Step by Step solution about How to resolve the algorithm Draw a sphere step by step in the Haskell programming language

This code is a program that renders a sphere using OpenGL and GLUT.

Here's a detailed breakdown of the code:

• The import statements at the beginning of the code import the necessary libraries for 3D graphics, user interface, and input/output.

• The setProjection function sets up the projection matrix for the scene.

• The grey1, grey9, red, and white constants define colors that are used in the scene.

• The setLights function sets up the lighting for the scene.

• The setMaterial function sets up the material properties for the sphere.

• The display function is the main rendering function. It clears the screen, renders the sphere, and swaps the buffers to display the rendered image.

• The main function is the entry point of the program. It initializes GLUT, creates a window, sets up the rendering environment, and registers the display function as the display callback.

• The shades variable defines a string of characters that are used to create a grayscale gradient.

• The n variable stores the length of the shades string.

• The dot function calculates the dot product of two vectors.

• The normalize function normalizes a vector.

• The sphere function takes the radius, shininess, ambient light intensity, and light intensity as arguments and returns a string representing the sphere.

• The outer list comprehension in the sphere function generates a list of lists of characters. Each inner list represents a row of the sphere.

• The inner list comprehension in the sphere function calculates the color value for each character in the row.

import Graphics.Rendering.OpenGL.GL
import Graphics.UI.GLUT.Objects
import Graphics.UI.GLUT

setProjection :: IO ()
setProjection = do
  matrixMode $= Projection
  ortho (-1) 1 (-1) 1 0 (-1)
         
grey1,grey9,red,white :: Color4 GLfloat
grey1 = Color4 0.1 0.1 0.1 1
grey9 = Color4 0.9 0.9 0.9 1
red   = Color4 1   0   0   1
white = Color4 1   1   1   1

setLights :: IO ()
setLights = do
  let l = Light 0
  ambient  l $= grey1
  diffuse  l $= white
  specular l $= white
  position l $= Vertex4 (-4) 4 3 (0 :: GLfloat)
  light    l $= Enabled
  lighting   $= Enabled

setMaterial :: IO ()
setMaterial = do
  materialAmbient   Front $= grey1
  materialDiffuse   Front $= red
  materialSpecular  Front $= grey9
  materialShininess Front $= (32 :: GLfloat)

display :: IO()
display = do
  clear [ColorBuffer]
  renderObject Solid $ Sphere' 0.8 64 64
  swapBuffers

main :: IO()
main = do
  _ <- getArgsAndInitialize
  _ <- createWindow "Sphere"
  clearColor $= Color4 0.0 0.0 0.0 0.0
  setProjection
  setLights
  setMaterial
  displayCallback $= display
  mainLoop


import Data.List (genericLength)

shades = ".:!*oe%#&@"
n = genericLength shades
dot a b = sum $ zipWith (*) a b
normalize x = (/ sqrt (x `dot` x)) <$> x

sphere r k amb light = unlines $
  [ [ if x*x + y*y <= r*r
      then let vec = normalize [x, y, sqrt (r*r-x*x-y*y)]
               b = (light `dot` vec) ** k + amb
               intensity = (1 - b)*(n - 1)
           in shades !! round ((0 `max` intensity) `min` n)
      else ' '
    | y <- map (/2.12) [- 2*r - 0.5 .. 2*r + 0.5]  ]
  | x <- [ - r - 0.5 .. r + 0.5] ]