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Eighth-Degree Polynomial Curve The eighth-degree polynomial has acceleration characteristics between the harmonic and cycloidal curves It has an asymmetrical acceleration at the dwell rise or end The curve can also be blended conveniently with other curves at its maximum rise point For the rise action: q q q y = h 609755 - 2078040 + 2673155 b b b q q - 1360965 + 256095 b b y = h b q q q 1829265 = 1 - 390200 + 16038930 b b b

21:

Here is an example that uses Sqrt( ) to help implement the Pythagorean theorem It computes the length of the hypotenuse given the lengths of the two opposing sides of a right triangle

The Round function will return a numeric input_parameter rounded to a specified number of decimal places provided in number decimal_places

// Implement the Pythagorean Theorem using System; class Pythagorean { static void Main() { double s1; double s2; double hypot; string str; ConsoleWriteLine("Enter length of first side: "); str = ConsoleReadLine(); s1 = DoubleParse(str); ConsoleWriteLine("Enter length of second side: "); str = ConsoleReadLine(); s2 = DoubleParse(str); hypot = MathSqrt(s1*s1 + s2*s2); ConsoleWriteLine("Hypotenuse is " + hypot); } }

6 7 2 4 5 7 8 3 5 6

When one type of data is assigned to another type of variable, an implicit type conversion will take place automatically if The two types are compatible The destination type has a range that is greater than the source type When these two conditions are met, a widening conversion takes place For example, the int type is always large enough to hold all valid byte values, and both int and byte are compatible integer types, so an implicit conversion can be applied For widening conversions, the numeric types, including integer and floating-point types, are compatible with each other For example, the following program is perfectly valid since long to double is a widening conversion that is automatically performed

number Round(number input_parameter; number decimal_places)

// Demonstrate implicit conversion from long to double using System; class LtoD { static void Main() { long L; double D; L = 100123285L; D = L; ConsoleWriteLine("L and D: " + L + " " + D); } }

y =

Part I:

The Sign function will return the sign of the number input_parameter provided: 1 is returned to indicate a negative number; 0 is returned to indicate a zero; 1 is returned to indicate a positive

Although there is an implicit conversion from long to double, there is no implicit conversion from double to long since this is not a widening conversion Thus, the following version of the preceding program is invalid:

h q q q 3658530 - 41560800 + 80194650 2 b b b b q q - 57160530 + 14341320 b b

// *** This program will not compile *** using System; class LtoD { static void Main() { long L; double D; D = 1001232850; L = D; // Illegal!!! ConsoleWriteLine("L and D: " + L + " " + D); } }

number Sign(number input_parameter)

In addition to the restrictions just described, there are no implicit conversions between decimal and float or double, or from the numeric types to char or bool Also, char and bool are not compatible with each other

6 7 2 5

Although the implicit type conversions are helpful, they will not fulfill all programming needs because they apply only to widening conversions between compatible types For all other cases you must employ a cast A cast is an instruction to the compiler to convert the outcome of an expression into a specified type Thus, it requests an explicit type conversion A cast has this general form: (target-type) expression Here, target-type specifies the desired type to convert the specified expression to For example, given

number Sin(number input_parameter)

double x, y;

(int) (x / y)

q q q - 317060 - 687795 + 256095 b b b y = h b q q q -526830 + 1390275 + 1902360 b b b

number Sqrt(number input_parameter)