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向下滚动到编辑以阅读第 2 部分

所以我正在做一个项目，我需要使用给定的 X 和 Y 坐标创建一个多边形。以逻辑顺序给定坐标并创建路径。现在我需要计算一个 poligon 的所有位置，如果路径宽度为 [w]（例如 20 米）。我们都知道线条没有宽度。

这张图片解释了我想要做的事情：

小路

黑点是路径的位置，它们的 X 和 Y 坐标是已知的。红线的宽度是已知的，它们都是[w]（例如20米，路径将它们从中间切开）。

我不知道如何获得所有紫色点的 X、Y 位置。我需要它们，这样我就可以创建绿色多边形形状。

如何在 C++ 中计算这些位置？有没有让它更容易的功能？

PS：如您所见，红线与两条蓝线夹角的一半成角度。

编辑：

我在 Visual Basic .NET 中创建了一个可视化应用程序，并获得了可以移植到 C++ 的公式。还有一个问题，请看这张图： 在此处输入图像描述

（应用下载链接： http: //gpb.googlecode.com/files/DRAWER2.zip）

现在的问题是，当路径转弯时，它会反转创建多边形点的边。这会产生一个损坏的多边形（或者，它没有提供想要的效果）。

代码如下所示：

Dim MainImage As New DynamicBitmap

Private Sub Form1_Load(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles MyBase.Load
    Dim temp As New DynamicBitmap
    MainImage.CreateGrid(500, 500, 1, 1)
    temp.LoadBitmap("map.jpg")
    MainImage.DrawOnSurface(temp.Bitmap, temp.Rectangle, MainImage.Rectangle)
    MainImage.Surface.DrawLine(Pens.Black, 0, 250, 500, 250)
    MainImage.Surface.DrawLine(Pens.Black, 250, 0, 250, 500)
    PictureBox1.Image = MainImage.Bitmap
    PictureBox1.Refresh()
End Sub
Dim CPG(0) As Point
Dim CurrCount As Integer = 0
Dim Distance As Double = 30.0
Function CalculatePositions(ByVal PointStart As Point, ByVal PointMiddle As Point, ByVal PointEnd As Point) As Point()

    Dim DeltaX As Double
    Dim DeltaY As Double
    Dim AdderX As Double
    Dim AdderY As Double
    Dim Length As Double
    Dim CP(9) As Point
    CP(0) = PointMiddle
    CP(1) = PointStart
    CP(2) = PointEnd
    Dim RetP(1) As Point
    DeltaX = CP(1).X - CP(0).X
    DeltaY = CP(1).Y - CP(0).Y
    Length = Math.Sqrt(((DeltaX * DeltaX) + (DeltaY * DeltaY))) + 0.0000000001
    AdderX = (DeltaX / Length)
    AdderY = (DeltaY / Length)
    CP(3).X = (CP(0).X + (AdderX * Distance))
    CP(3).Y = (CP(0).Y + (AdderY * Distance))

    DeltaX = CP(2).X - CP(0).X
    DeltaY = CP(2).Y - CP(0).Y
    Length = Math.Sqrt(((DeltaX * DeltaX) + (DeltaY * DeltaY))) + 0.0000000001
    AdderX = (DeltaX / Length)
    AdderY = (DeltaY / Length)
    CP(4).X = (CP(0).X + (AdderX * Distance))
    CP(4).Y = (CP(0).Y + (AdderY * Distance))

    DeltaX = CP(3).X - CP(4).X
    DeltaY = CP(3).Y - CP(4).Y
    Length = Math.Sqrt(((DeltaX * DeltaX) + (DeltaY * DeltaY))) + 0.0000000001
    AdderX = (DeltaX / Length)
    AdderY = (DeltaY / Length)
    CP(8).X = (CP(4).X + (AdderX * Length / 2.0))
    CP(8).Y = (CP(4).Y + (AdderY * Length / 2.0))

    DeltaX = CP(8).X - CP(0).X
    DeltaY = CP(8).Y - CP(0).Y
    Length = Math.Sqrt(((DeltaX * DeltaX) + (DeltaY * DeltaY))) + 0.0000000001
    AdderX = (DeltaX / Length)
    AdderY = (DeltaY / Length)
    CP(7).X = (CP(0).X - (AdderX * Distance))
    CP(7).Y = (CP(0).Y - (AdderY * Distance))
    CP(9).X = (CP(0).X + (AdderX * Distance))
    CP(9).Y = (CP(0).Y + (AdderY * Distance))

