两条线段是否使用xna在c#或vb.net中相交？

我一直在寻找一种合适的方法来确定两条直线段（每两组x，y坐标）是否截距。我见过很多（包括：），但我见过的都有缺点。主要是，如果直线平行但相互重叠，它们不会检测到碰撞

我也不需要返回交点，只要一个布尔值就可以了

---

如果有人能给我指出正确的方向，我会非常感激，因为我显然在几何方面很差劲（

当然有数学上优雅的方法可以做到这一点，但如果您正在寻找一种使用基本代数的易于理解的算法，请尝试以下方法（这不是代码）：

让我们通过其端点定义两条线段：

l0 : { (x0, y0), (x1, y1) }
l1 : { (x2, y2), {x3, y3) }

首先，获取每条直线的斜率截距形式。您可以查找m、b的公式，也可以自己推导公式：

l0 : m0 * x + b0
l1 : m1 * x + b1

如果

（m0！=m1）

直线不平行。要找到潜在交点，请求解

l0=l1

：

x = (b1 - b0) / (m0 - m1)
y = m0 * x + b0

当且仅当

（x，y）

位于两条线段上时，线段才会相交。请注意，仅检查x坐标就足够了，因为我们已经确定

（x，y）

位于两条直线上：

[编辑以反映@KenoguLabz的出色输入]

---

（x0这是我最近编写的一个小类。坡度和角度的+/-可能并不总是正确的（例如，当角度应为-90时，它返回90，但我使用的trig函数不受此影响）。您可能最感兴趣的函数是GetCrossion，它不返回任何值（null）对于平行线，否则返回一个点。代码如下：

Public Class LineData
    Public Property Point1() As Point
    Public Property Point2() As Point
    Public ReadOnly Property Slope() As Double
        Get
            # 0=Horizontal Line, NaN=Vertical Line
            Return If(Me.Point1.X = Me.Point2.X, Double.NaN, (Me.Point1.Y - Me.Point2.Y) / (Me.Point1.X - Me.Point2.X))
        End Get
    End Property
    Public ReadOnly Property YIntercept() As Double
        Get
            Return If(Double.IsNaN(Me.Slope), Double.NaN, Me.Point1.Y - Me.Slope * Me.Point1.X)
        End Get
    End Property
    Public ReadOnly Property Angle() As Double
        Get
            Return If(Double.IsNaN(Me.Slope), Math.PI / 2, Math.Atan(Me.Slope))
        End Get
    End Property

    Public Sub New(pt1 As Point, pt2 As Point)
        Me.Point1 = pt1
        Me.Point2 = pt2
    End Sub
    Public Sub New(x1 As Double, y1 As Double, x2 As Double, y2 As Double)
        Me.Point1 = New Point(x1, y1)
        Me.Point2 = New Point(x2, y2)
    End Sub
    Public Sub New(ln As Line)
        Me.New(ln.X1, ln.Y1, ln.X2, ln.Y2)
    End Sub

    Public Function GetParallel(spacing As Double) As LineData
        Return Me.GetParallel(spacing, ParallelPosition.Below)
    End Function

