Calculate if an x,y value falls in to the area on an polygon shape

Hi All

I have a polygon, min 3 vertices, max 999. Each vertice has an xy of it position and it also stores the forward and backward vertices that it is connected to.

I need to know how to calculate if a give x,y falls in the area of the polygon.

Polygon values are :


a=38,20 - not in polygon area
b15,25   - in polygon area

All help is greatly appreciated
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JMu5667Author Commented:
Hi Infinity08

any chance of a conversion please ?

int pnpoly(int npol, float *xp, float *yp, float x, float y)
      int i, j, c = 0;
      for (i = 0, j = npol-1; i < npol; j = i++) {
        if ((((yp[i]<=y) && (y<yp[j])) ||
             ((yp[j]<=y) && (y<yp[i]))) &&
            (x < (xp[j] - xp[i]) * (y - yp[i]) / (yp[j] - yp[i]) + xp[i]))

          c = !c;
      return c;
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>> any chance of a conversion please ?

A conversion ? You mean to VB ? I don't know VB very well, so I'll probably not be of a lot of help there. But you can read the algorithm (in text), and implement it yourself.
Hamed ZaghaghiProgrammerCommented:
Hi JMu5667,

it's not hard to undrastand what the code does!

from each point x,y you must check that the number of lines that intersect with y horizontal line.
if the number of intersect lines will be odd the point is an interior and else it is exterior.
I think this uses a similar algorithm.

Option Explicit
Private Sub Command1_Click()
Dim VertexX(13) As Single
Dim VertexY(13) As Single
VertexX(0) = 20
VertexX(1) = 15
VertexX(2) = 10
VertexX(3) = 10
VertexX(4) = 30
VertexX(5) = 30
VertexX(6) = 25
VertexX(7) = 25
VertexX(8) = 30
VertexX(9) = 35
VertexX(10) = 40
VertexX(11) = 40
VertexX(12) = 45
VertexX(13) = 45
VertexY(0) = 10
VertexY(1) = 15
VertexY(2) = 20
VertexY(3) = 30
VertexY(4) = 30
VertexY(5) = 20
VertexY(6) = 25
VertexY(7) = 15
VertexY(8) = 15
VertexY(9) = 15
VertexY(10) = 15
VertexY(11) = 20
VertexY(12) = 20
VertexY(13) = 10
Dim ax As Single
Dim ay As Single
Dim bx As Single
Dim by As Single
ax = 38: ay = 20
bx = 15: by = 25
Debug.Print IsInside(14, VertexX(), VertexY(), ax, ay)
Debug.Print IsInside(14, VertexX(), VertexY(), bx, by)
End Sub
Function IsInside(iSideCount As Integer, sPointsX() As Single, sPointsY() As Single, x As Single, y As Single) As Boolean
    Dim i As Integer
    Dim bOddVertex As Boolean
    Dim j As Integer
    j = iSideCount - 1
    For i = 0 To iSideCount - 1
        If (sPointsY(i) < y And sPointsY(j) >= y Or sPointsY(j) < y And sPointsY(i) >= y) Then
            If (sPointsX(i) + (y - sPointsY(i)) / (sPointsY(j) - sPointsY(i)) * (sPointsX(j) - sPointsX(i)) < x) Then
                bOddVertex = Not bOddVertex
            End If
        End If
        j = i
    Next i
    IsInside = bOddVertex
End Function

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Mike TomlinsonMiddle School Assistant TeacherCommented:
You can use GDI APIs to help out...

The CreatePolygonRgn() API stores the point data and then the PtInRegion() API tells you if a point is inside that polygon.


Here's a cool solution:
Add up the angles between the point in question and adjacent points on the polygon taken in order. If the total of all the angles is 2 * PI or -2 * PI, then the point is inside the polygon. If the total is zero, the point is outside.
> Add up the angles
is a lot of unnecessary evaluations of trig function
All you need to add up is whether the sum is positive or negative or zero,
which for the non-zero winding number definition of "inside", (which can differs from odd winding number or odd jordan curve crossings in cases when the polygon can intersect itself)
You can check that by keeping track of the sign of the intersects with y horizontal line instead of just the number
Mike TomlinsonMiddle School Assistant TeacherCommented:
Here is a bare bones example of using your sample data with the APIs I mentioned above:
Option Base 0
Option Explicit
Private Const ALTERNATE = 1
Private Type POINT
    x As Long
    y As Long
End Type
Private Declare Function CreatePolygonRgn Lib "gdi32" (lpPoint As Any, ByVal nCount As Long, ByVal nPolyFillMode As Long) As Long
Private Declare Function DeleteObject Lib "gdi32" (ByVal hObject As Long) As Long
Private Declare Function PtInRegion Lib "gdi32" (ByVal hRgn As Long, ByVal x As Long, ByVal y As Long) As Long
Private points() As POINT
Private polygonRegion As Long
Private Sub Form_Load()
    ReDim points(13)
    Dim pt As POINT
    pt.x = 20
    pt.y = 10
    points(0) = pt
    pt.x = 15
    pt.y = 15
    points(1) = pt
    pt.x = 10
    pt.y = 20
    points(2) = pt
    pt.x = 10
    pt.y = 30
    points(3) = pt
    pt.x = 30
    pt.y = 30
    points(4) = pt
    pt.x = 30
    pt.y = 20
    points(5) = pt
    pt.x = 0
    pt.y = 0
    points(6) = pt
    pt.x = 25
    pt.y = 15
    points(7) = pt
    pt.x = 30
    pt.y = 15
    points(8) = pt
    pt.x = 35
    pt.y = 15
    points(9) = pt
    pt.x = 40
    pt.y = 15
    points(10) = pt
    pt.x = 40
    pt.y = 20
    points(11) = pt
    pt.x = 45
    pt.y = 20
    points(12) = pt
    pt.x = 45
    pt.y = 10
    points(13) = pt
    polygonRegion = CreatePolygonRgn(points(0), UBound(points) + 1, ALTERNATE)
End Sub
Private Sub Form_Unload(Cancel As Integer)
    If polygonRegion <> 0 Then
        DeleteObject polygonRegion
    End If
End Sub
Public Function PointInRegion(ByVal rgn As Long, ByVal x As Long, ByVal y As Long) As Boolean
    If rgn = 0 Then
        PointInRegion = False
        PointInRegion = PtInRegion(rgn, x, y)
    End If
End Function
Private Sub Command1_Click()
    Dim i As Integer
    Debug.Print "Polygon Points:"
    For i = LBound(points) To UBound(points)
        Debug.Print points(i).x, points(i).y
    Debug.Print "Hit Testing:"
    Dim ptA As POINT
    ptA.x = 38
    ptA.y = 20
    Debug.Print ptA.x, ptA.y, PointInRegion(polygonRegion, ptA.x, ptA.y)
    Dim ptB As POINT
    ptB.x = 15
    ptB.y = 25
    Debug.Print ptB.x, ptB.y, PointInRegion(polygonRegion, ptB.x, ptB.y)
End Sub

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JMu5667Author Commented:
Hi Guys, in the spirit of good will I have split the points as I feel there was a joint effort. Thanks to all how contributed.
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