Ellipse Region Detection in VB.Net | Ellipse Boundary & Collision Detection

Understanding the Ellipse Region | Maths Explanation for VB.Net Kids

In this tutorial, we'll learn how to use VB.Net ellipse region detection to determine whether a point or object lies inside a defined ellipse boundary. This concept combines two important ideas: geometry (the equation of an ellipse) and programming logic (using conditions in VB.Net).

Being able to test if a point lies within an ellipse is useful in many areas — such as collision detection, interactive graphics, and educational simulations. Let's break it down step by step.

Checking the Boundaries of an Ellipse in VB.Net | The Mathematics Behind the Ellipse

We'll use the standard ellipse equation to calculate if an (x, y) coordinate is within the ellipse region in VB.Net.

As explained in the Equation of an Ellipse in VB.Net tutorial, an ellipse centered at (h, k) with semi-major axis a and semi-minor axis b is defined by:

(x - h)²	+	(y - k)²	= 1
a²		b²

Every point (x, y) that satisfies this equation lies on the boundary of the ellipse. If the sum on the left-hand side is less than 1, then the point is inside the ellipse. If it's greater than 1, the point lies outside.

It can be deduced that y = k ± ^b/_a√(a² - (x - h)²) ;
And conversely x = h ± ^a/_b√(b² - (y - k)²)
Hence, the boundaries of any ellipse lie in the range
y ≥ k - ^b/_a√(a² - (x_external - h)²);
y ≤ k + ^b/_a√(a² - (x_external - h)²)
and
x ≥ h - ^a/_b√(b² - (y_external - k)²);
x ≤ h + ^a/_b√(b² - (y_external - k)²)

Tip: The equation (x - h)² / a² + (y - k)² ≤ 1 defines the entire region of the ellipse, not just its outline.

Step-by-Step Explanation for VB.Net Algorithm

Use the ellipse equation to test points.
Apply the test to detect when an object enters the ellipse region.
Visualize the region on the VB.Net windows form.

Code to Detect Entrance into an Elliptical Region in VB.Net

Any point (x, y) that satisfies (x - h)² / a² + (y - k)² ≤ 1 lies inside the ellipse region. We'll translate this into VB.Net code to perform region detection.

To check for when a second body enters the ellipse, we will continually use the x position of this second body in the ellipse equation to detect when its y position lies between the top and bottom limits at the x position in question:
y_{2nd_img}(top) > k - ^b/_a√(a² - (x_{2nd_img} - h)²)
and y_{2nd_img}(bottom) < k + ^b/_a√(a² - (x_{2nd_img} - h)²) ;
At the same time, we will use the y position of the second body in the ellipse equation to detect when its x position lies between the left and right limits at the y position in question:
x_{2nd_img}(left) > h - ^a/_b√(b² - (y_{2nd_img} - k)²)
and x_{2nd_img}(right) < h + ^a/_b√(b² - (y_{2nd_img} - k)²)

Figure: VB.Net elliptical region detection example on VB.Net windows form

Here's a VB.Net code for ellipse region check using the VB.Net windows form element. This approach works well for ellipse region collision detection in graphics or games.

Create a new Visual Basic Windows Forms Application project ; call it Dymetric_VB.
Create 3 new VB.Net classes;
Call them Facet, Dymetric and EllipticalRegion.
Type out the adjoining VB.Net code for detecting the instance a travelling body crosses the boundary of an ellipse.

By The Way: Notice how the equations for a circle are similar to those of an ellipse;
No surprise there!
A circle is just an ellipse in its simplest form.

How the VB.Net Elliptical Region Detection Code Works

The ellipse is centered at (h, k) with radii a (horizontal) and b (vertical).
For each point (x, y), we calculate ((x - h)² / a²) + ((y - k)² / b²).
If the result is less than or equal to 1, the point lies inside the elliptical region.
Otherwise, it is outside the region.

This same principle is used in collision detection algorithms for games and simulations, where objects have elliptical or circular boundaries.

