//************************************************************************ //Elif Tosun //274b-ab //An Applet that shows three line segments on the screen, and at the same time //computes whether they intersect or not. The results of the computations are //printed on the java console. //************************************************************************ import java.applet.*; import java.awt.*; import java.io.*; //importing java libraries //************************************************ //myApplet //used in checking if given segments cross or not // //************************************************ public class myApplet extends Applet { private Point A, B, C, D, E, F; //declaring variables of type Point //************************************************ // Init // This function is called when the applet is // loaded. It initializes the variables and // calls crossSeg to find out if the lines cross // or not. //************************************************ public void init() { A = new Point(-25, -75); B = new Point(-25, 40); C = new Point(25, -100); //initialize points D = new Point(-25, 100); E = new Point(5, -20); F = new Point(-100, -50); if (crossSeg(A, B, C, D)) System.out.println("AB and CD are crossing segments."); else System.out.println("AB and CD are NOT crossing."); // checks if segments AB and CD cross if (crossSeg(C, D, E, F)) System.out.println("CD and EF are crossing segments."); else System.out.println("CD and EF are NOT crossing."); // checks if segments CD and EF cross if (crossSeg(A, B, E, F)) System.out.println("AB and EF are crossing segments."); else System.out.println("AB and EF are NOT crossing."); // checks if segments AB and EF cross }//end init //************************************************ // Paint // This function is does all the graphic work. // It draws the axes, the segments, the endpoints // of segments, and their labels on screen. //************************************************ public void paint(Graphics g){ g.setColor(Color.red); //set color to red, to distinguish //between the axes and the //real segments g.drawLine(0, 150, 300, 150); //draw axes g.drawLine(150, 0, 150, 300); g.setColor(Color.black); //set color back to black myDrawSeg(A, B, g); g.drawString("A("+A.x+","+A.y+")", 144+A.x, 161-A.y); g.drawString("B("+B.x+","+B.y+")", 135+B.x, 145-B.y); //draw segment AB and label it myDrawSeg(C, D, g); g.drawString("C("+C.x+","+C.y+")", 145+C.x, 161-C.y); g.drawString("D("+D.x+","+D.y+")", 155+D.x, 146-D.y); //draw segment CD and label it myDrawSeg(E, F, g); g.drawString("E("+E.x+","+E.y+")", 155+E.x, 160-E.y); g.drawString("F("+F.x+","+F.y+")", 155+F.x, 160-F.y); //draw segment EF and label it }// end paint //************************************************************************ // USER-DEFINED FUNCTIONS // //************************************************************************ //************************************************ // myDrawSeg // This function draws the segments with their // end points. // Called in paint. //************************************************ public void myDrawSeg(Point A, Point B, Graphics g) { g.fillOval(148+A.x,150-A.y, 4, 4); //draw endpoints g.fillOval(148+B.x,150-B.y, 4, 4); g.drawLine(150+A.x, 150-A.y, 150+B.x, 150-B.y); //draw segment }//end myDrawSeg //************************************************ // Det // This functioncomputes the determinant of 3 points. // It also gives twice the area of triangle formed by // these three points. The sign of the determinant // gives information about left/right turns. // Called in leftTurn and Collinear functions. //************************************************ public int Det(Point A, Point B, Point C) { return (A.x*B.y + A.y*C.x + B.x*C.y - C.x*B.y - A.x*C.y - B.x*A.y); //from definition of determinant }// end Det //************************************************ // LeftTurn // This function finds out if it is a left turn // when you are moving on AB and turn towards C. // Used for finding out about corssing of segments. // Called in CrossSeg function. //************************************************ public boolean leftTurn(Point A, Point B, Point C) { if (Det(A, B, C) > 0) //if the determenant of three points return true; //is positive then it is a left turn. else return false; //else it is not. }//end leftTurn //************************************************ // Collinear // This function finds out if the given three points // are collinear or not. // Called in CrossSeg and Between functions. //************************************************ public boolean Collinear(Point A, Point B, Point C) { if (Det(A, B, C) == 0) //the determinant of three collinear return true; //points is zero. else return false; }//end Collinear //************************************************ // Between // This function finds out among the given three // points, whether the third one is in between the // first and the second one. // Called in CrossSeg. //************************************************ public boolean Between(Point A, Point B, Point C) { if (!Collinear(A, B, C)) //for a point to be in between the other return false; //two all three has to be collinear else { if (A.x != B.x) //if A and B are not vertical //check x coordintes return (((A.x <= C.x) && (C.x <= B.x)) || ((A.x >= C.x) && (C.x >= B.x))); else //else check y coordinates return (((A.y <= C.y) && (C.y <= B.y)) || ((A.y >= C.y) && (C.y >= B.y))); } }//end Between //************************************************ // CrossSeg // This function actually finds out if two segments // cross or not. It takes in the endpoints of the // two segments. // Called in init. //************************************************ public boolean crossSeg(Point A, Point B, Point C, Point D) { if (!Collinear(A,B,C) && !Collinear(A,B,D) && !Collinear(C,D,A) && !Collinear(C,D,B)) //if they are not collienar { if (((!leftTurn(A,B,D) && leftTurn(A,B,C)) ||(!leftTurn(A,B,C) && leftTurn(A,B,D))) && ((leftTurn(C,D,A) && !leftTurn(C,D,B)) || (!leftTurn(C,D,A) && leftTurn(C,D,B)))) //and if the endpoints of one //segment lie on diff sides of //the other one return true; //they cross else return false; //else they don;t } else //if they are collinear { if (Between(A, B, C) || Between(A, B, D) || Between (C, D, A) || Between(C, D, B)) //check if the third one lies //between the other two. return true; //if so, they cross else return false; //else they don't } }//end crosseg }//end myApplet