====== L07. For expressions ======

In this lab, we will use matrices to encode Bitmap images. The format is called BPM, and more details are available [[https://en.wikipedia.org/wiki/Netpbm#File_formats|here]]. Our format will be grayscale only. Each pixel of the matrix is encoded as an integer, with values from 0 to 255. Some examples are shown below:

<code>
    0 0 1 0 0
    0 1 0 1 0
    0 1 1 1 0    letter A
    1 0 0 0 1
    1 0 0 0 1
    
    5 4 3 2 1
    5 4 3 2 1
    5 4 3 2 1    shader
    5 4 3 2 1
    5 4 3 2 1
</code>

Add the following type definition for the rest of your lab:
<code scala>
type Img = List[List[Int]]
</code>

Also, in order to benefit from visualisation, instead of using a worksheet, you can create a new Scala project, containing an object with a main method:
<code scala>
object Matrix {
// define your functions here

  def main(args: Array[String]) = {
  // write your tests here
  }
}
</code> 

**7.1.** Write a function which converts an image to a string (Hint: you can draw inspiration from a similar one from the lecture):
<code scala>
def show(m: Img): String = ???
</code>

**7.2.** Write a function which performs a horizontal flip on an image. Try to first visualise (you may use pen and paper) how the transformation would look like.
<code scala>
def hFlip(img: Img): Img = ???
</code>

**7.3.** Write a function which performs vertical flip.
<code scala>
def vFlip(img: Img): Img = ???
</code> 

**7.4.**  Write a function which performs a 90 degrees rotation to the right. (Hint: you need an ingredient from the lecture. Also, note that there are multiple possible implementations.)
<code scala>
def rot90Right(img: Img): Img = ???
</code>

**7.5.** Write a function which performs a 90 degrees rotation to the left.
<code scala>
def rot90Left(img: Img): Img = ???
</code>

**7.6.** Write a function which inverts an image (values 0 become 255, 1 - 254, and so forth).

**7.7.** Write a function which crops a given image, using two, two-dimensional coordinates: the higher-left point x and y, and the lower-right point x and y. An example is shown below:
<code scala>
val img = List(List(0,0,1,0,0), List(0,1,0,1,0), List(0,1,1,1,0), List(1,0,0,0,1), List(1,0,0,0,1))
/*
      0 0 1 0 0
*     0 1 0 1 0                                           1 0 1
*     0 1 1 1 0     cropping from 1,1  to  2,3  yields:   1 1 1
*     1 0 0 0 1
*     1 0 0 0 1

 */

def cropAt(img: Img, xSt:Int, ySt:Int, xEnd: Int, yEnd: Int): Img = ??
</code> 

**7.8.** Write a function which returns a list of all positions which have pixels of larger intensity than x
<code scala>
def largerPos(img: Img, int: Int): List[(Int,Int)] = ???
</code>

**7.9.** Write a function which adds ''x'' to the intensity of each pixel.
<code scala>
def contrast(x: Int)(img: Img): Img = ???
</code>

**7.10.** Write a function which takes two images ''X'' and ''Y'' and //glues// them on the horizontal axis (the resulting image will be ''XY'')
<code scala>
def hglue(img1: Img, img2: Img): Img = ???
</code>

**7.11.** Write a function which takes two images ''X'' and ''Y'' and //glues// them on the vertical axis:
<code scala>
def vglue(img1: Img, img2: Img): Img = ???
</code>

**7.12.** Define a function that takes a **square** image, and draws two diagonal lines of intensity 1 across it. Use ''_.until(_)'' and ''_.toList''.
<code scala>
def diag(img: Img): Img = ???
</code>

**7.13.** Define a function which blurs an image as follows:
  * for each pixel p of intensity > 1: make all neighbouring pixels of intensity 0 equal to p-1 (including diagonals).
  * if some pixel of intensity 0 is in the vicinity of two different >1 pixels of different intensities, the one which is larger should be taken into account
  * to make the implementation easier, you do not need to implement the blur on the image edges.

<code scala>
def blur(img: Img): Img = ???
</code> 

**7.14. (!) ** Define a function which builds an effect of intensity x as shown below:
<code scala>
val img2 = List(
  List(0,0,0,0,0,0,0,0,0),
  List(0,0,0,0,0,0,0,0,0),
  List(0,0,0,0,0,0,0,0,0),
  List(0,0,0,0,1,0,0,0,0),
  List(0,0,0,1,2,1,0,0,0),
  List(0,0,0,0,1,0,0,0,0),
  List(0,0,0,0,0,0,0,0,0),
  List(0,0,0,0,0,0,0,0,0),
  List(0,0,0,0,0,0,0,0,0)
)

/*
Before:                   After (for x = 2)

    0 0 0 0 0 0 0 0 0      0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0      0 0 1 1 1 1 1 0 0
    0 0 0 0 0 0 0 0 0      0 1 1 2 2 2 1 1 0
    0 0 0 0 1 0 0 0 0      0 1 2 2 3 2 2 1 0
    0 0 0 1 2 1 0 0 0      0 1 2 3 4 3 2 1 0
    0 0 0 0 1 0 0 0 0      0 1 2 2 3 2 2 1 0
    0 0 0 0 0 0 0 0 0      0 1 1 2 2 2 1 0 0
    0 0 0 0 0 0 0 0 0      0 0 1 1 1 1 1 0 0
    0 0 0 0 0 0 0 0 0      0 0 0 0 0 0 0 0 0


Hint: a single foldRight is sufficient. Which is the list you should apply it on?
 */
def effect(intensity: Int, img: Img): Img = ???
</code>