Step by Step solution about How to resolve the algorithm Xiaolin Wu's line algorithm step by step in the Ruby programming language

This Ruby code appears to define a method called draw_line_antialised within a class named Pixmap. It's designed to draw anti-aliased lines (smooth lines) between two points, p1 and p2, with a specified colour. Let's break down the code step by step:

1. Setup:
   • The method starts by extracting the x and y coordinates from the p1 and p2 points.
2. Steepness Check:
   • It determines if the line is "steep" based on the difference in y-coordinates being greater than the difference in x-coordinates.
   • If it's steep, it swaps the x and y coordinates for later calculations.
   • It also ensures that x1 is less than or equal to x2 to simplify calculations.
3. Gradient Calculation:
   • The gradient of the line is calculated as the change in y divided by the change in x. This represents the slope of the line.
4. Endpoint Handling:
   • It calculates the first endpoint by rounding x1 to the nearest integer, then computing the corresponding y value using the gradient.
   • It also calculates the fractional part of x1 and stores this in xgap.
   • The put_colour method is called twice to set the color at two pixels based on the computed fractional part.
   • The itery variable is initialized to yend + gradient for subsequent endpoint calculations.
5. Second Endpoint Handling:
   • Similar to the first endpoint, it calculates the coordinates for the second endpoint (xend, yend) and fractional part (xgap).
   • It calls put_colour twice to set the color at two pixels based on the fractional part.
6. Interpolation:
   • It iterates through the remaining pixels between xpxl1 and xpxl2, setting the color at each pixel using the calculated gradient and fractional parts.
7. Color Blending:
   • The put_colour method contains logic for blending colors using the anti_alias method.
   • It calculates a weighted average of the new color and the existing old color based on the c ratio.
   • The resulting RGBColour object is then used to set the color at the specified pixel.

This code allows you to draw anti-aliased lines in a Pixmap object, which would typically represent an image or canvas where you're drawing pixels. The result is a smoother, less pixelated line.

def ipart(n); n.truncate; end
def fpart(n); n - ipart(n); end
def rfpart(n); 1.0 - fpart(n); end

class Pixmap
  def draw_line_antialised(p1, p2, colour)
    x1, y1 = p1.x, p1.y
    x2, y2 = p2.x, p2.y
 
    steep = (y2 - y1).abs > (x2 - x1).abs
    if steep
      x1, y1 = y1, x1
      x2, y2 = y2, x2
    end
    if x1 > x2
      x1, x2 = x2, x1
      y1, y2 = y2, y1
    end
    deltax = x2 - x1
    deltay = (y2 - y1).abs
    gradient = 1.0 * deltay / deltax
 
    # handle the first endpoint
    xend = x1.round
    yend = y1 + gradient * (xend - x1)
    xgap = rfpart(x1 + 0.5)
    xpxl1 = xend
    ypxl1 = ipart(yend)
    put_colour(xpxl1, ypxl1, colour, steep, rfpart(yend)*xgap)
    put_colour(xpxl1, ypxl1 + 1, colour, steep, fpart(yend)*xgap)
    itery = yend + gradient
 
    # handle the second endpoint
    xend = x2.round
    yend = y2 + gradient * (xend - x2)
    xgap = rfpart(x2 + 0.5)
    xpxl2 = xend
    ypxl2 = ipart(yend)
    put_colour(xpxl2, ypxl2, colour, steep, rfpart(yend)*xgap)
    put_colour(xpxl2, ypxl2 + 1, colour, steep, fpart(yend)*xgap)
 
    # in between
    (xpxl1 + 1).upto(xpxl2 - 1).each do |x|
      put_colour(x, ipart(itery), colour, steep, rfpart(itery))
      put_colour(x, ipart(itery) + 1, colour, steep, fpart(itery))
      itery = itery + gradient
    end
  end

  def put_colour(x, y, colour, steep, c)
    x, y = y, x if steep
    self[x, y] = anti_alias(colour, self[x, y], c)
  end

  def anti_alias(new, old, ratio)
    blended = new.values.zip(old.values).map {|n, o| (n*ratio + o*(1.0 - ratio)).round}
    RGBColour.new(*blended)
  end
end

bitmap = Pixmap.new(500, 500)
bitmap.fill(RGBColour::BLUE)
10.step(430, 60) do |a|
  bitmap.draw_line_antialised(Pixel[10, 10], Pixel[490,a], RGBColour::YELLOW)
  bitmap.draw_line_antialised(Pixel[10, 10], Pixel[a,490], RGBColour::YELLOW)
end
bitmap.draw_line_antialised(Pixel[10, 10], Pixel[490,490], RGBColour::YELLOW)