Option Explicit On
Imports System.IO
Imports DRAWER.DoublePoint

Public Class Form1

    Dim MainImage As New DynamicBitmap 'the image we can draw on

    ' our points
    Dim Points() As DPoint =
    {
        New DPoint(0.0, 0.0),
        New DPoint(100.0, 100.0),
        New DPoint(100.0, 150.0),
        New DPoint(150.0, 150.0),
        New DPoint(200.0, -200.0),
        New DPoint(-200.0, -200.0),
        New DPoint(0.0, -100.0),
        New DPoint(-100.0, -100.0),
        New DPoint(-100.0, 0.0),
        New DPoint(-50.0, 50.0),
        New DPoint(-100.0, 200.0),
        New DPoint(-180.0, 220.0),
        New DPoint(250.0, 250.0)
    } ' our points

    Private Sub Form1_Load(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles MyBase.Load
        Dim temp As New DynamicBitmap ' temporary image
        temp.LoadBitmap("map.jpg") 'load map.jpg from working directory

        MainImage.CreateGrid(500, 500, 1, 1) 'create a 500x500 grid, each 1 by 1 pixel
        MainImage.DrawOnSurface(temp.Bitmap, temp.Rectangle, MainImage.Rectangle) 'draw temp onto mainimage

        MainImage.Surface.DrawLine(Pens.Black, 0, 250, 500, 250) 'draw Y axis from (0,250) to (500,250) <- image, not "XY-system", coordinates!1!1!
        MainImage.Surface.DrawLine(Pens.Black, 250, 0, 250, 500) 'draw X axis ""

        For i As Integer = 0 To Points.Length - 2 'create all the lines from Points()
            MainImage.Surface.DrawLine(Pens.Black, PointToImage(Points(i).ToInt()), PointToImage(Points(i + 1).ToInt()))
        Next

        PictureBox1.Image = MainImage.Bitmap 'assign mainimage to picturebox
        PictureBox1.Refresh() ' refresh picturebox
    End Sub

    'BEGIN--------------ANSWER 2-----------------------
    Function func_u(ByVal P As DPoint) As DPoint 'function u((x,y))
        Return P / ((P.X * P.X) + (P.Y * P.Y)) ' (1)
    End Function
    Function func_r(ByVal P As DPoint) As DPoint 'function r((x,y))
        Return func_u(New DPoint(P.Y, -P.X)) ' (2)
    End Function

    Private Sub Button2_Click(sender As Object, e As EventArgs) Handles Button2.Click
        Dim P() As DPoint = Points 'aquire our list of points into the array P
        Dim B(0 To 1)() As DPoint 'declare our "purple" points array, (0) will be the + ones and (1) the - ones
        Dim distance As Double = 5.0 ' distance we want
        For k As Integer = 1 To P.Length - 2 'loop from k = 1 to k = amount of Points()-1
            ReDim Preserve B(0)(k - 1) 'just allocation stuff for the program memory
            ReDim Preserve B(1)(k - 1) 'just allocation stuff for the program memory
            B(0)(k - 1) = P(k) + ((func_r(func_u(P(k + 1) - P(k)) - func_u(P(k - 1) - P(k)))) * distance) 'calculation +(3)
            B(1)(k - 1) = P(k) - ((func_r(func_u(P(k + 1) - P(k)) - func_u(P(k - 1) - P(k)))) * distance) 'calculation -(3)
        Next
        'skipping (4) and (5) because for now we just need the purple points around the lines
        DrawCross(B(0), Pens.Red) 'draw all points in B(0) -> +(3) on the image
        DrawCross(B(1), Pens.Blue) 'draw all points in B(1) -> -(3) on the image
        PictureBox1.Refresh() 'refresh our picture
    End Sub
    'END---------------ANSWER 2-----------------------

    'BEGIN--------------ANSWER 1-----------------------
    Private Sub Button1_Click(sender As Object, e As EventArgs) Handles Button1.Click
        Dim B() As DPoint = Points
        Dim len As Integer = 0
        len = (B.Length - 2)
        Dim u(len) As DPoint
        len = (u.Length - 2)
        Dim bs(len) As DPoint
        Dim n(len) As DPoint

        Dim dist As Double = 10.0
        Dim PL(len) As DPoint
        Dim PR(len) As DPoint
        Dim P((PL.Length + PR.Length) - 1) As DPoint
        For i As Integer = 0 To u.Length - 1 '1.Determine each u(k)
            u(i) = B(i + 1) - B(i)
        Next
        For i As Integer = 0 To bs.Length - 1 '2.Determine each bisector b(k)   and unit bisector n(k)
            bs(i) = New DPoint(-(u(i) + u(i + 1)).Y, (u(i) + u(i + 1)).X)
            Dim divider As Double = ((bs(i).X * bs(i).X) + (bs(i).Y * bs(i).Y))
            n(i) = bs(i) / Math.Sqrt(divider)
        Next
        For i As Integer = 0 To PL.Length - 1 '3.Determine the points P′ and P′′. | ′ = 0, ′′ = 1
            PL(i) = B(i + 1) + (n(i) * dist)
            PR(i) = B(i + 1) - (n(i) * dist)
            P(i) = PL(i)
        Next
        For i As Integer = 0 To PL.Length - 1 'combine PL and PR
            P(PL.Length + i) = PR((PL.Length - 1) - i)
        Next

