Quadratic Region in VB.Net

Checking the Boundaries of a Quadratic Curve in Visual Basic

Remember that any quadratic equation always have two roots for any value of y (except at it's maximum or minimum point).
All we need to do is use these two roots (x values) as boundaries for our check.
y = ax² + bx + c
ax² + bx + (c-y) = 0

x =	-b ± √(b² - 4a(c-y))
	2a

Our range will then be:

-b - √(b² - 4a(c-y))	≤ x ≤	-b + √(b² - 4a(c-y))
2a	≤ x ≤	2a

where a, b, and c are constants.

We will reuse the moving ball graphic and check for when it enters the region of our curve.

Code to Detect Entrance into Quadratic Region in Visual Basic

To check for when our ball enters the quadratic curve, we will continually check the x position of the ball against the x position gotten using the quadratic equation at the same y position as that of the ball.

We'll designate the coordinates of the ball as (x_b, y_b), and those of the curve as (x_q, y_q).

Create a class;
Call it and QuadraticRegion.
Type out the adjoining VB.Net code for detecting the instance a travelling body crosses the boundary of a quadratic curve.

Dymetric class

Public Class Dymetric
    Private quad_region As New QuadraticRegion
    Private do_simulation = False

    ' decide what course of action to take
    Public Sub decideAction(sender As Object, g As Graphics, click_check As Boolean)
        If do_simulation And click_check Then
            ' do animation
            quad_region.play(sender, g)
            do_simulation = False
        Else
            ' Put ball on screen
            quad_region.prep(sender, g)
            do_simulation = True
        End If
    End Sub
End Class

VB.Net code for QuadraticRegion class

Public Class QuadraticRegion

    ' ball coordinates
    Private x_ball, y_ball As Integer
    Private previous_x As Integer = 0
    Private previous_y As Integer = 0
    Private Const ballDIAMETER = 80
    Dim ball_colour As New System.Drawing.SolidBrush(System.Drawing.Color.Yellow)

    ' quadratic variables
    Private xq_start, yq_start, xq_min, yq_min, xq_stop, x, y As Integer
    Private xq_lb, xq_ub As Double ' curve lower and upper boundary
    Private a, b, c, discriminant As Double
    Private Const dotDIAMETER = 5
    Dim dot_colour As New System.Drawing.SolidBrush(System.Drawing.Color.Black)

    Dim bg_colour As New System.Drawing.SolidBrush(System.Drawing.Color.LightGray)

    ' draw first appearance of ball on the screen
    Public Sub prep(sender As Object, g As Graphics)
        x_ball = 10
        y_ball = Math.Round(sender.Height / 2)
        ball_colour = New System.Drawing.SolidBrush(System.Drawing.Color.Yellow)

        xq_start = Math.Round(sender.Width / 2) - 200
        yq_start = 70
        xq_min = Math.Round(sender.Width / 2)
        yq_min = sender.Height - 70
        xq_stop = Math.Round(sender.Width / 2) + 200

        ' constants
        a = (yq_start - yq_min) / Math.Pow((xq_start - xq_min), 2)
        b = -2 * a * xq_min
        c = yq_min + a * Math.Pow(xq_min, 2)

        discriminant = Math.Sqrt(b * b - 4 * a * (c - (y_ball - ballDIAMETER / 2)))
        If a < 0 Then ' a is negative
            xq_lb = (-b + discriminant) / (2 * a) ' lower boundary
            xq_ub = (-b - discriminant) / (2 * a) ' upper boundary
        Else
            xq_lb = (-b - discriminant) / (2 * a) ' lower boundary
            xq_ub = (-b + discriminant) / (2 * a) ' upper boundary
        End If

        ' draw quadratic curve
        For x = xq_start To xq_stop
            y = CInt(Math.Round(a * x * x + b * x + c))
            ' redraw dot
            g.FillEllipse(dot_colour, x, y, dotDIAMETER, dotDIAMETER)
        Next x

        If previous_x > 0 Then
            ' clear previous ball using background colour
            g.FillEllipse(bg_colour, previous_x, previous_y, ballDIAMETER, ballDIAMETER)
        End If
        ' draw ball
        g.FillEllipse(ball_colour, x_ball, y_ball, ballDIAMETER, ballDIAMETER)
        previous_x = x_ball
        previous_y = y_ball
    End Sub

    ' repetitively clear and draw ball on the screen - Simulate motion
    Public Sub play(sender As Object, g As Graphics)
        ' condition for continuing motion
        Do While x_ball < sender.Width - ballDIAMETER
            ' yellow outside the quadratic region
            ball_colour = New System.Drawing.SolidBrush(System.Drawing.Color.Yellow)
            If (x_ball <= xq_lb And x_ball + ballDIAMETER >= xq_lb) _
                Or (x_ball <= xq_ub And x_ball + ballDIAMETER >= xq_ub) Then
                ' red on the quadratic outline
                ball_colour = New System.Drawing.SolidBrush(System.Drawing.Color.Red)
            ElseIf x_ball >= xq_lb And x_ball + ballDIAMETER <= xq_ub Then
                ' green inside the quadratic region
                ball_colour = New System.Drawing.SolidBrush(System.Drawing.Color.Green)
            End If

            ' clear previous ball using background colour
            g.FillEllipse(bg_colour, previous_x, previous_y, ballDIAMETER, ballDIAMETER)
            ' redraw ball
            g.FillEllipse(ball_colour, x_ball, y_ball, ballDIAMETER, ballDIAMETER)

            previous_x = x_ball
            x_ball += 5
            ' take a time pause
            Threading.Thread.Sleep(50)
        Loop
    End Sub
End Class

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