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This method compares the invoking object against the value in obj It returns greater than zero if the invoking object is greater than obj, zero if the two objects are equal, and less than zero if the invoking object is less than obj IComparable<T> is the generic version of IComparable It defines the generic version of CompareTo( ): int CompareTo(T obj) The generic version of CompareTo( ) works like the non-generic version It compares the invoking object against the value in obj It returns greater than zero if the invoking object is greater than obj, zero if the two objects are equal, and less than zero if the invoking object is less than obj The advantage of using IComparable<T> is type safety because the type of data being operated upon is explicitly specified There is no need to cast the object being compared from object into the desired type Here is an example that illustrates sorting and searching an array of user-defined class objects:

// Sort and search an array of objects using System; class MyClass : IComparable<MyClass> { public int i; public MyClass(int x) { i = x; } // Implement IComparable<MyClass> public int CompareTo(MyClass v) { return i - vi; } public bool Equals(MyClass v) { return i == vi; } } class SortDemo { static void Main() { MyClass[] nums = new MyClass[5]; nums[0] nums[1] nums[2] nums[3] nums[4] = = = = = new new new new new MyClass(5); MyClass(2); MyClass(3); MyClass(4); MyClass(1);

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EXAMPLE 4: A Case with a Large Number of Constraints In this example a total of 20 constraints has been speci ed These constraints are listed in Table 54 The results obtained using a polynomial of degree 19 and sixth-order splines with uniform knot spacing are shown in Figs 58, 59, and 510 The better characteristics of the spline function, particularly of the derivatives near the boundaries of the motion interval, are apparent No attempt was made at further enhancement of the curves by adjusting the knot sequence

// Display original order ConsoleWrite("Original order: "); foreach(MyClass o in nums) ConsoleWrite(oi + " "); ConsoleWriteLine(); // Sort the array ArraySort(nums);

Part II:

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116 1

// Display sorted order ConsoleWrite("Sorted order: foreach(MyClass o in nums) ConsoleWrite(oi + " "); ConsoleWriteLine();

// Search for MyClass(2) MyClass x = new MyClass(2); int idx = ArrayBinarySearch(nums, x); ConsoleWriteLine("Index of MyClass(2) is " + idx); } }

Displacement (cm) Velocity (cm/rad) Acceleration (cm/rad/rad) Constraint 1 0 45 90 Cam rotation angle (deg)

The output is shown here:

There are two types of functions: polynomial and transcendental A polynomial of degree k is a function of the form p(x) = a0 + a1 x + a2 x 2 + + ak x k Such a polynomial has precisely k roots, and there are algorithms that enable us to solve for those roots For most purposes, polynomials are the most accessible and easy-to-understand functions But there are other functions that are important in mathematics and physics These are the transcendental functions Among this more sophisticated type of functions are sine, cosine, the other trigonometric functions, and also the logarithm and the exponential The present chapter is devoted to the study of transcendental functions

Sometimes it is useful to reverse the contents of an array For example, you might want to change an array that has been sorted in ascending order into one sorted in descending order Reversing an array is easy: Simply call Reverse( ) Using Reverse( ), you can reverse all or part of an array The following program demonstrates the process:

FIGURE 55 Cam follower displacement, velocity, and acceleration obtained by polynomial synthesis in Example 3

// Reverse an array using System; class ReverseDemo { static void Main() { int[] nums = { 1, 2, 3, 4, 5 }; // Display original order ConsoleWrite("Original order: "); foreach(int i in nums) ConsoleWrite(i + " "); ConsoleWriteLine(); // Reverse the entire array ArrayReverse(nums); // Display reversed order ConsoleWrite("Reversed order: "); foreach(int i in nums) ConsoleWrite(i + " "); ConsoleWriteLine(); // Reverse a range ArrayReverse(nums, 1, 3); // Display reversed order ConsoleWrite("Range reversed: "); foreach(int i in nums)

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