    Public Function GetParallel(spacing As Double, pos As ParallelPosition) As LineData
        If Me.Slope = 0 Then # Horizontal Line
            If pos = ParallelPosition.Above OrElse pos = ParallelPosition.Left Then : Return If(Me.Point2.X > Me.Point1.X, New LineData(Me.Point1.X - spacing, Me.Point1.Y - spacing, Me.Point2.X + spacing, Me.Point2.Y - spacing), New LineData(Me.Point1.X + spacing, Me.Point1.Y - spacing, Me.Point2.X - spacing, Me.Point2.Y - spacing))
            Else : Return If(Me.Point2.X > Me.Point1.X, New LineData(Me.Point1.X - spacing, Me.Point1.Y + spacing, Me.Point2.X + spacing, Me.Point2.Y + spacing), New LineData(Me.Point1.X + spacing, Me.Point1.Y + spacing, Me.Point2.X - spacing, Me.Point2.Y + spacing))
            End If
        ElseIf Double.IsNaN(Me.Slope) Then # Vertical Line
            If pos = ParallelPosition.Above OrElse pos = ParallelPosition.Left Then : Return If(Me.Point2.Y > Me.Point1.Y, New LineData(Me.Point1.X - spacing, Me.Point1.Y - spacing, Me.Point2.X - spacing, Me.Point2.Y + spacing), New LineData(Me.Point1.X - spacing, Me.Point1.Y + spacing, Me.Point2.X - spacing, Me.Point2.Y - spacing))
            Else : Return If(Me.Point2.Y > Me.Point1.Y, New LineData(Me.Point1.X + spacing, Me.Point1.Y - spacing, Me.Point2.X + spacing, Me.Point2.Y + spacing), New LineData(Me.Point1.X + spacing, Me.Point1.Y + spacing, Me.Point2.X + spacing, Me.Point2.Y - spacing))
            End If
        Else #Sloped Line
            Dim verticalshift As Double = Math.Abs(spacing / Math.Cos(-Me.Angle))
            Dim horizontalshift As Double = Math.Abs(spacing / Math.Sin(-Me.Angle))
            If Math.Sign(Me.Slope) = -1 Then
                If Me.Point2.X > Me.Point1.X Then
                    If pos = ParallelPosition.Above OrElse pos = ParallelPosition.Left Then : Return New LineData(Me.Point1.X - horizontalshift, Me.Point1.Y, Me.Point2.X, Me.Point2.Y - verticalshift)
                    Else : Return New LineData(Me.Point1.X, Me.Point1.Y + verticalshift, Me.Point2.X + horizontalshift, Me.Point2.Y)
                    End If
                Else
                    If pos = ParallelPosition.Above OrElse pos = ParallelPosition.Left Then : Return New LineData(Me.Point1.X, Me.Point1.Y - verticalshift, Me.Point2.X - horizontalshift, Me.Point2.Y)
                    Else : Return New LineData(Me.Point1.X + horizontalshift, Me.Point1.Y, Me.Point2.X, Me.Point2.Y + verticalshift)
                    End If
                End If
            Else
                If Me.Point2.X > Me.Point1.X Then
                    If pos = ParallelPosition.Above OrElse pos = ParallelPosition.Right Then : Return New LineData(Me.Point1.X, Me.Point1.Y - verticalshift, Me.Point2.X + horizontalshift, Me.Point2.Y)
                    Else : Return New LineData(Me.Point1.X - horizontalshift, Me.Point1.Y, Me.Point2.X, Me.Point2.Y + verticalshift)
                    End If
                Else
                    If pos = ParallelPosition.Above OrElse pos = ParallelPosition.Right Then : Return New LineData(Me.Point1.X + horizontalshift, Me.Point1.Y, Me.Point2.X, Me.Point2.Y - verticalshift)
                    Else : Return New LineData(Me.Point1.X, Me.Point1.Y + verticalshift, Me.Point2.X - horizontalshift, Me.Point2.Y)
                    End If
                End If
            End If
        End If
    End Function

    Public Function CalculateX(y As Double) As Double
        If Me.Slope = 0 Then # Horizontal Line
            If y = Me.Point1.Y OrElse y = Me.Point2.Y Then Return 0 Else Return Double.NaN
        ElseIf Double.IsNaN(Me.Slope) Then # Vertical Line
            Return Me.Point1.X
        Else
            Return (y - Me.YIntercept) / Me.Slope
        End If
    End Function
    Public Function CalculateY(x As Double) As Double
        If Me.Slope = 0 Then # Horizontal Line
            Return Me.Point1.Y
        ElseIf Double.IsNaN(Me.Slope) Then # Vertical Line
            If x = Me.Point1.X OrElse x = Me.Point2.X Then Return 0 Else Return Double.NaN
        Else
            Return Me.Slope * x + Me.YIntercept
        End If
    End Function

    Public Function GetIntersection(ln As LineData) As Point
        If Me.Slope = ln.Slope OrElse (Double.IsNaN(Me.Slope) AndAlso Double.IsNaN(ln.Slope)) Then : Return Nothing
        Else
            If Double.IsNaN(Me.Slope) Then : Return New Point(Me.Point1.X, ln.CalculateY(Me.Point1.X))
            ElseIf Double.IsNaN(ln.Slope) Then : Return New Point(ln.Point1.X, Me.CalculateY(ln.Point1.X))
            ElseIf Me.Slope = 0 Then : Return New Point(ln.CalculateX(Me.Point1.Y), Me.Point1.Y)
            ElseIf ln.Slope = 0 Then : Return New Point(Me.CalculateX(ln.Point1.Y), ln.Point1.Y)
            Else
                Dim x As Double = (Me.YIntercept - ln.YIntercept) / (ln.Slope - Me.Slope)
                Return New Point(x, Me.CalculateY(x))
            End If
        End If
    End Function

    Public Function GetLine() As Line
        Dim templine As New Line
        templine.X1 = Me.Point1.X
        templine.Y1 = Me.Point1.Y
        templine.X2 = Me.Point2.X
        templine.Y2 = Me.Point2.Y
        Return templine
    End Function
End Class

