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Trilateration Computation

Posted on 2004-09-02
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Last Modified: 2010-08-05
Hello eveybody;

I need program to compute three point assuming x1=0, y1=0, B=PI=180 degree =200 grades) in VB 6.0

by entering three distance like: Dist3,Dist2,Dist1

computing poits : point 2, Point 3

result like : p1(0,0) , p2(?,?), p3(?,?) .. Using Trilateration Comptation Method!

Thanks alot.
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Question by:LoveBii
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8 Comments
 
LVL 76

Expert Comment

by:GrahamSkan
ID: 11962397
Not sure what this bit means :  B=PI=180 degree =200 grades

I suppose that one point is at the origin and that one liies on the X-Axis. You may be trying to say something different.

 ********* In a module :

Option Explicit

Type XY
    x As Single
    y As Single
End Type

********* In a Form:

Option Explicit

Private Sub Command1_Click()
Dim a As Single
Dim b As Single
Dim c As Single

Dim Points(2) As XY

a = Val(Text1.Text)
b = Val(Text2.Text)
c = Val(Text3.Text)

Select Case True
 Case a > b + c, b > a + c, c > a + b
    MsgBox "Invalid triangle"
    Exit Sub
End Select

'Point 0 is at origin (given)
Points(0).x = 0
Points(0).y = 0

'Point 1 is on X-Axis (given)
Points(1).x = c
Points(1).y = 0

Points(2).x = (a ^ 2 + c ^ 2 - b ^ 2) / (2 * c)
Points(2).y = Sqr(a ^ 2 - Points(2).x ^ 2)



End Sub


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Author Comment

by:LoveBii
ID: 11963225
Dear GrahamSka;

thanks alot for your interest with my question, but this is too much far from what i want.

i'll give you some hints in trilateration computation:

for point 2 you have to calculate:
   dx=sin(b)*dist3
   dy=cos(b)*dist3

for point 3 you have to calculate:
   generate dx1,dy1 from x2-x1,y2-y1
   TAN2(DX1,DY1) * (2*PI)
   D3=SQRT(DX1^2+DY1^2)
   D4=DIST1+DIST2
IF (D3.LT.D4) ERROR
   B=(D3^2+DIST1^2-DIST2^2)/(2*D3*DIST1)
   BETA=ACOS(B)
   G=(DIST2^2+D3^2-DIST1^2)/(2*DIST2*D3)
   GAMA=ACOS(G)
   V13=V12-BETA
   V23=V12-PI+GAMA
   DX13=DIST1*SIN(V13)
   DY13=DIST1*COS(V13)
   X13=X1+DX13
  Y13=Y1+DY13
 DX23=DIST2*SIN(V23)
 DY23=DIST2*COS(V23)

-------------------- USE THESE FORMULA'S AS SHOULD BE IN VB, AND MAKE SURE FROM THE SIN & COS VALUE PLUS TAN2 (FUNCTION) .. MAKE SURE THAT U R USING RADIUS!!! AND NOT NEGATIVE VALUES

IF YOU GOT ANYTHING PLEASE SEND ME! ... THANKS ALOT.

Regards;
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LVL 76

Expert Comment

by:GrahamSkan
ID: 11965375
I now see that you do not accept that the co-ordinates be drawn to allow the second point to lie on the X-axis. My solution would therefore require that points 2 and 3 be rotated through the angle b.

However, here is a translation of code that you supplied. I have not analysed it in any great depth.

Note that I don't understand your first line, so I have commented it out. Also, be aware that VB uses radians in its trigonometric functions.

You'll notice that I have provided an ArcCos function (called Acos to match the name in your code), because VB does not have one built in.

Option Explicit

Function Acos(Theta As Single) As Single
    Acos = Atn(-Theta / Sqr(-Theta * Theta + 1)) + 2 * Atn(1)
End Function

Private Sub Command1_Click()
    'TAN2(DX1,DY1) * (2*PI)
    D3 = Sqr(DX1 ^ 2 + DY1 ^ 2)
    D4 = DIST1 + DIST2
    If D3 < D4 Then
        MsgBox "Distances Error"
        Exit Sub
    End If
    B = (D3 ^ 2 + DIST1 ^ 2 - DIST2 ^ 2) / (2 * D3 * DIST1)
    BETA = Acos(B)
    G = (DIST2 ^ 2 + D3 ^ 2 - DIST1 ^ 2) / (2 * DIST2 * D3)
    GAMA = Acos(G)
    V13 = V12 - BETA
    V23 = V12 - PI + GAMA
    DX13 = DIST1 * Sin(V13)
    DY13 = DIST1 * Cos(V13)
    X13 = X1 + DX13
    Y13 = Y1 + DY13
    DX23 = DIST2 * Sin(V23)
    DY23 = DIST2 * Cos(V23)
End Sub

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Author Comment

by:LoveBii
ID: 11983568
Hello every body;

I got something ,,, meanningfull and very close to what i want,,, in fact its what i want?

here's the code .... fully ... but i have doubt about resulting values ... i think there's a negative values plus sometime division by zero ... i'll increase the point's of challenge!! who will get it first!! ... Reply now!?