    MainImage.Surface.DrawLine(Pens.Red, New Point(CP(7).X - 3, CP(7).Y - 3), New Point(CP(7).X + 3, CP(7).Y + 3))
    MainImage.Surface.DrawLine(Pens.Red, New Point(CP(7).X + 3, CP(7).Y - 3), New Point(CP(7).X - 3, CP(7).Y + 3))
    MainImage.Surface.DrawLine(Pens.Blue, New Point(CP(9).X - 3, CP(9).Y - 3), New Point(CP(9).X + 3, CP(9).Y + 3))
    MainImage.Surface.DrawLine(Pens.Blue, New Point(CP(9).X + 3, CP(9).Y - 3), New Point(CP(9).X - 3, CP(9).Y + 3))
    Return RetP
End Function

Private Sub PictureBox1_Click(sender As System.Object, e As System.EventArgs) Handles PictureBox1.Click
    'MsgBox(DirectCast(e, MouseEventArgs).X.ToString() + ":" + DirectCast(e, MouseEventArgs).Y.ToString())

    ReDim Preserve CPG(CurrCount)
    'i -= 1
    CPG(CurrCount) = New Point(DirectCast(e, MouseEventArgs).X, DirectCast(e, MouseEventArgs).Y)
    MainImage.Surface.DrawLine(Pens.Yellow, New Point(CPG(CurrCount).X - 3, CPG(CurrCount).Y - 3), New Point(CPG(CurrCount).X + 3, CPG(CurrCount).Y + 3))
    MainImage.Surface.DrawLine(Pens.Yellow, New Point(CPG(CurrCount).X + 3, CPG(CurrCount).Y - 3), New Point(CPG(CurrCount).X - 3, CPG(CurrCount).Y + 3))
    CurrCount += 1
    If CurrCount = 1 Then

    Else
        If CurrCount = 2 Then
            Dim DeltaX As Double
            Dim DeltaY As Double
            Dim AdderX As Double
            Dim AdderY As Double
            Dim Length As Double
            DeltaX = CPG(CurrCount - 2).X - CPG(CurrCount - 1).X
            DeltaY = CPG(CurrCount - 2).Y - CPG(CurrCount - 1).Y
            Length = Math.Sqrt(((DeltaX * DeltaX) + (DeltaY * DeltaY))) + 0.0000000001
            AdderX = (DeltaX / Length)
            AdderY = (DeltaY / Length)
            Dim Temp(1) As Point
            Dim Angle01 As Double = Math.Atan2(CPG(CurrCount - 1).X - CPG(CurrCount - 2).X, CPG(CurrCount - 1).Y - CPG(CurrCount - 2).Y) * 180.0 / Math.PI
            Dim SinMin As Double
            Dim CosMin As Double
            SinMin = Math.Sin(((-Angle01) + 0.0) / 180.0 * Math.PI)
            CosMin = Math.Cos(((-Angle01) + 0.0) / 180.0 * Math.PI)
            Temp(0).X = CPG(CurrCount - 2).X + (CosMin * Distance) + AdderX * Distance
            Temp(0).Y = CPG(CurrCount - 2).Y + (SinMin * Distance) + AdderY * Distance
            Temp(1).X = CPG(CurrCount - 2).X - (CosMin * Distance) + AdderX * Distance
            Temp(1).Y = CPG(CurrCount - 2).Y - (SinMin * Distance) + AdderY * Distance
            MainImage.Surface.DrawLine(Pens.Red, New Point(Temp(0).X - 3, Temp(0).Y - 3), New Point(Temp(0).X + 3, Temp(0).Y + 3))
            MainImage.Surface.DrawLine(Pens.Red, New Point(Temp(0).X + 3, Temp(0).Y - 3), New Point(Temp(0).X - 3, Temp(0).Y + 3))
            MainImage.Surface.DrawLine(Pens.Blue, New Point(Temp(1).X - 3, Temp(1).Y - 3), New Point(Temp(1).X + 3, Temp(1).Y + 3))
            MainImage.Surface.DrawLine(Pens.Blue, New Point(Temp(1).X + 3, Temp(1).Y - 3), New Point(Temp(1).X - 3, Temp(1).Y + 3))
        End If
        MainImage.Surface.DrawLine(Pens.Blue, CPG(CurrCount - 2), CPG(CurrCount - 1))
        If CurrCount > 2 Then
            CalculatePositions(CPG(CurrCount - 3), CPG(CurrCount - 2), CPG(CurrCount - 1))
        End If
    End If

