>
transformationSequence :: [Image -> Image] -> Image -> Image
</code>
Test it with the following sequence
<code haskell>
seq1 = transformationSequence [invert, unionp mask, rotate90r]
</code>

===== 7.3 Number Matrices =====

7.3.1. Write a function that computes the scalar product with an integer:

$math[ \displaystyle 2 * \left(\begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \\ \end{array}\right) = \left(\begin{array}{ccc} 2 & 4 & 6 \\ 8 & 10 & 12 \\ 14 & 16 & 18 \\ \end{array}\right)] 

<code haskell>
vprod :: Integer -> Matrix -> Matrix
vprod v = 
</code>

7.3.2. Write a function which adjoins two matrices by extending rows:

$math[ \displaystyle \left(\begin{array}{cc} 1 & 2 \\ 3 & 4\\\end{array}\right)  hjoin \left(\begin{array}{cc} 5 & 6 \\ 7 & 8\\\end{array}\right) = \left(\begin{array}{cc} 1 & 2 & 5 & 6 \\ 3 & 4 & 7 & 8\\\end{array}\right) ]

<code haskell>
hjoin :: Matrix -> Matrix -> Matrix
hjoin = 
</code>

7.3.3. Write a function which adjoins two matrices by adding new rows:

$math[ \displaystyle \left(\begin{array}{cc} 1 & 2 \\ 3 & 4\\\end{array}\right)  vjoin \left(\begin{array}{cc} 5 & 6 \\ 7 & 8\\\end{array}\right) = \left(\begin{array}{cc} 1 & 2 \\ 3 & 4 \\ 5 & 6\\ 7 & 8\\ \end{array}\right) ]

<code haskell>
vjoin :: Matrix -> Matrix -> Matrix
vjoin = 
</code>

7.3.4. Write a function which adds two matrices.

<code haskell>
msum :: Matrix -> Matrix -> Matrix
msum = 
</code>

===== Appendix =====

<code haskell>
logo = [l1,l2,l3,l4,l5,l6,l7,l8,l9,l10,l11,l12,l13,l14,l15,l16,l17,l18,l19]
    where l1 ="        ***** **            ***** **    "
          l2 ="     ******  ****        ******  ****   "
          l3 ="    **   *  *  ***      **   *  *  ***  "
          l4 ="   *    *  *    ***    *    *  *    *** "
          l5 ="       *  *      **        *  *      ** "
          l6 ="      ** **      **       ** **      ** "
          l7 ="      ** **      **       ** **      ** "
          l8 ="    **** **      *      **** **      *  "
          l9 ="   * *** **     *      * *** **     *   "
          l10="      ** *******          ** *******    "
          l11="      ** ******           ** ******     "
          l12="      ** **               ** **         "
          l13="      ** **               ** **         "
          l14="      ** **               ** **         "
          l15=" **   ** **          **   ** **         "
          l16="***   *  *          ***   *  *          "
          l17=" ***    *            ***    *           "
          l18="  ******              ******            "
          l19="    ***                 ***             "
</code>

<code haskell>
mask = [l1,l2,l3,l4,l5,l6,l7,l8,l9,l10,l11,l12,l13,l14,l15,l16,l17,l18,l19]
    where l1 ="                       *****************"
          l2 ="                       *****************"
          l3 ="                       *****************"
          l4 ="                       *****************"
          l5 ="                       *****************"
          l6 ="                       *****************"
          l7 ="                       *****************"
          l8 ="                       *****************"
          l9 ="                       *****************"
          l10="                       *****************"
          l11="                       *****************"
          l12="                       *****************"
          l13="                       *****************"
          l14="                       *****************"
          l15="                       *****************"
          l16="                       *****************"
          l17="                       *****************"
          l18="                       *****************"
          l19="                       *****************"
</code>