How to get the points (coordinates) on 2D Line?

Question

When I plot point1(p1) and point2(p2), the line between p1 and p2 is drawn. I wanna know a set of the points making the line. For example, I wanna get x, y coordinates (as array type: x[], y[]). Is there any algorithms or code?

Answer 1

Here's what I have come up with: It is fair to say that we need to use the slope formula, y = m*x + b to find the slope so we can plot our points along that line. We need the following:

• (x1, y1)
• (x2, y2)

to find the following:

• m = (y2 - y1) / (x2 - x1)
• b = y1 - (m * x1)
• minX = min(x1, x2) used for limiting our lower bound
• maxX = max(x1, x2) used for limiting our upper bound

Now that everything is set, we can plot our line pixel by pixel and obtain all (x,y) coordinates we need. The logic is simple:

let x loop from minX to maxX and plug it in y = m*x + b (we already have all the variables except y). Then, store the (x,y) pair.

I have used Java for coding this logically and visually. Also, I used LinkedList instead of arrays (because I we can't know the number of points we will obtain).

I have also drawn what Java would draw (in blue) and my approach (in red). They are almost perfectly the exact output and coordinates. The image below is zoomed 5x the original size.

Note! The above explanation is what you would use if the line is not vertical (because the slope would be undefined, division by zero). If it is, then you will plug y (instead of x) values and find the x (instead of y) value from the following formula x = (y - b) / m (instead of y = m*x + b). Though, the code takes care of vertical lines.

import java.awt.Canvas;
import java.awt.Color;
import java.awt.Graphics;
import java.awt.Point;
import java.util.LinkedList;
import javax.swing.JFrame;

public class LineDrawing extends Canvas {

    int x1 = 5;
    int y1 = 10;
    int x2 = 105;
    int y2 = 100;
    double m = ((double) (y2 - y1)) / ((double) (x2 - x1));//slope
    double b = y1 - (m * ((double) x1));//vertical shift

    //Takes care of the domain we will loop between.
    //min and max will be assigned minX and maxX if the line is not vertical.
    //minY and maxY are assigned to min and max otherwise.
    int minX = Math.min(x1, x2);//minimum x value we should consider
    int maxX = Math.max(x1, x2);//maximum x value we should consider
    int minY = Math.min(y1, y2);//minimum y value we should consider
    int maxY = Math.max(y1, y2);//maximum y value we should consider
    int min = 0;
    int max = 0;
    boolean plugX = true;//if true, the line is not vertical.
    LinkedList<Point> points = new LinkedList<>();//Store all points here

    public LineDrawing() {

        if (x1 == x2) {//plug the y value instead the x, this is a vertical line.
            plugX = false;
            min = minY;
            max = maxY;
        } else {//dont change and plug x values.
            min = minX;
            max = maxX;
        }
    }

    @Override
    public void paint(Graphics g) {
        super.paint(g);

        //Draw the line, using default java drawLine in blue.
        g.setColor(Color.BLUE);
        g.drawLine(x1, y1, x2, y2);

        //change the color to red, it will draw our verison.
        g.setColor(Color.RED);

        //Draw the points, point by point on screen.
        //Plug m, x, and b in the formula y = m*x + b
        //to obtain the y value.
        //OR
        //Plug m, y, and b in the formula x = (y - b) / m
        //to obtain the x value if vertical line.
        //Then plot (x,y) coordinate on screen and add the point to our linkedList.
        for (int i = min; i <= max; i++) {
            int obtained = 0;
            if (plugX) {//not a vertical line
                obtained = (int) Math.round((m * i + b));
                System.out.println("x = " + i + "  ,  y = " + obtained);
                points.add(new Point(i, obtained));
                //Uncomment to see the full blue line.
                g.drawLine(i, obtained, i, obtained);
            } else {//vertical line
                obtained = (int) Math.round((double) (i - b) / (double) m);
                System.out.println("x = " + x1 + "  ,  y = " + i);
                g.drawLine(x1, i, x1, i);//Uncomment to see the full blue line.
                points.add(new Point(x1, i));
            }
        }

        //Print out the number of points as well as the coordinates themselves.
        System.out.println("Total points: " + points.size());
        for (int i = 0; i < points.size(); i++) {
            System.out.println(i + "      ( " + points.get(i).x
                + ", " + points.get(i).y + " )");
        }
    }

    public static void main(String[] args) {
        JFrame frame = new JFrame();
        frame.setSize(120, 150);
        frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        frame.add(new LineDrawing());
        frame.setVisible(true);
    }
}