--------------------------------------- The Code -------------------------------------------
Option Explicit
Const iX1 As Integer = 0
Const iY1 As Integer = 0


Private Sub Command1_Click()
Dim DX As Double ' double
Dim DY As Double
Dim iB As Single
Const iPI As Single = 3.14159265

If DIST3.Text = "" Or DIST2.Text = "" Or DIST1.Text = "" Then
    MsgBox "All distance values must be enterd!", vbCritical, Form1.Caption
    DIST3.SetFocus
    Exit Sub
Else
    X1.Text = iX1
    Y1.Text = iY1
    iB = 180 'degree
    DX = Val(DIST3.Text) * Sin(RadiansToDegrees(iB))
    DY = Val(DIST3.Text) * Cos(RadiansToDegrees(iB))
    X2.Text = Format(Val(X1.Text) + DX, "###.###")
    Y2.Text = Format(Val(Y1.Text) + DY, "###.###")
    Dim DX1, DY1, V12, V13, D3, D4, B, BETA, G, GAMA, V23, DX13, DY13, X13, Y13, DX23, DY23, X23, Y23 As Double
        DX1 = Val(X2.Text) - Val(X1.Text)
        DY1 = Val(Y2.Text) - Val(Y1.Text)
        'V12 = DATAN2D(DX1, DY1) ' ----
        V12 = atan2(DY1, DX1)
        V12 = V12 + (2 * iPI)
        D3 = Sqr((DX1 ^ 2) + (DY1 ^ 2))
        D4 = Val(DIST2.Text) + Val(DIST1.Text)
        If (D4 < D3) Then
            MsgBox "Distances Error", vbExclamation, Form1.Caption
            Exit Sub
        Else
            B = ((D3 ^ 2) + (Val(DIST1.Text) ^ 2) - (Val(DIST2.Text) ^ 2)) / (2 * D3 * Val(DIST1.Text))
            BETA = ArcCos(B)
            G = ((Val(DIST2.Text) ^ 2) + (D3 ^ 2) - (Val(DIST1.Text) ^ 2)) / (2 * Val(DIST2.Text) * D3)
            GAMA = ArcCos(G)
            V13 = V12 - BETA
            V23 = (V12 - iPI) + GAMA
            DX13 = Val(DIST1.Text) * Sin(V13)
            DY13 = Val(DIST1.Text) * Cos(V13)
            X13 = Val(X1.Text) + DX13
            Y13 = Val(Y1.Text) + DY13
            DX23 = Val(DIST2.Text) * Sin(V23)
            DY23 = Val(DIST2.Text) * Cos(V23)
            X23 = Val(X2.Text) + DX23
            Y23 = Val(Y2.Text) + DY23
            X3.Text = Format((X23 + X13) / 2, "###.###")
            Y3.Text = Format((Y23 + Y13) / 2, "###.###")
        End If
       
        T_D1.Text = Sqr(((Val(X3.Text) - Val(X1.Text)) ^ 2) + ((Val(Y3.Text) - Val(Y1.Text)) ^ 2))
        T_D2.Text = Sqr(((Val(X3.Text) - Val(X2.Text)) ^ 2) + ((Val(Y3.Text) - Val(Y2.Text)) ^ 2))
        T_D3.Text = Sqr(((Val(X2.Text) - Val(X1.Text)) ^ 2) + ((Val(Y2.Text) - Val(Y1.Text)) ^ 2))
   
End If
End Sub

Private Sub Command2_Click()
Unload Me
End Sub

Private Sub Command3_Click()
DIST3.Text = ""
DIST2.Text = ""
DIST1.Text = ""
X1.Text = ""
Y1.Text = ""
X2.Text = ""
Y2.Text = ""
X3.Text = ""
Y3.Text = ""
T_D1.Text = ""
T_D2.Text = ""
T_D3.Text = ""
DIST3.SetFocus
End Sub

Private Sub Form_Activate()
DIST3.SetFocus
End Sub

Public Function ArcCos(ByVal X As Double) As Double
   ArcCos = Atn(-X / Sqr(-X * X + 1)) + 2 * Atn(1)
End Function
Function RadiansToDegrees(ByVal radians As Single) As Single
    RadiansToDegrees = radians * 57.29578
End Function


Public Function DATAN2D(ByVal X As Double, ByVal Y As Double) As Double
    Dim localTan As Double
    Dim Angle As Double

    If X <> 0 Then
        localTan = Y / X
        Angle = Atn(localTan) * 180 / 3.1415926
    Else
        Angle = 0# 'Angle = 0#
    End If
    If X < 0 Then
        If Y > 0 Then
            Angle = 90 - Angle
        Else
            Angle = 180 + Angle
        End If
    Else
        If Y < 0 Then
            Angle = 360 + Angle
        End If

    End If
    DATAN2D = Angle
End Function

Function atan2(ys, xs)
 ' Given y and x coords returns atan2
 Dim theta, pi
    pi = 3.14159265358979
    If xs <> 0 Then
        theta = Atn(ys / xs)
        If xs < 0 Then
            theta = theta + pi
        End If
    Else
        If ys < 0 Then
            theta = 3 * pi / 2 '90
        Else
            theta = pi / 2 '270
        End If
    End If
 atan2 = theta
End Function

---------------------- waiting to hear from you ---------------------- Good Luck ------------------- ;)
0
 

Author Comment

by:LoveBii
ID: 11983581
TIPs:
* Make Sure there's no negative values in (x2,y2) , (x3,y3).
* No division by zero or error's appear's inside code.
* The result of your entering distance should be the same to T_D1.TEXT,T_D2.TEXT,T_D3.TEXT, THIS IS A CHECK BACK!!
   if its true ... then go ahead.
* get back to me soon to give you the piont's.
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Accepted Solution

by:
modulo earned 0 total points
ID: 12689649
PAQed with points refunded (250)

modulo
Community Support Moderator
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