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Maths Behind The Bezier Curve in Visual Basic

Article by:

Thaha Hussain (10/12/2002)

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Summary:

Explains how we can draw a Bezier Curve! The maths behind a Cubic Bezier.Very simple. No API's used. Key words : paint brush, draw, curve, graphics, picture, technique, smooth curve

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Maths Behind The Bezier Curve in Visual Basic

Explains how we can draw a Bezier Curve! The maths behind a Cubic Bezier.Very simple. No API's used.

Select All Code

 
'A cubic Bezier curve is defined by four
'     points.
'(x0,y0) & (x3,y3) are endpoints and
'(x1,y1) & (x2,y2) are control points.
'The following equations define the poin
'     ts 
'on the curve.
'Both are evaluated for an arbitrary num
'     ber of values
' of t between 0 and 1.
'
' X(t) = ax * t ^ 3 + bx * t ^ 2 + cx * 
'     t + x0
'
' X1 = x0 + cx / 3
' X2 = X1 + (cx + bx) / 3
' x3 = x0 + cx + bx + ax
'
' Y(t) = ay * t ^ 3 + by * t ^ 2 + cy * 
'     t + y0
'
' Y1 = y0 + cy / 3
' Y2 = Y1 + (cy + by) / 3
' y3 = y0 + cy + by + ay
Option Explicit
Dim HitCounter As Integer
Dim XPoint(3) As Integer, YPoint(3) As Integer
Dim Drag As Boolean


Private Sub DrawBezier()
    Dim ax, bx, cx, ay, by, cy, xt, yt, t, I As Integer
    On Error Resume Next
    Me.Cls
    Me.DrawWidth = 1
    'Draws control lines
    Me.ForeColor = vbBlue
    Me.Line (XPoint(1), YPoint(1))-(XPoint(0), YPoint(0))
    Me.Line (XPoint(2), YPoint(2))-(XPoint(3), YPoint(3))
    Me.ForeColor = vbRed
    'The following is the core of the progra
    '     m.
    ' All others are just for dragging.
    cx = 3 * (XPoint(1) - XPoint(0))
    bx = 3 * (XPoint(2) - XPoint(1)) - cx
    ax = XPoint(3) - XPoint(0) - cx - bx
    
    cy = 3 * (YPoint(1) - YPoint(0))
    by = 3 * (YPoint(2) - YPoint(1)) - cy
    ay = YPoint(3) - YPoint(0) - cy - by


    For t = 0 To 1 Step 0.001
        xt = ax * t ^ 3 + bx * t ^ 2 + cx * t + XPoint(0)
        yt = ay * t ^ 3 + by * t ^ 2 + cy * t + YPoint(0)


        Form1.PSet (xt, yt) 'Draw Lines for a finer curve
        Next t
        Me.ForeColor = vbYellow
        Me.DrawWidth = 4


        For I = 0 To 3
            Me.PSet (XPoint(I), YPoint(I))
            Print " (x" & I & ", y" & I & ")"
        Next I
    End Sub


Private Sub Form_Load()
    Me.ScaleMode = vbTwips
    MsgBox "Put four points and drag them To adjust the" & _
    "curve..", , "Cubic Bezier Demo"
    Me.Caption = "Cubic Bezier by K. O. Thaha Hussain"
End Sub


Private Sub Form_MouseMove(Button As Integer, _
    Shift As Integer, X As Single, Y As Single)


    If CheckHit(X, Y) And Button = vbLeftButton Then
        XPoint(HitCounter) = X
        YPoint(HitCounter) = Y
        Call DrawBezier
        Drag = True
    Else
        Drag = False
    End If
End Sub


Private Sub Form_MouseUp(Button As Integer, _
    Shift As Integer, X As Single, Y As Single)
    Static count As Integer


    If count > 3 Then
        Call DrawBezier
        Exit Sub
    End If
    XPoint(count) = X
    YPoint(count) = Y
    If count = 3 Then Call DrawBezier
    count = count + 1
    Drag = False
End Sub


Function CheckHit(C As Single, V As Single) As Boolean
    Dim I As Integer


    If Drag Then
        CheckHit = True
        Exit Function
    End If


    For I = 0 To 3
        'if the mouse pointer approaches the poi
        '     nts..


        If ((Abs(C - XPoint(I)) < 50 And Abs(V - YPoint(I)) < 50)) Then
            Me.MousePointer = vbCrosshair
            CheckHit = True
            HitCounter = I
            Exit Function
        Else
            Me.MousePointer = vbDefault
            CheckHit = False
        End If
    Next I
End Function

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User Comments on 'Maths Behind The Bezier Curve in Visual Basic'

Posted by : Archive Import (mohammad) at 04:40 on Tuesday, November 05, 2002

hi.
the Xpoint function is not valid!!!!
if you could explain me how can i use or create it.
thanks.

