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The square root of 1 is 1 Whole number part: 1 Fractional part: 0 The square root of 2 is 14142135623731 Whole number part: 1 Fractional part: 0414213562373095 The square root of 3 is 173205080756888 Whole number part: 1 Fractional part: 0732050807568877 The square root of 4 is 2 Whole number part: 2 Fractional part: 0 The square root of 5 is 223606797749979 Whole number part: 2 Fractional part: 023606797749979 The square root of 6 is 244948974278318 Whole number part: 2 Fractional part: 0449489742783178 The square root of 7 is 264575131106459 Whole number part: 2 Fractional part: 0645751311064591 The square root of 8 is 282842712474619 Whole number part: 2 Fractional part: 082842712474619 The square root of 9 is 3 Whole number part: 3 Fractional part: 0 The square root of 10 is 316227766016838 Whole number part: 3 Fractional part: 016227766016838

[ N (f 2 )] =

Part I:

As the output shows, the cast of MathSqrt( ) to int results in the whole number component of the value In this expression

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Follower Motion Synthesis for the Three-Dimensional Cam Before examining the synthesis process, some basic requirements should be noted: 1 The number of motion constraints is not limited However, for the nonparametric forms of the B-spline surface interpolation used here, the pattern of the motion constraints must be a rectangular grid data form 2 To guarantee jerk continuity, the synthesized motion function in each parametric direction must be of at least degree = 4 This means that the order of the B-spline functions must be greater than or equal to 5 3 Since the pro le is a closed surface in the parametric direction of rotation, the motion function along that parametric direction, ie, f2, which is used to form the must

MathSqrt(n) - (int) MathSqrt(n)

You Try It: Write the equation of the line that passes through the point ( 3, 2) and has slope 4 EXAMPLE 111

the cast to int obtains the whole number component, which is then subtracted from the complete value, yielding the fractional component Thus, the outcome of the expression is double Only the value of the second call to MathSqrt( ) is cast to int

be continuous everywhere, including the ends (as noted earlier) The general form of the B-spline surface interpolation can guarantee the continuity only of the internal region of the interpolated surface but not between the two ends Closed periodic B-spline functions produced from uniform knot sequences cited earlier solve this problem 4 No special consideration of continuity is required at the surface edges in the direction of translation so the multiple uniform knot sequence is used The systematic procedure for implementing the B-spline surface interpolation can be established as follows: 1 Set up the motion constraints in a n m rectangular grid If any data are absent in the rectangular grid, they can be lled in by using the B-spline interpolation applied along either the rotating or the translating directions 2 Select the appropriate order of the B-spline functions As shown in Eq (537), the proper value of the order is between two and the number of motion constraints Recall that the degrees of the functions are one less than the order 3 Construct the knot sequence according to the demand of each parametric direction The knot sequence, xI, for the closed periodic B-spline (along the rotation coordinate) can be obtained by f 2min i = 1 xi = f 2max - f 2min - 2 i n + 1 xi -1 + n The knot sequence in the translation coordinate can be found as s2min 1 j k2 s2 - s2min y j = y j -1 + max k2 + 1 j m m - k2 + 1 s2 m + 1 j m + k2 max

# provides an extensive set of operators that give the programmer detailed control over the construction and evaluation of expressions Most of C# s operators fall into the following categories: arithmetic, bitwise, relational, and logical These operators are examined in this chapter Also discussed are the assignment operator and the operator C# also defines several other operators that handle specialized situations, such as array indexing, member access, and the lambda operator These special operators are examined later in this book, when the features to which they apply are described

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