# Piecewise Curves in Visual Basic QuickStart Sample

Illustrates working with piecewise constant and piecewise linear curves using classes from the Extreme.Mathematics.Curves namespace in Visual Basic.

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```
Option Infer On
' The piecewise curve classes reside in the
' Extreme.Mathematics.Curves namespace.
Imports Extreme.Mathematics.Curves
Imports Extreme.Mathematics
' Illustrates the use of the PiecewiseConstantCurve and
' PiecewiseLinearCurve classes.
Module PiecewiseCurves
Sub Main()
' The license is verified at runtime. We're using
' a demo license here. For more information, see
' https://numerics.net/trial-key
Extreme.License.Verify("Demo license")
' A piecewise curve is a curve that has a different definition
' on subintervals of its domain.
'
' This QuickStart Sample illustrates constant and linear piecewise
' curves, which - as the name suggest - are constant or linear
' on each interval.
'
' For an example of cubic splines, see the CubicSplines QuickStart
' Sample.
'
'
' Piecewise constants
'
' All piecewise curves inherit from the PiecewiseCurve class.
' Piecewise constant curves are implemented by the
' PiecewiseConstantCurve class. It has three constructors.
' The first constructor takes two double arrays as parameters.
' These contain the x and y values of the data points:
Dim xValues As Double() = {1, 2, 3, 4, 5, 6}
Dim yValues As Double() = {1, 3, 4, 3, 4, 2}
Dim constant1 As New PiecewiseConstantCurve(xValues, yValues)
' The second constructor takes two Vector objects, containing the
' x and y-values of the data points:
Dim xVector = Vector.Create(xValues)
Dim yVector = Vector.Create(yValues)
Dim constant2 As New PiecewiseConstantCurve(xVector, yVector)
' The third constructor only takes one parameter: an array of
' Point structures that represent the data point.
Dim dataPoints = New Point() _
{New Point(1, 1), New Point(2, 3), New Point(3, 4),
New Point(4, 3), New Point(5, 4), New Point(6, 2)}
Dim constant3 As New PiecewiseConstantCurve(dataPoints)
'
' 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.
'
' Piecewise constant curves have 2n parameters, where n is the number of
' data points. The first n parameters are the x-values. The next
' n parameters are the y-values.
Console.WriteLine("constant1.Parameters.Count = {0}", constant1.Parameters.Count)
' Parameters can easily be retrieved:
Console.WriteLine("constant1.Parameters(0) = {0}", constant1.Parameters(0))
' Parameters can also be set:
constant1.Parameters(0) = 1
'
' Curve Methods
'
' The ValueAt method returns the y value of the
' curve at the specified x value:
Console.WriteLine("constant1.ValueAt(2.4) = {0}", constant1.ValueAt(2.4))
' The SlopeAt method returns the slope of the curve
' a the specified x value:
Console.WriteLine("constant1.SlopeAt(2.4) = {0}", constant1.SlopeAt(2.4))
' The slope at the data points is Double.NaN if the value of the constant
' is different on either side of the data point:
Console.WriteLine("constant1.SlopeAt(2) = {0}", constant1.SlopeAt(2))
' Piecewise constant curves do not have a defined derivative.
' The GetDerivative method returns a GeneralCurve:
Dim derivative As Curve = constant1.GetDerivative()
Console.WriteLine("Type of derivative: {0}", derivative.GetType().ToString())
Console.WriteLine("derivative(2.4) = {0}", derivative.ValueAt(2.4))
' You can get a Line that is the tangent to a curve
' at a specified x value using the TangentAt method:
Dim tangent = constant1.TangentAt(2.4)
Console.WriteLine("Slope of tangent line at 2.4 = {0}", tangent.Parameters(1))
' The integral of a piecewise constant curve can be calculated exactly.
Console.WriteLine("Integral of constant1 between 1.4 and 4.6 = {0}",
constant1.Integral(1.4, 4.6))
'
' Piecewise linear curves
'
' Piecewise linear curves are used for linear interpolation
' between data points. They are implemented by the
' PiecewiseLinearCurve class. It has three constructors,
' similar to the constructors for the PiecewiseLinearCurve
' class..These constructors create the linear interpolating
' curve between the data points.
' The first constructor takes two double arrays as parameters.
' These contain the x and y values of the data points:
Dim xValues2 As Double() = {1, 2, 3, 4, 5, 6}
Dim yValues2 As Double() = {1, 3, 4, 3, 4, 2}
Dim line1 As PiecewiseLinearCurve = New PiecewiseLinearCurve(xValues2, yValues2)
' The second constructor takes two Vector objects, containing the
' x and y-values of the data points:
Dim xVector2 = Vector.Create(xValues2)
Dim yVector2 = Vector.Create(yValues2)
Dim line2 As PiecewiseLinearCurve = New PiecewiseLinearCurve(xVector2, yVector2)
' The third constructor only takes one parameter: an array of
' Point structures that represent the data point.
Dim dataPoints2 As Point() = New Point() _
{New Point(1, 1), New Point(2, 3), New Point(3, 4),
New Point(4, 3), New Point(5, 4), New Point(6, 2)}
Dim line3 As PiecewiseLinearCurve = New PiecewiseLinearCurve(dataPoints)
'
' Curve Parameters
'
' Piecewise linear curves have 2n parameters, where n is the number of
' data points. The first n parameters are the x-values. The next
' n parameters are the y-values.
Console.WriteLine("line1.Parameters.Count = {0}", line1.Parameters.Count)
' Parameters can easily be retrieved:
Console.WriteLine("line1.Parameters(0) = {0}", line1.Parameters(0))
' Parameters can also be set:
line1.Parameters(0) = 1
'
' Curve Methods
'
' The ValueAt method returns the y value of the
' curve at the specified x value:
Console.WriteLine("line1.ValueAt(2.4) = {0}", line1.ValueAt(2.4))
' The SlopeAt method returns the slope of the curve
' a the specified x value:
Console.WriteLine("line1.SlopeAt(2.4) = {0}", line1.SlopeAt(2.4))
' The slope at the data points is Double.NaN if the slope of the line
' is different on either side of the data point:
Console.WriteLine("line1.SlopeAt(2) = {0}", line1.SlopeAt(2))
' Piecewise line curves do not have a defined derivative.
' The GetDerivative method returns a GeneralCurve:
derivative = line1.GetDerivative()
Console.WriteLine("Type of derivative: {0}", derivative.GetType().ToString())
Console.WriteLine("derivative(2.4) = {0}", derivative.ValueAt(2.4))
' You can get a Line that is the tangent to a curve
' at a specified x value using the TangentAt method:
tangent = line1.TangentAt(2.4)
Console.WriteLine("Slope of tangent line at 2.4 = {0}", tangent.Parameters(1))
' The integral of a piecewise line curve can be calculated exactly.
Console.WriteLine("Integral of line1 between 1.4 and 4.6 = {0}",
line1.Integral(1.4, 4.6))
Console.Write("Press Enter key to exit...")
Console.ReadLine()
End Sub
End Module
```