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

The provided C++ code implements the Wu line algorithm, which is used to draw lines between two points on a raster display. Here's a detailed explanation of the code:

1. Function Signature:

   void WuDrawLine(float x0, float y0, float x1, float y1,
                 const std::function<void(int x, int y, float brightess)>& plot)

   • x0, y0: Coordinates of the starting point of the line.
   • x1, y1: Coordinates of the ending point of the line.
   • plot: A callback function that takes the coordinates (x, y) and a brightness value and is responsible for plotting a point on the display.

2. Helper Functions:

   • ipart(float x): Returns the integer part of x.
   • round(float x): Rounds x to the nearest integer.
   • fpart(float x): Returns the fractional part of x.
   • rfpart(float x): Returns 1 - fpart(x).

3. Variables:

   • steep: A boolean variable to determine if the line is steep (i.e., has a greater slope than 1).
   • If the line is steep, the x and y coordinates are swapped.
   • If the starting point is to the right of the ending point, the coordinates are swapped.

4. Calculating Line Parameters:

   • dx: The difference between x1 and x0.
   • dy: The difference between y1 and y0.
   • gradient: The slope of the line (ratio of dy to dx).

5. Initial Point Calculation:

   • xpx11: The integer part of the x-coordinate of the initial point.
   • intery: The initial y-coordinate of the line.
   • The values for xpx11, ypx11, and intery are calculated based on the xend, yend, and xgap values.
   • xgap represents the fractional part of the x-coordinate of the initial point.

6. Endpoint Calculation:

   • xpx12: The integer part of the x-coordinate of the endpoint.
   • ypx12: The integer part of the y-coordinate of the endpoint.
   • Similar to the initial point calculation, these values are computed based on the xend, yend, and xgap values.

7. Drawing the Line:

   • The code iterates over x values between xpx11 and xpx12.
   • For each x, the intery value is calculated.
   • The plot callback is called four times for each x value to set brightness values at four pixel locations around the line.
   • Depending on whether the line is steep or not, the plot calls are adjusted.

8. Algorithm Overview:

   • The algorithm first determines if the line is steep and swaps the coordinates if necessary.
   • It then calculates the line's gradient and initial and endpoint coordinates.
   • The line is then drawn by iterating over x values and calculating the corresponding y values.
   • For each x, it determines the brightness values at four pixel locations around the line and uses the plot callback to set these values on the display.

#include <functional>
#include <algorithm>
#include <utility>

void WuDrawLine(float x0, float y0, float x1, float y1,
                const std::function<void(int x, int y, float brightess)>& plot) {
    auto ipart = [](float x) -> int {return int(std::floor(x));};
    auto round = [](float x) -> float {return std::round(x);};
    auto fpart = [](float x) -> float {return x - std::floor(x);};
    auto rfpart = [=](float x) -> float {return 1 - fpart(x);};
        
    const bool steep = abs(y1 - y0) > abs(x1 - x0);
    if (steep) {
        std::swap(x0,y0);
        std::swap(x1,y1);
    }
    if (x0 > x1) {
        std::swap(x0,x1);
        std::swap(y0,y1);
    }
        
    const float dx = x1 - x0;
    const float dy = y1 - y0;
    const float gradient = (dx == 0) ? 1 : dy/dx;
        
    int xpx11;
    float intery;
    {
        const float xend = round(x0);
        const float yend = y0 + gradient * (xend - x0);
        const float xgap = rfpart(x0 + 0.5);
        xpx11 = int(xend);
        const int ypx11 = ipart(yend);
        if (steep) {
            plot(ypx11,     xpx11, rfpart(yend) * xgap);
            plot(ypx11 + 1, xpx11,  fpart(yend) * xgap);
        } else {
            plot(xpx11, ypx11,    rfpart(yend) * xgap);
            plot(xpx11, ypx11 + 1, fpart(yend) * xgap);
        }
        intery = yend + gradient;
    }
    
    int xpx12;
    {
        const float xend = round(x1);
        const float yend = y1 + gradient * (xend - x1);
        const float xgap = rfpart(x1 + 0.5);
        xpx12 = int(xend);
        const int ypx12 = ipart(yend);
        if (steep) {
            plot(ypx12,     xpx12, rfpart(yend) * xgap);
            plot(ypx12 + 1, xpx12,  fpart(yend) * xgap);
        } else {
            plot(xpx12, ypx12,    rfpart(yend) * xgap);
            plot(xpx12, ypx12 + 1, fpart(yend) * xgap);
        }
    }
        
    if (steep) {
        for (int x = xpx11 + 1; x < xpx12; x++) {
            plot(ipart(intery),     x, rfpart(intery));
            plot(ipart(intery) + 1, x,  fpart(intery));
            intery += gradient;
        }
    } else {
        for (int x = xpx11 + 1; x < xpx12; x++) {
            plot(x, ipart(intery),     rfpart(intery));
            plot(x, ipart(intery) + 1,  fpart(intery));
            intery += gradient;
        }
    }
}