Step by Step solution about How to resolve the algorithm Xiaolin Wu's line algorithm step by step in the Mathematica/Wolfram Language programming language

The provided Wolfram code is designed for drawing lines in an image using the Bresenham line algorithm. It operates by setting the pixel values along the line to white, effectively "drawing" the line.

Here's a detailed breakdown of the code:

ClearAll[ReverseFractionalPart, ReplacePixelWithAlpha, DrawEndPoint, DrawLine]: This line clears any previously defined values for the specified functions and variables.

ReverseFractionalPart[x_] := 1 - FractionalPart[x]: Defines a function that calculates the reverse of the fractional part of a number. In other words, it subtracts the fractional part from 1.

ReplacePixelWithAlpha[img_Image, pos_ -> colvals : {_, _, }, alpha]: This function replaces the pixel value at the specified position (pos) in the image (img) with the provided color values (colvals) while blending the new color with the existing color using the alpha value.

DrawEndPoint[img_Image, pt : {x_, y_}, grad_, p_]: The DrawEndPoint function is used to draw the endpoints of a line. It takes the image (img), the endpoint coordinates (pt), the gradient (grad) of the line, and a function (p) that reverses the coordinates. This function determines the exact positions of the pixels to be set based on the endpoint and gradient.

DrawLine[img_Image, p1 : {_, }, p2 : {, _}]: The DrawLine function is the main function for drawing lines. It takes the image (img) and the start and end points of the line (p1 and p2).

Inside the DrawLine function:

1. It initializes various parameters, including the starting and ending coordinates of the line, the change in x and y (dx and dy), and whether the line is steep (i.e., the absolute value of dy is greater than the absolute value of dx).

2. It checks if the line is steep and swaps the coordinates accordingly.

3. It calculates the gradient (grad) of the line and the y-intercept (intery) at the starting point.

4. It calls the DrawEndPoint function to draw the starting point.

5. It iterates over the x-coordinates along the line, starting from the next pixel after the starting point and ending at the ending point.

6. For each x-coordinate, it calculates the corresponding y-coordinate using the gradient and the y-intercept.

7. It uses the ReplacePixelWithAlpha function to set the pixels at the calculated coordinates to white, blending the new color with the existing color.

8. It updates the y-intercept by adding the gradient to it.

9. Finally, it returns the modified image with the line drawn on it.

image = ConstantImage[Black, {100, 100}]: Creates a 100x100 black image as the canvas for drawing.

Fold[DrawLine[#1, {20, 10}, #2] &, image, AngleVector[{20, 10}, {75, #}] & /@ Subdivide[0, Pi/2, 10]]: This part of the code uses the Fold function to iterate over a list of angles (created using AngleVector and Subdivide) and draw lines from the point {20, 10} to points along a circle with radius 75 at those angles. Each line is drawn using the DrawLine function. The result is an image with lines radiating from the center point.

ClearAll[ReverseFractionalPart, ReplacePixelWithAlpha, DrawEndPoint, DrawLine]
ReverseFractionalPart[x_] := 1 - FractionalPart[x]
ReplacePixelWithAlpha[img_Image, pos_ -> colvals : {_, _, _}, 
  alpha_] := Module[{vals,},
  vals = PixelValue[img, pos];
  vals = (1 - alpha) vals + alpha colvals;
  ReplacePixelValue[img, pos -> vals]
  ]
DrawEndPoint[img_Image, pt : {x_, y_}, grad_, p_] := 
 Module[{xend, yend, xgap, px, py, i},
  xend = Round[x];
  yend = y + grad (xend - x);
  xgap = ReverseFractionalPart[x + 0.5];
  {px, py} = Floor[{xend, yend}];
  i = ReplacePixelWithAlpha[img, p[{x, py}] -> {1, 1, 1}, ReverseFractionalPart[yend] xgap];
  i = ReplacePixelWithAlpha[i, p[{x, py + 1}] -> {1, 1, 1}, FractionalPart[yend] xgap];
  {px, i}
  ]
DrawLine[img_Image, p1 : {_, _}, p2 : {_, _}] := 
 Module[{x1, x2, y1, y2, steep, p, grad, intery, xend, yend, x, y, 
   xstart, ystart, dx, dy, i},
  {x1, y1} = p1;
  {x2, y2} = p2;
  dx = x2 - x1;
  dy = y2 - y1;
  steep = Abs[dx] < Abs[dy];
  p = If[steep, Reverse[#], #] &;
  If[steep,
   {x1, y1, x2, y2, dx, dy} = {y1, x1, y2, x2, dy, dx}
   ];
  If[x2 < x1,
   {x1, x2, y1, y2} = {x2, x1, y2, y1}
   ];
  grad = dy/dx;
  intery = y1 + ReverseFractionalPart[x1] grad;
  {xstart, i} = DrawEndPoint[img, p[p1], grad, p];
  xstart += 1;
  {xend, i} = DrawEndPoint[i, p[p2], grad, p];
  Do[
   y = Floor[intery];
   i = ReplacePixelWithAlpha[i, p[{x, y}] -> {1, 1, 1}, ReverseFractionalPart[intery]];
   i = ReplacePixelWithAlpha[i, p[{x, y + 1}] -> {1, 1, 1}, FractionalPart[intery]];
   intery += grad
   ,
   {x, xstart, xend}
   ];
  i
  ]
image = ConstantImage[Black, {100, 100}];
Fold[DrawLine[#1, {20, 10}, #2] &, image, AngleVector[{20, 10}, {75, #}] & /@ Subdivide[0, Pi/2, 10]]