Applications of Ellipse Region Logic

Graphics and Animation: Detecting when a sprite enters an elliptical area on the canvas.
Mathematics Education: Demonstrating geometric regions and inequalities involving ellipses.
Game Development: Checking collisions or hitboxes shaped like ellipses instead of rectangles.
Data Visualization: Highlighting focus zones or interactive selections shaped as ellipses.

In all these cases, VB.Net ellipse detection helps make interfaces interactive and geometrically accurate.

Key Takeaways on Elliptical Region Detection in VB.Net

In this tutorial, you've learned:

The equation of an ellipse and how to test point positions,
How to use VB.Net and VB.Net windows form to visualize the region,
Practical applications of ellipse region detection in programming and mathematics.

Using VB.Net ellipse boundary code, we can check if a moving object or point enters the defined elliptical region. This method is useful in maths programming and interactive learning for senior secondary students.

This simple concept links algebra, geometry, and coding — showing how mathematics powers real programming!

Summary: Visualizing Elliptical Region in VB.Net

In this tutorial, we learned how to perform ellipse boundary detection in VB.Net. By using the standard ellipse equation, you can efficiently determine whether a point lies inside or outside the elliptical region. This logic is widely used in collision detection, interactive graphics, and data visualization.

So! VB.Net Fun Practice Exercise - Detect Elliptical Region

As a fun practice exercise, try implementing the same VB.Net code but using the parmetric equation of an ellipse this time. This will really validate your understanding of coordinate geometry interpretation and VB.Net graphical programming for ellipse region detection and mathematics application.

VB.Net Elliptical Boundary Window Display Code Stub

Public Class Form1

    Private form_details As New Facet
    Private action_class As New Dymetric

    Private Sub Form1_Load(sender As Object, e As EventArgs) Handles MyBase.Load
        ' Fill in Form - Put button on form
        form_details.formFeatures(sender)
    End Sub

    Private Sub Form1_Paint(sender As Object, e As PaintEventArgs) Handles Me.Paint
        ' Colour button area
        form_details.decorateButtonArea(sender, e)

        ' Call MovingBody class into action
        action_class.decideAction(sender, Me.CreateGraphics(), form_details.CLICK_OCCURRED)

        ' Reset click variable
        form_details.CLICK_OCCURRED = False
    End Sub
End Class

VB.Net Elliptical Boundary Facet Window Code Stub

Public Class Facet

    Dim screen_rect As Rectangle
    Public CLICK_OCCURRED As Boolean = False

    Public Sub formFeatures(sender As Object)
        'Set window position, width and height
        screen_rect = Screen.PrimaryScreen.Bounds
        sender.SetDesktopBounds(0, 0, screen_rect.Width, screen_rect.Height)

        ' Set a display text
        sender.Text = "useOfMaths.com"

        ' Set a background colour
        sender.BackColor = System.Drawing.Color.LightGray

        ' Set an icon image
        Dim path = System.IO.Path.GetDirectoryName(System.Reflection.Assembly.GetExecutingAssembly().CodeBase)
        path = New Uri(path).LocalPath
        Try
            sender.Icon = New Icon(path & "\useOfMaths.ico")
        Catch ex As System.IO.FileNotFoundException
            ' Well, just go on and use default pic
        End Try

        '
        'create a button - response_btn
        '
        Dim response_btn As New Button()
        response_btn.BackColor = System.Drawing.Color.Magenta
        response_btn.ForeColor = System.Drawing.Color.Blue
        response_btn.Name = "response_btn"
        response_btn.SetBounds(CInt(Math.Round(screen_rect.Width / 2)) - 50, 5, 100, 40)
        response_btn.Text = "Move"
        sender.Controls.Add(response_btn)
        AddHandler response_btn.Click, AddressOf response_btn_Click
    End Sub

    Public Sub decorateButtonArea(sender As Object, e As PaintEventArgs)
        ' Draw a dotted line
        Dim pencil As New System.Drawing.Pen(System.Drawing.Color.Black)
        pencil.DashStyle = Drawing2D.DashStyle.DashDot
        pencil.Width = 5
        e.Graphics.DrawLine(pencil, 0, 50, sender.Width, 50)
        pencil.Dispose()

