Implementation of Line Drawing Algorithm doesn't work properly

Question

First question, I have tried to calculate the expression, di+1=di+2*Δy−2*Δx(yi+1−yi) for the four quadrants. Irrespective of the quadrant, the expression was found to be the same, including signs. Am I right, or, there has been some mistakes in my calculations (hence, I am wrong)?

Second question, if this expression is only applicable for the first octet, how can I apply this to other octets? To me, there is no way to determine which octet I am working on. Coz, the value of m always represent two opposite octets. For example, if 0<m<1, it represents 1st and 5th octet. Right?

Thirdly, how can we determine the initial/starting value of di?

#include <iostream>
#include "utils.h"

void BresenhamLine(double x1, double y1, double x2, double y2, int color)
{
    if(x1>x2 || y1>y2)
    {
        Swap(x1, x2);
        Swap(y1, y2);
    }
    double x = x1;
    double y = y1;
    double dx = x2 - x1;
    double dy = y2 - y1;
    double dt = 2 * (dy - dx);
    double ds = 2 * dy;
    double d = 2*dy - dx;

    PlotPixel(x, y, color);

    if(dx>=dy)
    {
        while(x<=x2)
        {
            x++;
            if(d<0)
            {
                d = d + ds;
            }
            else
            {
                y++;
                d = d + dt;
            }
            PlotPixel(x, y, color);
        }
    }
    else
    {
        while(y<=y2)
        {
            y++;
            if(d<0)
            {
                x++;
                d = d + dt;
            }
            else
            {               
                d = d + ds;
            }
            PlotPixel(x, y, color);
        }
    }
}

int main()
{
int gm = DETECT;
int gd = DETECT;

initgraph(&gm, &gd, "");

double x1 = 0;
double y1 = 0;
double r = 50;
double x2 = 0;
double y2 = 0;
double signx = 0;
double signy = 0;

for(int theta=0 ; theta<=360 ; theta++)
{
    x2 = r * cos(DegreeToRad((double) theta));
    y2 = r * sin(DegreeToRad((double) theta));

    x1 = 5 * cos(DegreeToRad((double) theta));
    y1 = 5 * sin(DegreeToRad((double) theta));

    BresenhamLine(x1, y1, x2, y2, YELLOW);
}

getch();
closegraph();
return 0;
}

The lines that go through 2nd and 4th quadrant are not showing up.

How to fix that with some minor changes in my code?

Maybe saying it is your implementation that isn't working, rather than the algorithm, would be more accurate? ;) — Yakk - Adam Nevraumont, Aug 20 '15 at 15:59
Work through your implementation on paper. Compare it with the real algorithm. Find the bug. We are not a bug-hunting service. — Lightness Races in Orbit, Aug 20 '15 at 16:49
@perreal, actually, I was changing the signs like binary number. 0101. Nothing important. — user366312, Aug 23 '15 at 05:31
Please explain clearly what you have vaguely summarized by " Irrespective of the quadrant, the expression was found to be the same, including signs." — philipxy, Aug 27 '15 at 02:00
Bresenham is notable for using only INTEGER arithmetic. If you have floating point hardware, you do not need Bresenham. https://en.wikipedia.org/wiki/Bresenham%27s_line_algorithm — John Schmitt, Aug 28 '15 at 17:10

score 4 · Accepted Answer · answered Aug 23 '15 at 05:42

4

With this input: x1: 100 y1: -100 x2: -100 y2: 100

this logic:

if(x1>x2 || y1>y2)
{   
    Swap(x1, x2);
    Swap(y1, y2);
}

fails.

answered Aug 23 '15 at 05:42

perreal

94,503
21
155
181

handle magnitude and direction separately – perreal Aug 23 '15 at 05:49

score 1 · Answer 2 · answered Aug 24 '15 at 07:48

This page is a good place to start. It shows code as well for 1 of the octants:

http://www.cs.helsinki.fi/group/goa/mallinnus/lines/bresenh.html

I think you need to swap the x if x1 > x2 and swap the y if y1 > y2 but not swap both if only 1 of those is true.

The external links section of the Wikipedia page contains several links to ready-made implementations that you can study.

score 1 · Answer 3 · answered Aug 28 '15 at 18:35

Try this:

void BresenhamLine( double x1, double y1, double x2, double y2, int color )
{
  const bool steep = (std::abs(y2 - y1) > std::abs(x2 - x1));
  if(steep)
  {
    std::swap(x1, y1);
    std::swap(x2, y2);
  }

  if(x1 > x2)
  {
    std::swap(x1, x2);
    std::swap(y1, y2);
  }

  double dx = x2 - x1;
  double dy = std::abs(y2 - y1);

  double error = dx / 2;
  int ystep = (y1 < y2) ? 1 : -1;
  int y = (int)y1;

  int maxX = (int)x2;

  for(int x=(int)x1; x<maxX; x++)
  {
    if(steep)
    {
        PlotPixel(y, x, color);
    }
    else
    {
        PlotPixel(x, y, color);
    }

    error -= dy;
    if(error < 0)
    {
        y += ystep;
        error += dx;
    }
  }
}

I got this by slightly modifying the code here:http://rosettacode.org/wiki/Bitmap/Bresenham's_line_algorithm#C.2B.2B

Ok. It works. But, I was talking about some minor modification of my code so that I can understand the theory. — user366312, Aug 29 '15 at 10:10
then mainly you need to change `if(x1>x2 || y1>y2) { Swap(x1, x2); Swap(y1, y2); }` into `if(x1>x2) Swap(x1, x2); if(y1>y2) Swap(y1, y2);` — alle_meije, Sep 09 '15 at 08:26

Implementation of Line Drawing Algorithm doesn't work properly

3 Answers3