Posted by : Archive Import (Smidge204) at 18:02 on Thursday, December 26, 2002

According to the code snippet, XPoint() is an Integer array of 3 elements. Looks like somebody didn't copy all the code or didn't put it into their project properly :)

Works just fine for me. Great stuff!
=Smidge=

Posted by : Archive Import (Peter Goodier) at 00:10 on Friday, December 27, 2002

How do you construct a BEZIER curve (spline), from more than 4 points
eg. 50 "X , Y" co-ordinance points.

Kind Regards
Peter Goodier

Posted by : Archive Import (Thaha Hussain (Author)) at 03:56 on Tuesday, February 18, 2003

Pls copy and paste the code to your general declaration section. It will work.

Bezier curve is made always with 4 control points.

Pls see another wonderful snippet.

http://www.planetsourcecode.com/vb/scripts/ShowCodeAsText.asp?txtCodeId=1871&lngWId=1

Best,
Thaha Hussain

Posted by : Archive Import (Paul) at 10:42 on Thursday, February 27, 2003

Thaha - excellent piece of code. Very impressive.

Posted by : Archive Import (Shu Yih) at 22:27 on Wednesday, March 19, 2003

how could i trace the action of user clicking on the curve?your code trace the action click on the control point only. Thanks

Posted by : Archive Import (Raja Kumar) at 00:34 on Tuesday, April 15, 2003

I saw your curve program for my ref. but i need somthing like a ecg reading.
I have time and thickness values from that i want to write a continues drawing line a ecg scan reading graph.
can you help me.

with advance thanks
Raja Kumar D.S

Posted by : Archive Import (Andrés Vilegas R) at 14:17 on Wednesday, April 23, 2003

The code is excellent!!. Except don´t function for values that don't fit in the range of a Interger. I Changed the line: Dim XPoint(3) As Integer, YPoint(3) As Integer to this: Dim XPoint(3) As Long, YPoint(3) As Long, and the code runs very well.

Posted by : Archive Import (Thaha Hussain) at 10:55 on Wednesday, June 04, 2003

Dear Readers,

Thanx.

If you have queries, please contact me thro' my mail id.

Regs,
Thaha Hussain
thaha_ko(a)yahoo.com

Posted by : Archive Import (mohamed) at 13:57 on Sunday, June 08, 2003

i think it's better to deal with bezire curve by more better graphics representation
to enhance ur program
thnx and good luck

Posted by : Archive Import (sudha) at 03:32 on Monday, June 30, 2003

the taask is just ok! this movement is every one knows.
You will find try to move the line without selecting end or starting point user can move mid point of the line.
You will find the solution means that is powerful
ok!

Posted by : Archive Import (enix) at 20:04 on Tuesday, July 01, 2003

yes, this was exacly the kind of theory and implementation i was looking for! thank you Thaha, codetoad and google :)

Posted by : Archive Import (Robert Canty) at 11:01 on Monday, July 07, 2003

Very very good indeed!

Posted by : Archive Import (Thaha Hussain(Author)) at 10:56 on Wednesday, July 16, 2003

As Enix said, my aim was to teach the simple maths behind Bezier Curve. Enhancements.. upto you!

Regards,
Thaha Hussain

Posted by : Archive Import (sanosi ) at 05:04 on Thursday, July 31, 2003

Iwant you to Call Me in my Email

Posted by : Archive Import (Senthil) at 08:56 on Monday, August 04, 2003

I saw ur code for bezier curve. I got this concept from other website. But now I try to create a tapered bezier curve.It is done by using drawwidth change for each points. but it is not smoothly. If u know any option for smooth plz send it to me.

Posted by : Archive Import (Abdul) at 12:41 on Wednesday, September 03, 2003

Is this code or anything similar to it avaiable in C++?

Posted by : Archive Import (victor ) at 19:56 on Friday, September 05, 2003

Sorry for my bad english. I want to make a question, is it posible to create a graph like wich are done with Excel, inside a form in visual Basic?. How can I do that?
Thanks for your help

Posted by : JAD at 08:51 on Thursday, March 23, 2006

hello all , my best friend is in deep trouble , coz we couldnt figure out how to code this one , the submission is tomorrow ...
here's the link to the pdf

http://www.geocities.com/jad_4ev3r/Semester_2_Coursework.pdf

it's a Bezier curve , if anyone can do it tonight , we'll be very very thankful ..

Posted by : JAD at 09:17 on Thursday, March 23, 2006

oh forget to say that it has to be done in C++ , here's the download for the program that has to be done in it
http://www.salfordsoftware.co.uk/software/downloads/compilers.html

thanks again

Posted by : zagros at 03:50 on Tuesday, November 07, 2006

hi
please help me for drawing bezier curve with four points which all located on bezier curve.(Drawing a Bezier curve through four data point)

regards
zag

Posted by : mjane at 13:08 on Tuesday, February 12, 2008

I'm trying to make a bezier curve display on a chart in Access...any suggestions on how to change the code to pass the points from a table?

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