        ' Colour region
        Dim paint_brush As New System.Drawing.SolidBrush(System.Drawing.Color.Pink)
        e.Graphics.FillRectangle(paint_brush, 0, 0, sender.Width, 50)
        paint_brush.Dispose()
    End Sub

    Public Sub response_btn_Click(sender As Object, e As EventArgs)
        ' turn this on on every button click
        CLICK_OCCURRED = True
        sender.Refresh()
    End Sub
End Class

VB.Net Elliptical Boundary Code for Dymetric Class

Public Class Dymetric
    Private ellipse_zone As New EllipticalRegion
    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
            ellipse_zone.play(sender, g)
            do_simulation = False
        Else
            ' Put ball on screen
            ellipse_zone.prep(sender, g)
            do_simulation = True
        End If
    End Sub
End Class

VB.Net Animation Code for Elliptical Region Class

Public Class EllipticalRegion

    ' square coordinates
    Private x_square, y_square As Integer
    Private previous_x As Integer = 0
    Private previous_y As Integer = 0
    Private Const squareLENGTH = 100
    Dim square_pen As New System.Drawing.Pen(System.Drawing.Color.Yellow)

    ' circle variables
    Private h, k, a, b As Integer
    Private Const dotDIAMETER = 10

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

    ' draw first appearance of square on the screen
    Public Sub prep(sender As Object, g As Graphics)
        x_square = 10
        y_square = Math.Round(sender.Height / 2)
        square_pen.Width = 5

        ' ellipse centre coordinates
        h = Math.Round(sender.Width / 2)
        k = Math.Round(sender.Height / 2)
        ' ellipse major and minor semi-axes
        a = sender.Width / 3
        b = sender.Height / 3

        ' draw an ellipse
        g.DrawEllipse(Pens.Black, h - a, k - b, 2 * a, 2 * b)

        If previous_x > 0 Then
            ' clear previous square using background colour
            g.FillRectangle(bg_colour, previous_x - 5, previous_y - 5, squareLENGTH + 10, squareLENGTH + 10)
        End If
        ' draw square
        g.DrawRectangle(square_pen, x_square, y_square, squareLENGTH, squareLENGTH)
        previous_x = x_square
        previous_y = y_square
    End Sub

    ' repetitively clear and draw square on the screen - Simulate motion
    Public Sub play(sender As Object, g As Graphics)
        ' condition for continuing motion
        Do While x_square < sender.Width - squareLENGTH

            Dim square_left = x_square
            Dim square_right = x_square + squareLENGTH
            Dim square_top = y_square
            Dim square_bottom = y_square + squareLENGTH
            ' determinants for each side of the square
            Dim x_left_det = Math.Round((b / a) * Math.Sqrt(Math.Pow(a, 2) - Math.Pow((square_left - h), 2)))
            Dim x_right_det = Math.Round((b / a) * Math.Sqrt(Math.Pow(a, 2) - Math.Pow((square_right - h), 2)))
            Dim y_up_det = Math.Round((a / b) * Math.Sqrt(Math.Pow(b, 2) - Math.Pow((square_top - k), 2)))
            Dim y_down_det = Math.Round((a / b) * Math.Sqrt(Math.Pow(b, 2) - Math.Pow((square_bottom - k), 2)))

            ' check the bounds of the circle
            ' yellow outside the circle
            square_pen = New System.Drawing.Pen(System.Drawing.Color.Yellow)
            If square_top > k - x_left_det And square_bottom < k + x_left_det _
            And square_top > k - x_right_det And square_bottom < k + x_right_det _
            And square_left > h - y_up_det And square_right < h + y_up_det _
            And square_left > h - y_down_det And square_right < h + y_down_det Then
                ' green inside the circle
                square_pen = New System.Drawing.Pen(System.Drawing.Color.Green)
            End If
            square_pen.Width = 5

            ' clear previous square using background colour
            g.FillRectangle(bg_colour, previous_x - 5, previous_y - 5, squareLENGTH + 10, squareLENGTH + 10)
            ' redraw square
            g.DrawRectangle(square_pen, x_square, y_square, squareLENGTH, squareLENGTH)

            previous_x = x_square
            x_square += 10
            ' take a time pause
            Threading.Thread.Sleep(50)
        Loop
    End Sub
End Class

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