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// A three-dimensional coordinate class class ThreeD { int x, y, z; // 3-D coordinates public ThreeD() { x = y = z = 0; } public ThreeD(int i, int j, int k) { x = i; y = j; z = k; } // Overload binary + for ThreeD + ThreeD public static ThreeD operator +(ThreeD op1, ThreeD op2) { ThreeD result = new ThreeD(); /* This adds together the coordinates of the two points and returns the result */ resultx = op1x + op2x; resulty = op1y + op2y; resultz = op1z + op2z; return result; } // Overload binary + for object + int public static ThreeD operator +(ThreeD op1, int op2) { ThreeD result = new ThreeD(); resultx = op1x + op2; resulty = op1y + op2; resultz = op1z + op2; return result; } // Show X, Y, Z coordinates public void Show() { ConsoleWriteLine(x + ", " + y + ", " + z); } } class ThreeDDemo { static void Main() { ThreeD a = new ThreeD(1, 2, 3); ThreeD b = new ThreeD(10, 10, 10); ThreeD c = new ThreeD(); ConsoleWrite("Here is a: "); aShow(); ConsoleWriteLine(); ConsoleWrite("Here is b: ");

YOU TRY IT What are the principal angles associated with 7 , 11 /2, 8 /3,

Part I:

bShow(); ConsoleWriteLine(); c = a + b; // ThreeD + ThreeD ConsoleWrite("Result of a + b: "); cShow(); ConsoleWriteLine(); c = b + 10; // ThreeD + int ConsoleWrite("Result of b + 10: "); cShow(); } }

The output from this program is shown here:

14 /5, and 16 /7

Here is a: 1, 2, 3 Here is b: 10, 10, 10 Result of a + b: 11, 12, 13 Result of b + 10: 20, 20, 20

Here s what Brad said: I decided to use a combination The summary statistics that I planned to attach would be organized by category For the report itself, I decided to start with a PAR paragraph, followed by Q&A I thought it would work well

As the output confirms, when the + is applied to two ThreeD objects, their coordinates are added together When the + is applied to a ThreeD object and an integer, the coordinates are increased by the integer value While the overloading of + just shown certainly adds a useful capability to the ThreeD class, it does not quite finish the job Here is why The operator+(ThreeD, int) method allows statements like this: ob1 = ob2 + 10; It does not, unfortunately, allow ones like this: ob1 = 10 + ob2; The reason is that the integer argument is the second argument, which is the right-hand operand, but the preceding statement puts the integer argument on the left To allow both forms of statements, you will need to overload the + yet another time This version must have its first parameter as type int and its second parameter as type ThreeD One version of the operator+( ) method handles ThreeD + integer, and the other handles integer + ThreeD Overloading the + (or any other binary operator) this way allows a built-in type to occur on the left or right side of the operator Here is a version ThreeD that overloads the + operator as just described:

// Overload the + for ThreeD + ThreeD, ThreeD + int, and int + ThreeD using System; // A three-dimensional coordinate class class ThreeD { int x, y, z; // 3-D coordinates

9:

What does the concept of angle and sine and cosine that we have presented here have to do with the classical notion using triangles Notice that any angle such that 0 < /2 has associated to it a right triangle in the first quadrant, with vertex on the unit circle, such that the base is the segment connecting (0, 0) to (x, 0) and the height is the segment connecting (x, 0) to (x, y) See Figure 135 Then sin = y = and cos = x = adjacent side of triangle x = 1 hypotenuse opposite side of triangle y = 1 hypotenuse

public ThreeD() { x = y = z = 0; } public ThreeD(int i, int j, int k) { x = i; y = j; z = k; }