Detecting Regions Divided by a Diagonal Line | Maths Explanation for VB.Net Kids
In this tutorial, you'll learn how to detect when an object crosses a straight line in VB.Net. We'll explore how to check which side of a line a point lies on, and how to apply this logic to a VB.Net canvas animation.
When working with graphics or simulations in VB.Net, you might need to check which side of a line a ball or object is on. This technique is common in VB.Net canvas collision detection and helps define regions divided by a line.
Consider a moving body (circle). When it moves across a diagonal straight line, we can perform an action - such as changing the ball's colour - after it crosses from one region to another.
Understanding the Straight Line Equation in VB.Net
We use the slope-intercept formula (y = mx + c) to define boundaries for region detection in VB.Net.
To implement straight line region detection, we'll compare the ball's x-position with the
position of the line at the same y-coordinate, using the line equation in VB.Net.
If the ball's midpoint is (xb, yb)
and the line at that height is (xl, yl),
then:
xl = myd + c
The ball crosses the line when:
xd >= xl.
This logic uses the line equation in VB.Net to check when an object moves from one region to another.
This can also help with collision detection and
boundary demarcation in VB.Net graphics or HTML canvas.
VB.Net Code: Detecting Line Crossing in Canvas
To determine which side of a diagonal boundary a point belongs to, we use a simple line equation. This VB.Net example demonstrates line region detection using the slope-intercept method.
Create a new Visual Basic Windows Forms Application
project
;
call it Dymetric_VB.
Create 3 new VB.Net classes;
Call them Facet, Dymetric and StraightLineRegion.
Type out the adjoining VB.Net code for detecting the instance a travelling
body crosses the path of a straight line.
This VB.Net line crossing detection example changes the ball's colour once it moves across the line.
Summary: Detecting Line Boundaries with VB.Net
You've learned how to use the line equation in VB.Net to **detect regions divided by a straight line and trigger actions when objects cross the line**. This simple logic forms the foundation of VB.Net graphics and animation algorithms.
By now, you can use VB.Net to detect when an object crosses a straight line and determine which region it belongs to. This simple mathematical approach is useful for animations, physics simulations, and canvas line region detection.
Applying the Line Region Detection Logic in VB.Net
This tutorial teaches you to:
- Detect when a ball crosses a straight or diagonal line.
- Identify which side of a line a point lies on.
- Create interactive VB.Net canvas projects with region-based logic.
You can extend this principle to handle collision detection, line-segment intersection, or more complex 2D graphics region detection.
So! VB.Net Fun Practice Exercise - Detect Straight Line Boundary
As a fun practice exercise, try modifying the VB.Net code to explore different coordinates and intercepts. This will be a great way to connect mathematics and programming, and help you understand more about VB.Net animations and linear boundaries.
VB.Net Straight Line Boundary Window Display Code Stub
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 Straight Line Boundary Facet Window Code Stub
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 Straight Line Boundary Code for Dymetric class
Private line_region As New StraightLineRegion
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
line_region.play(sender, g)
do_simulation = False
Else
' Put ball on screen
line_region.prep(sender, g)
do_simulation = True
End If
End Sub
End Class
VB.Net Animation Code for Straight Line Region class
' 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
' line variables
Private x1, y1, x2, y2 As Integer
Private m, c As Double
Private x_line As Double
Dim ball_colour As New System.Drawing.SolidBrush(System.Drawing.Color.Yellow)
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)
x1 = Math.Round(sender.Width / 2) - 100
y1 = 70
x2 = Math.Round(sender.Width / 2) + 100
y2 = sender.Height - 50
m = (y2 - y1) / (x2 - x1) ' slope
c = (x2 * y1 - x1 * y2) / (x2 - x1) ' y-intercept
' Point where ball will cross line
x_line = (y_ball - c) / m
' draw line
g.DrawLine(Pens.Black, x1, y1, x2, y2)
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
If x_ball >= x_line Then
' change colour as ball crosses line
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 += 10
' take a time pause
Threading.Thread.Sleep(50)
Loop
End Sub
End Class