    PictureBox1.Image = MainImage.Bitmap
    PictureBox1.Refresh()

    'MsgBox(CP(i).ToString())
End Sub

Private Sub Button1_Click(sender As System.Object, e As System.EventArgs) Handles Button1.Click
    Dim DeltaX As Double
    Dim DeltaY As Double
    Dim AdderX As Double
    Dim AdderY As Double
    Dim Length As Double
    DeltaX = CPG(CurrCount - 2).X - CPG(CurrCount - 1).X
    DeltaY = CPG(CurrCount - 2).Y - CPG(CurrCount - 1).Y
    Length = Math.Sqrt(((DeltaX * DeltaX) + (DeltaY * DeltaY))) + 0.0000000001
    AdderX = (DeltaX / Length)
    AdderY = (DeltaY / Length)
    Dim Temp(1) As Point
    Dim Angle01 As Double = Math.Atan2(CPG(CurrCount - 1).X - CPG(CurrCount - 2).X, CPG(CurrCount - 1).Y - CPG(CurrCount - 2).Y) * 180.0 / Math.PI
    Dim SinMin As Double
    Dim CosMin As Double
    SinMin = Math.Sin(((-Angle01) + 0.0) / 180.0 * Math.PI)
    CosMin = Math.Cos(((-Angle01) + 0.0) / 180.0 * Math.PI)
    Temp(0).X = CPG(CurrCount - 1).X + (CosMin * Distance) - AdderX * Distance
    Temp(0).Y = CPG(CurrCount - 1).Y + (SinMin * Distance) - AdderY * Distance
    Temp(1).X = CPG(CurrCount - 1).X - (CosMin * Distance) - AdderX * Distance
    Temp(1).Y = CPG(CurrCount - 1).Y - (SinMin * Distance) - AdderY * Distance
    MainImage.Surface.DrawLine(Pens.Red, New Point(Temp(0).X - 3, Temp(0).Y - 3), New Point(Temp(0).X + 3, Temp(0).Y + 3))
    MainImage.Surface.DrawLine(Pens.Red, New Point(Temp(0).X + 3, Temp(0).Y - 3), New Point(Temp(0).X - 3, Temp(0).Y + 3))
    MainImage.Surface.DrawLine(Pens.Blue, New Point(Temp(1).X - 3, Temp(1).Y - 3), New Point(Temp(1).X + 3, Temp(1).Y + 3))
    MainImage.Surface.DrawLine(Pens.Blue, New Point(Temp(1).X + 3, Temp(1).Y - 3), New Point(Temp(1).X - 3, Temp(1).Y + 3))

    PictureBox1.Image = MainImage.Bitmap
    PictureBox1.Refresh()
End Sub

我该如何解决这个问题？我想要一侧的红色 X-es 和另一侧的蓝色 X-es，并且我希望它不依赖于路径的转弯方式。如何做到这一点？

4

2 回答 2

2

您可以检测点位于直线的哪一侧。

position = Math.Sign( (Bx-Ax)*(Y-Ay) - (By-Ay)*(X-Ax) )

where(Ax,Ay)是起点，(Bx,By)是直线的终点。(X,Y)是您要检查的点。

如果position为正，则在左侧，在右侧（0在行上）为负。

有了这个，如果它们在路径的错误一侧，你可以交换粉红色的点。

于 2012-07-02T08:10:05.780 回答
1

首先，获取第一个和最后一个段的紫色点的位置（这很简单）。

然后，对于每条蓝线，创建两条与其平行但适当间隔的绿线。对于最后一条和第一条蓝线，您必须在这些点处明确终止这些线。最简单的方法是创建一条适当长度的蓝线，例如 0,0，生成两条绿线，然后将它们转换为位置。它还可以让您更轻松地跟踪哪条线是哪条线。

然后，只需计算每一侧的绿线与下一段的绿线的交点。

这是我相当糟糕的绘画马拉松。可怕，我知道。 是手绘的。 在油漆。

如您所见，紫色点的位置很容易得出。

于 2012-07-02T03:49:48.383 回答