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is permissible because a base class reference, x2 in this case, can refer to a derived class object (which is the object referred to by y) It is important to understand that it is the type of the reference variable not the type of the object that it refers to that determines what members can be accessed That is, when a reference to a derived class object is assigned to a base class reference variable, you will have access only to those parts of the object defined by the base class This is why x2 can t access b even when it refers to a Y object This makes sense because the base class has no knowledge of what a derived class adds to it This is why the last line of code in the program is commented out Although the preceding discussion may seem a bit esoteric, it has some important practical applications One is described here The other is discussed later in this chapter, when virtual methods are covered An important place where derived class references are assigned to base class variables is when constructors are called in a class hierarchy As you know, it is common for a class to define a constructor that takes an object of its class as a parameter This allows the class to construct a copy of an object Classes derived from such a class can take advantage of this feature For example, consider the following versions of TwoDShape and Triangle Both add constructors that take an object as a parameter

This new integral is a bit easier to understand if we write the square root as a fractional power:

Next, explicit formulas are discussed that are applicable to piecewise-linear approximations of boundaries of solids of arbitrary shapes

// Pass a derived class reference to a base class reference using System; class TwoDShape { double pri_width; double pri_height; // Default constructor public TwoDShape() { Width = Height = 00; } // Constructor for TwoDShape public TwoDShape(double w, double h) { Width = w; Height = h; } // Construct object with equal width and height public TwoDShape(double x) { Width = Height = x; }

Part I:

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One simple approximation of the boundary can be obtained by means of a polyhedron formed by polygonal faces The integrals appearing in Eqs (758 to 760), therefore, can be expressed as sums of integrals over the polyhedral faces, the whole boundary S thus being approximated as S U Si

// Construct a copy of a TwoDShape object public TwoDShape(TwoDShape ob) { Width = obWidth; Height = obHeight; } // Properties for Width and Height public double Width { get { return pri_width; } set { pri_width = value < 0 -value : value; } } public double Height { get { return pri_height; } set { pri_height = value < 0 -value : value; } } public void ShowDim() { ConsoleWriteLine("Width and height are " + Width + " and " + Height); } } // A derived class of TwoDShape for triangles class Triangle : TwoDShape { string Style; // A default constructor public Triangle() { Style = "null"; } // Constructor for Triangle public Triangle(string s, double w, double h) : base(w, h) { Style = s; } // Construct an isosceles triangle public Triangle(double x) : base(x) { Style = "isosceles"; } // Construct a copy of a Triangle object public Triangle(Triangle ob) : base(ob) { Style = obStyle; } // Return area of triangle public double Area() { return Width * Height / 2; }

u3/2 du = 3/2

11:

24:

(761)

Method public int IndexOfValue(TV v)

Description Returns the index of the first occurrence of the value specified by v Returns 1 if the value is not in the list Removes the key/value pair associated with k from the list Returns true if successful Returns false if k is not in the list Removes the key/value pair at the index specified by idx

2 103/2 2 103/2 13/2 = 3/2 3 3 3/2

where each part Si is a polygonal portion of a plane The integral formulas thus can be approximated as

public bool Remove(TK k)

public void RemoveAt(int idx) public void TrimExcess( )

V3

TABLE 24-18 Several Commonly Used Methods De ned by SortedList<TK, TV> (continued)

Math Note: Just as with integration by parts, we always have the option of rst evaluating the inde nite integral and then evaluating the limits at the very end The next example illustrates this idea EXAMPLE 710

In addition to the properties defined by the interfaces that it implements, SortedList<TK, TV> defines the following properties:

(762) (763) (764)

Property public int Capacity { get; set; } public IComparer<TK> Comparer { get; } public IList<TK> Keys { get; } public IList<TV> Values { get; } Description Obtains or sets the capacity of the invoking list Obtains the comparer for the invoking list Obtains a collection of the keys Obtains a collection of the values

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