DDA (Numerical Differentiation Method) to draw straight lines (C++, VS2019)

1、DDA（Digital Differential Analyzer）算法

The DDA algorithm is the simplest algorithm for drawing straight lines in computer graphics.
The two endpoints P0(x0,y0) and P1(x1,y1) of the line segment are known .
Then the slope of the straight line can be obtained:

  k = (y2 - y1) / (x2 - x1)

Under the condition that both k and b are calculated, as long as we know a value of x, we can calculate a value of y.

  y = kx + b

If the abscissa x increases by 1 each time (we call this step 1, that is, x = x +1), then the step of y is k+b.

  x = x + 1
  y = y + (k + b)

Also knowing a value of y can also calculate the value of x. At this time, the step of y is 1, and the step of x is (1-b)/k.

   y = y + 1
   x = x +(1 - b) / k

According to the calculated x and y values, round down to get the coordinates (x',y'), and draw a point on the straight line segment at (x',y').

In order to further simplify the calculation, we can usually set b to 0, and regard the starting point as (0,0).
Suppose the coordinates of the current point are (x _i , y _i ), and the coordinates of the next pixel point are (x _i+1 , y _i+1 ),
then use the DDA algorithm to solve the calculation formula of (xi+1, yi+1). Summarized as:

x _i+1 = x _i + xStep (1)
y _i+1 = y _i + yStep (2)

We generally determine xStep and yStep by calculating Δx and Δy:

If Δx> Δy, it means that the maximum difference of the x-axis is greater than the maximum difference of the y-axis, and the x-axis direction is the main direction of the step.

xStep = 1，yStep = k；

If Δy> Δx, it means that the maximum difference of the y-axis is greater than the maximum difference of the x-axis, and the y-axis direction is the main direction of the step.

yStep = 1，xStep = 1 / k。

According to this formula, (x _i , y _i ) can be iteratively calculated (x _i+1 , y _i+1 ), and then the calculated (x, y) coordinate point can be drawn in the coordinate system.

Implementation tools:
1) VS2019 (C++)
new project:

2) Download plug-in: Easyx. Please refer to the official website for usage and download: https://www.easyx.cn/
click to download and then install Click to install
at VC2019

The source code is as follows:

#include <iostream>
#include <graphics.h>
#include <math.h>
#include <conio.h>
using namespace std;

void DDALine(int x1, int y1, int x2, int y2)
{
    
    
    int x0 = 400;
    int y0 = 300;                  //记录原点坐标
    int steps;                     //记录步长
    int dx, dy;                    //记录起点和终点的坐标差值
    float x, y;                    //记录即时坐标
    float delta_x, delta_y;        //记录划线过程中的坐标增量
    dx = x2 - x1;
    dy = y2 - y1;
    if (abs(dx) > abs(dy))         //比较横纵坐标增量的大小
        steps = dx;
    else
        steps = dy;                //确保每次的增量不超过一个单位长度
    x = x1;
    y = y1;                        //记录画线起点
    delta_x = float(dx) / steps;
    delta_y = float(dy) / steps;   //计算相邻两个点的增量
    putpixel(x, y, RED);
    for (int i = 0; i < steps; i++)
    {
    
    
        x = x + delta_x;
        y = y + delta_y;
        putpixel(x +int( x0 + 0.5), y0 - int(y + 0.5), RED);
    }
}

int main()
{
    
    
    int x1, x2, y1, y2;
    int x0 = 400, y0 = 300;			                       //坐标轴中心（x0,y0)
    cout << "请输入两个整数点的坐标(x1,y1),(x2,y2)" << endl;
    cin >> x1 >> y1 >> x2 >> y2;
    initgraph(x0 * 2, y0 * 2);		                       //初始化图形窗口大小
    line(0, y0, x0 * 2, y0);			                   //坐标轴X
    line(x0, 0, x0, y0 * 2);			                   //坐标轴Y
    DDALine(x1, y1, x2, y2);                               //DDA画线算法
    _getch();                                              //等待一个任意输入结束
    closegraph();                                          //关闭图形窗口
    return 0;
}