Extreme Optimization > QuickStart Samples > Quadratic Curve QuickStart Sample (VB.NET)

Extreme Optimization QuickStart Samples

Quadratic Curve QuickStart Sample (VB.NET)

Illustrates the use of the Quadratic class (Extreme.Mathematics.Curves namespace) in Visual Basic .NET.

C# code Back to QuickStart Samples

' The Point structure and Quadratic class reside in the
' Extreme.Mathematics.Curves namespace.
Imports Extreme.Mathematics.Curves

Namespace Extreme.Mathematics.QuickStart.VB

    Module QuadraticCurve

        ' Illustrates the use of the Point structure and the Quadratic
        ' class in the Extreme.Mathematics.Curve namespace of the 
        ' Extreme Optimization Mathematics Library for .NET.
        Sub Main()
            ' All curves inherit from the Curve abstract base
            ' class. The Quadratic class overrides implements all
            ' the methods and properties of the Curve class,
            ' and adds a few more.
            '
            ' In a few places, we will need the Point structure.
            ' It simply containts an X and a Y component, much
            ' like the PointF structure in the System.Drawing
            ' namespace.
            '
            ' Let's create some points:
            Dim point1 As Point = New Point(-1, -4)
            Dim point3 As Point = New Point(0, -3)
            Dim point2 As Point = New Point(3, 12)

            '
            ' Quadratic constructors
            '

            ' The Quadratic class has multiple constructors. Each
            ' constructor derives from a different way to define
            ' a quadratic curve or parabola.

            ' 1st option: a quadratic curve through 3 points.
            Dim quadratic1 As Quadratic = New Quadratic( _
                point1, point2, point3)
            ' 2nd option: same as above, but we use the x and 
            ' y coordinates of the points directly.
            Dim quadratic2 As Quadratic = New Quadratic( _
                point1.x, point1.y, point2.x, point2.y, point3.x, point3.y)
            ' 3rd option: give the three coefficients, a, b, and c
            ' of thequadratic form ax^2+bx+c.
            Dim quadratic3 As Quadratic = New Quadratic(1, 2, 1)

            '
            ' Curve Parameters
            '

            ' The shape of any curve is determined by a set of parameters.
            ' These parameters can be retrieved and set through the
            ' Parameters collection. The number of parameters for a curve
            ' is given by this collection's Count property.
            '
            ' Quadratic curves have three parameters.
            Console.WriteLine("quadratic1.Parameters.Count = {0}", _
                quadratic1.Parameters.Count)
            ' Parameters can easily be retrieved:
            Console.WriteLine("quadratic1 parameters {0}, {1}, {2}", _
                quadratic1.Parameters(0) = , quadratic1.Parameters(1) = , _
                quadratic1.Parameters(2)
            ' We can see that quadratic2 defines the same quadratic 
            ' curve as quadratic1, but quadratic3 is different:
            Console.WriteLine("quadratic2 parameters {0}, {1}, {2}", _
                quadratic2.Parameters(0) = , quadratic2.Parameters(1) = , _
                quadratic2.Parameters(2)
            Console.WriteLine("quadratic3 parameters {0}, {1}, {2}", _
                quadratic3.Parameters(0) = , quadratic3.Parameters(1) = , _
                quadratic3.Parameters(2)
            ' Parameters can also be set:
            quadratic3.Parameters(0) = 1

            '
            ' Curve Methods
            '

            ' The ValueAt method returns the y value of the
            ' curve at the specified x value:
            Console.WriteLine("quadratic1.ValueAt(2) = {0}", _
                quadratic1.ValueAt(2))

            ' The SlopeAt method returns the slope of the curve
            ' a the specified x value:
            Console.WriteLine("quadratic1.SlopeAt(2) = {0}", _
                quadratic1.SlopeAt(2))

            ' You can also create a new curve that is the 
            ' derivative of the original:
            Dim derivative As Curve = quadratic1.GetDerivative()
            Console.WriteLine("Slope at 2 (derivative) = {0}", _
                derivative.ValueAt(2))
            ' For a quadratic curve, the derivative is a Line:
            Console.WriteLine("Type of derivative: {0}", _
                derivative.GetType().ToString())
            Console.WriteLine("Derivative parameters:")
            Console.WriteLine("  Y-intercept = {0}", _
                derivative.Parameters(0)
            Console.WriteLine("  Slope = {0}", _
                derivative.Parameters(1)

            ' You can get a Line that is the tangent to a curve
            ' at a specified x value using the TangentAt method:
            Dim tangent As Line = quadratic1.TangentAt(2)
            Console.WriteLine("Tangent line at 2:")
            Console.WriteLine("  Y-intercept = {0}", _
                tangent.Parameters(0)
            Console.WriteLine("  Slope = {0}", _
                tangent.Parameters(1)

            ' For many curves, you can evaluate a definite
            ' integral exactly:
            Console.WriteLine("Integral between 0 and 1 = {0}", _
                quadratic1.Integral(0, 1))

            ' You can find the zeroes or roots of the curve
            ' by calling the FindRoots method:
            Dim roots As Double() = quadratic1.FindRoots()
            Console.WriteLine("quadratic1 has {0} roots:", _
                roots.Length)
            Console.WriteLine("Value of root 1 = {0}", roots(0))
            Console.WriteLine("Value of root 2 = {0}", roots(1))
            ' quadratic3 has one double root at x = -1:
            roots = quadratic3.FindRoots()
            Console.WriteLine("Number of roots of quadratic3: {0}", _
                roots.Length)
            Console.WriteLine("Value of root = {0}", roots(0))

            ' Let's change quadratic3 so it has no real roots:
            quadratic3.Parameters(0) = 2
            roots = quadratic3.FindRoots()
            Console.WriteLine("New quadratic3 has {0} roots.", _
                roots.Length)

            Console.Write("Press Enter key to exit...")
            Console.ReadLine()

        End Sub

    End Module

End Namespace

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