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The IComparer<T> interface is the generic version of IComparer described earlier The main difference between the two is that IComparer<T> is type-safe, declaring the generic version of Compare( ) shown here: int Compare(T obj1, T obj2) This method compares obj1 with obj2 and returns greater than zero if obj1 is greater than obj2, zero if the two objects are the same, and less than zero if obj1 is less that obj2

The IEqualityComparer<T> interface is the equivalent of its non-generic relative IEqualityComparer It defines these two methods: bool Equals(T obj1, T obj2) int GetHashCode(T obj) Equals( ) must return true if obj1 and obj2 are equal GetHashCode( ) must return the hash code for obj

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The calculation of the presure angle and the curvature of the pro le at an arbitrary value of c outside of the set {yi}in calls for values of s (y) and s (y) or, correspondingly, f (y) and f (y) outside of the values arrayed in vectors y and y These derivative values can be readily calculated by means of Eq (737), namely, as y (y ) = 3 Ai (y - y i ) + 2 Bi (y - y i ) + Ci , y i y y i +1 y (y ) = 6 Ai (y - y i ) + 2 Bi , y i y y i +1

= (sin x) (sin x)

SystemCollectionsGeneric defines a structure called KeyValuePair<TK, TV>, which is used to store a key and its value It is used by the generic collection classes that store key/ value pairs, such as Dictionary<TK, TV> This structure defines the following two properties: public TK Key { get; }; public TV Value { get; }; These properties hold the key or value associated with an entry You can construct a KeyValuePair<TK, TV> object by using the following constructor: public KeyValuePair(TK k, TV v) Here, k is the key and v is the value

24:

(740) (741)

As mentioned at the start of this section, the generic collection classes largely parallel their non-generic relatives, although in some cases the names have been changed Also, some differences in organization and functionality exist The generic collections are defined in SystemCollectionsGeneric The ones described in this chapter are shown in Table 24-13 These classes form the core of the generic collections

is a synchronized collection based on IList<T> SynchronizedReadOnlyCollection<T> is a read-only synchronized collection based on IList<T> SynchronizedKeyCollection<K, V> is an abstract class used as a base class by SystemServiceModelUriSchemeKeyedCollection KeyedByTypeCollection<T> is a collection that uses types as keys

At rst blush, it appears that we have accomplished nothing For the new integral is just the same as the old integral But in fact we can move the new integral (on the right) to the left-hand side to obtain 2 sin x cos x dx = sin2 x

With the foregoing interpolated derivative values, the calculation of the pressure angle and the curvature at arbitrary values of y is straightforward 743 Global Properties The computation of the global geometric properties area for 2-D contours and volume for 3-D surfaces, centroid location, and inertia matrix of cam plates is the subject of this subsection Rather than using directly the de nitions of these concepts, as given in Sec 73, we resort to the Gauss divergence theorem (GDT) (Marsden and Tromba, 1988) to transform volume integrals into surface integrals One second application of the GDT readily leads to algorithms based on line integrals, which are computationally more economical than the direct formulas 7431 Two-Dimensional Regions In this subsection the general formulas introduced in Angeles et al (1990) and recalled below are applied to 2-D regions Thus, line-integration formulas will be derived for the computation of the area, the centroid position vector, and the inertia matrix of planar regions R bounded by a closed contour G Let A, qO, and IO denote the area, the vector rst moment, and the matrix second moment of R, qO, and IO being de ned with respect to a given point O in the plane of the region The computation of these quantities can be reduced to integration on the boundary G, by application of the GDT, namely, A= qO = 1 r nd G 2 G (742a) (742b) (742c)

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