8.33 (Geometry: polygon subareas) A convex 4-vertex polygon is divided into four
triangles, as shown in Figure 8.9.
Write a program that prompts the user to enter the coordinates of four vertices and
displays the areas of the four triangles in increasing order. Here is a sample run:
Enter x1, y1, x2, y2, x3, y3, x4, y4:
-2.5 2 4 4 3 -2 -2 -3.5
The areas are 6.17 7.96 8.08 10.42
triangles, as shown in Figure 8.9.
Write a program that prompts the user to enter the coordinates of four vertices and
displays the areas of the four triangles in increasing order. Here is a sample run:
Enter x1, y1, x2, y2, x3, y3, x4, y4:
-2.5 2 4 4 3 -2 -2 -3.5
The areas are 6.17 7.96 8.08 10.42
import java.util.Scanner; public class Exercise_33 { static final int X = 0; static final int Y = 1; public static void main(String[] args) { Scanner input = new Scanner(System.in); double[][] points = new double[4][2]; System.out.print("Enter x1 y1 x2 y2 x3 y3 x4 y4: "); for (int i = 0; i < points.length; i++) for (int j = 0; j < points[i].length; j++) points[i][j] = input.nextDouble(); double[] centerPoint = getIntersectingPoint(points); double[] area = new double[4]; for (int i = 0; i < points.length; i++) { int j = ((i + 1) % points.length); double[][] triangle = new double[][] { points[i], points[j], centerPoint }; double triangleArea = getTriangleArea(triangle); area[i] += triangleArea; } sort(area); System.out.print("The areas are "); for (int i = 0; i < area.length; i++) System.out.printf("%2.2f ", area[i]); } public static void sort(double[] list) { for (int i = 0; i < list.length - 1; i++) { double currentMin = list[i]; int currentIndex = i; for (int j = i + 1; j < list.length; j++) { if (currentMin > list[j]) { currentIndex = j; currentMin = list[j]; } } if (currentIndex != i) { list[currentIndex] = list[i]; list[i] = currentMin; } } } public static double getTriangleArea(double[][] points) { double side1 = distanceBetweenTwoPoints(points[0][0], points[0][1], points[1][0], points[1][1]); double side2 = distanceBetweenTwoPoints(points[0][0], points[0][1], points[2][0], points[2][1]); double side3 = distanceBetweenTwoPoints(points[2][0], points[2][1], points[1][0], points[1][1]); double s = (side1 + side2 + side3) / 2; double area = s * (s - side1) * (s - side2) * (s - side3); if (area < 0.000001) return 0; else return Math.sqrt(area); } public static double distanceBetweenTwoPoints(double x1, double y1, double x2, double y2) { return Math.sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2)); } public static double[][] findTwoFurthestPoints(double[][] points) { int index1 = 0; int index2 = 0; double[][] p = new double[2][2]; double distance = 0; for (int i = 0; i < points.length - 1; i++) { for (int j = 1 + i; j < points.length; j++) { double tDistance = distanceBetweenTwoPoints(points[i][0], points[i][1], points[j][0],points[j][1]); if (tDistance > distance) { p[0] = points[i]; p[1] = points[j]; distance = tDistance; } } } return new double[][] { p[0],p[1] }; } public static double[] getIntersectingPoint(double[][] points) { double[][] p1 = findTwoFurthestPoints(points); double[][] p2 = exclude(points, p1); double a = p1[0][Y] - p1[1][Y]; // y1 - y2 double b = -(p1[0][X] - p1[1][X]); // -(x1 - x2) double c = p2[0][Y] - p2[1][Y]; // y3 - y4 double d = -(p2[0][X] - p2[1][X]); // -(x3 - x4) // (y1 - y2) * x1 - (x1 - x2) * y1 double e = (p1[0][Y] - p1[1][Y]) * p1[0][X] - (p1[0][X] - p1[1][X]) * p1[0][Y]; // (y3 - y4) * x3 - (x3 - x4) * y3 double f = (p2[0][Y] - p2[1][Y]) * p2[0][X] - (p2[0][X] - p2[1][X]) * p2[0][Y]; double ab_Minus_bc = a * d - b * c; if (ab_Minus_bc == 0) return null; double[] point = new double[2]; point[X] = (e * d - b * f) / ab_Minus_bc; point[Y] = (a * f - e * c) / ab_Minus_bc; return point; } public static double[][] exclude(double[][] points, double[][] exclude) { double[][] p = new double[2][2]; for (int i = 0; i < points.length - 1; i++) { for (int j = 1 + i; j < points.length; j++) { if (exclude[0] != points[i] && exclude[1] != points[j]) { p[0] = points[i]; p[1] = points[j]; } } } return new double[][] {p[0],p[1]}; } }
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