Chapter 10, Problem 10.12PE

(Geometry: the Triangle2D class) Define the Triangle2D class that contains:

• Three points named p1, p2, and p3 of the type MyPoint with getter and setter methods. MyPoint is defined in Programming Exercise 10.4.
• A no-arg constructor that creates a default triangle with the points (0, 0), (1,1), and (2,5).
• A constructor that creates a triangle with the specified points.
• A method getArea () that returns the area of the triangle.
• A method getPerimeter () that returns the perimeter of the triangle.
• A method contains (MyPoint p) that returns true if the specified point p is inside this triangle (see Figure 10.22a).
• A method contains(Triang1e2D t) that returns true if the specified triangle is inside this triangle (see Figure 10.22b).
• A method overlaps(Triangle2D t) that returns true if the specified triangle overlaps with this triangle (see Figure 10.22c).

FIGURE 10.22    (a) A point is inside the triangle, (b) A triangle is inside another triangle. (c) A triangle overlaps another triangle.

Draw the UML diagram for the class and then implement the class. Write a test program that creates a Triangle2D object t1 using the constructor new Triangle2D(new MyPoint(2.5, 2), new MyPoint(4.2, 3), new MyPoint(5, 3.5)), displays its area and perimeter, and displays the result of t1.contains(3, 3), r1.contains(new Triangle2D(new MyPoint(2.9, 2), new MyPoint(4, 1). MyPoint(1, 3.4))).and t1 .overlaps(new Triangle2D(new MyPoint(2, 5.5), new MyPoint (4. –3), MyPoint(2, 6.5))).

(Hint: For the formula to compute the area of a triangle, sec Programming Exercise 2. 19. To detect whether a point is inside a triangle, draw three dashed lines, as shown in Figure 10.23. If the point is inside a triangle, each dashed line should intersect a side only once. If a dashed line intersects a side twice, then the point must be outside the triangle. For the algorithm of finding the intersecting point of two lines, see Programming Exercise 3.25.)

FIGURE 10.23    (a) A point is inside the triangle, (b) A point is outside the triangle.