Straight Lines in Java

Using the Equation of a Straight Line in Java

The equation of a straight line has the general form y = mx + c;
where m is the slope and c is the intercept on the y-axis.

For a vertical line, x is constant and for a horizontal line, y is constant.

Generating Straight Lines for Java

Given any 2 points (x₁, y₁) and (x₂, y₂); we'll have:

	y₂ - y₁	=	y - y₁
	x₂ - x₁		x - x₁
⇒ y = (	y₂ - y₁	) x +	x₂y₁ - x₁y₂
	x₂ - x₁		x₂ - x₁

Comparing this to the general equation of a straight line, i.e. y = mx + c

m =	y₂ - y₁
m =	x₂ - x₁
&
c =	x₂y₁ - x₁y₂
c =	x₂ - x₁

Say we are to find the equation for the line represented by the arbitrary points (50, 50) and (200, 100):

m =	100 - 50	=	50	=	1
	200 - 50		150		3
&
c =	200(50) - 50(100)		=	10000 - 5000
	200 - 50			150
=		5000	=		100
		150			3

Hence,
y = ¹/₃x + ¹⁰⁰/₃
or
3y = x + 100

Code to Animate a Graphic Object by a Line Equation in Java

To make a graphic (dot) travel by the equation of a line, continuously increment x, and use the equation to get the corresponding y value.
Let's do so with the above equation representing points (x₁, y₁) = (50, 50) and (x₂, y₂) = (100, 200).

Create 2 new classes; File, New.
Call them PanelsStraightLine and StraightLine.
Type out the adjoining Java code for animating an image body through the path of a straight line.

Canvas/Button class

package dymetric;

import java.awt.event.*;
import java.awt.*;
import javax.swing.*;

public class ButtonandCanvasPanels implements ActionListener {
    public JPanel button_panel, canvas_panel;
    public JButton motion_bttn;
    public StraightLine motion;

    public ButtonandCanvasPanels() {
        button_panel = new JPanel();
        // pick a background colour
        button_panel.setBackground(Color.PINK);
        button_panel.setLayout(new FlowLayout(FlowLayout.CENTER, 0, 0));
        // O my; but for convenience sake let's add our control button here
        motion_bttn = new JButton("Move");
        motion_bttn.setBackground(new Color(255, 0, 255));
        motion_bttn.addActionListener(this);
        // using the default layout manager
        button_panel.add(motion_bttn);


        canvas_panel = new JPanel();
        canvas_panel.setLayout(new BorderLayout());
        motion = new StraightLine();
        // attach appropriate drawing component
        canvas_panel.add(motion, BorderLayout.CENTER);
    }

    /**
     * Respond to the button click event
     */
    public void actionPerformed(ActionEvent evt) {
        motion.moveInLine();
    }
}

Java code for StraightLine class

package dymetric;

import java.awt.*;

public class StraightLine extends Canvas {

    protected Color ball_colour;
    protected int x1 = 50;
    protected int x2 = 800;
    protected int y1 = 50;
    protected int y2 = 300;
    protected int x = x1;
    protected int y = y1;
    protected double m, c; // slope and y-intercept of a straight line
    protected final int aWIDTH, aHEIGHT;

    public StraightLine() {
        setBackground(Color.LIGHT_GRAY); // canvas color
        ball_colour = Color.RED;
        aWIDTH = aHEIGHT = 10;

        m = (double) (y2 - y1) / (x2 - x1); // slope
        c = (double) (x2 * y1 - x1 * y2) / (x2 - x1); // y-intercept

    }

    // Feel free to double buffer if flickering occurs
    public void paint(Graphics g) {
        g.setColor(ball_colour);
        // draw a dot
        g.fillOval(x, y, aWIDTH, aHEIGHT);
    }

    public void moveInLine() {
        // condition for continuing motion
        while (x <= 700) {
            y = (int) Math.ceil(m * x + c);
            paint(this.getGraphics());

            x += 10;
            // introduce a delay between renderings
            try {
                Thread.sleep(50);
            } catch (InterruptedException e) {
            }
        }
    }
}

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