        Dim Polygon(P.Length + 2) As DPoint
        Polygon(0) = B(0)
        For i As Integer = 0 To PL.Length - 1
            Polygon(i + 1) = P(i)
        Next
        Polygon(PL.Length + 1) = B(B.Length - 1)
        For i As Integer = 0 To PL.Length - 1
            Polygon(PL.Length + i + 2) = P(PL.Length + i)
        Next
        Polygon(Polygon.Length - 1) = B(0)

        For i As Integer = 0 To Polygon.Length - 2
            MainImage.Surface.DrawLine(Pens.Red, PointToImage(Polygon(i).ToInt()), PointToImage(Polygon(i + 1).ToInt()))
        Next
        MainImage.Surface.DrawLine(Pens.Red, PointToImage(Polygon(Polygon.Length - 1).ToInt()), PointToImage(Polygon(0).ToInt()))

        PictureBox1.Image = MainImage.Bitmap
        PictureBox1.Refresh()
    End Sub
    'END--------------ANSWER 1-----------------------

    Public Sub DrawCross(ByVal Point As Point, ByVal color As Pen)
        ' draw a cross on the main image at a given point
        MainImage.Surface.DrawLine(color, Point.X - 1, Point.Y - 1, Point.X + 1, Point.Y + 1)
        MainImage.Surface.DrawLine(color, Point.X + 1, Point.Y - 1, Point.X - 1, Point.Y + 1)
    End Sub
    Public Sub DrawCross(ByVal Point() As DPoint, ByVal color As Pen)
        ' same as DrawCross but takes an array of points as input
        For i As Integer = 0 To Point.Length - 1
            MainImage.Surface.DrawLine(color, PointToImage(Point(i) - 1.0), PointToImage(Point(i) + 1.0))
            MainImage.Surface.DrawLine(color, PointToImage(Point(i) + New DPoint(1.0, -1.0)), PointToImage(Point(i) + New DPoint(-1.0, 1.0)))
        Next
    End Sub
End Class
''---------------end of answer results-----------------------
''---------------Dpoint structure here-----------------------
Public Class DoublePoint
    Public Structure DPoint
        Dim X As Double
        Dim Y As Double
        Sub New(ByVal pX As Double, ByVal pY As Double)
            X = pX
            Y = pY
        End Sub
        Public Function ToInt()
            Return New Point(CInt(Math.Round(X)), CInt(Math.Round(Y)))
        End Function
        Public Shared Operator <>(ByVal a As DPoint, ByVal b As DPoint) As Boolean
            If a.X <> b.X Then Return False
            If a.Y <> b.Y Then Return False
            Return True
        End Operator
        Public Shared Operator =(ByVal a As DPoint, ByVal b As DPoint) As Boolean
            If a.X <> b.X Then Return False
            If a.Y <> b.Y Then Return False
            Return True
        End Operator
        Public Shared Operator +(ByVal a As DPoint, ByVal b As DPoint) As DPoint
            Return New DPoint(a.X + b.X, a.Y + b.Y)
        End Operator
        Public Shared Operator -(ByVal a As DPoint, ByVal b As DPoint) As DPoint
            Return New DPoint(a.X - b.X, a.Y - b.Y)
        End Operator
        Public Shared Operator *(ByVal a As DPoint, ByVal b As DPoint) As DPoint
            Return New DPoint(a.X * b.X, a.Y * b.Y)
        End Operator
        Public Shared Operator /(ByVal a As DPoint, ByVal b As DPoint) As DPoint
            Return New DPoint(a.X / b.X, a.Y / b.Y)
        End Operator
        Public Shared Operator /(ByVal a As DPoint, ByVal b As Double) As DPoint
            Return New DPoint(a.X / b, a.Y / b)
        End Operator
        Public Shared Operator *(ByVal a As DPoint, ByVal b As Double) As DPoint
            Return New DPoint(a.X * b, a.Y * b)
        End Operator
        Public Shared Operator +(ByVal a As DPoint, ByVal b As Double) As DPoint
            Return New DPoint(a.X + b, a.Y + b)
        End Operator
        Public Shared Operator -(ByVal a As DPoint, ByVal b As Double) As DPoint
            Return New DPoint(a.X - b, a.Y - b)
        End Operator
    End Structure
    Public Shared Function PointToImage(ByVal P1 As Point) As Point
        ' convert XY coordinate points to image points, image (0,0) is at top left corner
        '(in a coordinate system it's the middle point)
        'and middle at (250,250) while the middle on an XY system equals (0,0), so we convert that here:
        Return New Point(250 + P1.X, 250 - P1.Y)
    End Function
    Public Shared Function PointToImage(ByVal P1() As Point) As Point()
        'this point to image variant takes a whole array of points instead of just one point
        Dim ret(0 To P1.Length - 1) As Point
        For i As Integer = 0 To P1.Length - 1
            ret(i) = PointToImage(P1(i))
        Next
        Return ret
    End Function
    Public Shared Function PointToImage(ByVal P1 As DPoint) As Point
        'special variation for the Dpoint type
        Return New Point(250 + CInt(P1.X), 250 - CInt(P1.Y))
    End Function
    Public Shared Function PointToImage(ByVal P1() As DPoint) As Point()
        'special variation for the Dpoint type
        Dim ret(0 To P1.Length - 1) As Point
        For i As Integer = 0 To P1.Length - 1
            ret(i) = PointToImage(P1(i))
        Next
        Return ret
    End Function
End Class

''---------------end of my code-----------------------
''bitmap class for drawing here, nothing "important"