Public Enum ParallelPosition As Byte
    Above
    Below
    Left
    Right
End Enum

希望这能有所帮助！
在我看来，“平行线”的情况需要单独处理。所有其他的求交算法都会测试一个交点。不过，我认为并行情况解决起来相当简单。不过，你多久会期望精确的平行线？如果你是这样的话，这几乎是不可能的使用浮点值表示直线。编辑：事实上，您发布的问题中给出的最上面的解决方案也为这种情况提供了解决方案。查找他给出的检验共线性的不等式的部分。如果我是诚实的，请阅读该问题的最上面的答案。我在第二句话中迷失了方向……我不认为我不会在不认真学习数学的情况下，能够将他所说的任何内容组织成可用的代码…我的atm编程已经足够了。我想我已经找到了一个合适的方法，虽然它不能解决平行线问题，但确实让我很容易拼凑出一些东西…完成后我会把它贴在这里。Alright、 我也可以试着稍后在这里发布一个答案，这将有助于解释如何将数学转化为代码。我想你会发现这并不像看上去那么难！：）最后的检查可以简化为简单地检查x或y坐标，我相信。还要注意的是，你需要确保x0谢谢你，我想我理解了更多。我不知道你是如何计算出解l0=l1的公式的。@KenoguLabz为什么你只需要检查x或y？这是否意味着你甚至不需要计算ox和y坐标中的ne？通过斜率截距形式，以代数方式找到l0=l1。y=m0*x+b0和y=m1*x+b1。当这两条线相交时，x和y是相同的。这允许我们独立求解x和y。如果我们从方程中取y值代替l0，并用方程l1中的y值代替，得到：m0*x+b0=m1*x+b1。求解x:m1*x-m0*x=b1-b0=>x=（b1-b0）/（m0-m1）。然后将您找到的值代入方程式l0或l1中的一个，以找到y的值。这可能最好在答案本身中公布，或作为另一个答案公布。我所说的“仅检查x或y”的意思是，您只需要使用他上面给出的测试的前两部分或后两部分。因此，您可以使用（x0@Gravitate）为了扩展Kenogu-Labz所说的，你只需要检查x或y坐标的原因是因为你已经确定
（x，y）
在直线上。如果x满足关系，那么y也会满足，反之亦然。
min(x0, x1) <= x <= max(x0, x1) AND min(x2, x3) <= x <= max(x2, x3)

Public Class LineData
    Public Property Point1() As Point
    Public Property Point2() As Point
    Public ReadOnly Property Slope() As Double
        Get
            # 0=Horizontal Line, NaN=Vertical Line
            Return If(Me.Point1.X = Me.Point2.X, Double.NaN, (Me.Point1.Y - Me.Point2.Y) / (Me.Point1.X - Me.Point2.X))
        End Get
    End Property
    Public ReadOnly Property YIntercept() As Double
        Get
            Return If(Double.IsNaN(Me.Slope), Double.NaN, Me.Point1.Y - Me.Slope * Me.Point1.X)
        End Get
    End Property
    Public ReadOnly Property Angle() As Double
        Get
            Return If(Double.IsNaN(Me.Slope), Math.PI / 2, Math.Atan(Me.Slope))
        End Get
    End Property

    Public Sub New(pt1 As Point, pt2 As Point)
        Me.Point1 = pt1
        Me.Point2 = pt2
    End Sub
    Public Sub New(x1 As Double, y1 As Double, x2 As Double, y2 As Double)
        Me.Point1 = New Point(x1, y1)
        Me.Point2 = New Point(x2, y2)
    End Sub
    Public Sub New(ln As Line)
        Me.New(ln.X1, ln.Y1, ln.X2, ln.Y2)
    End Sub

    Public Function GetParallel(spacing As Double) As LineData
        Return Me.GetParallel(spacing, ParallelPosition.Below)
    End Function

    Public Function GetParallel(spacing As Double, pos As ParallelPosition) As LineData
        If Me.Slope = 0 Then # Horizontal Line
            If pos = ParallelPosition.Above OrElse pos = ParallelPosition.Left Then : Return If(Me.Point2.X > Me.Point1.X, New LineData(Me.Point1.X - spacing, Me.Point1.Y - spacing, Me.Point2.X + spacing, Me.Point2.Y - spacing), New LineData(Me.Point1.X + spacing, Me.Point1.Y - spacing, Me.Point2.X - spacing, Me.Point2.Y - spacing))
            Else : Return If(Me.Point2.X > Me.Point1.X, New LineData(Me.Point1.X - spacing, Me.Point1.Y + spacing, Me.Point2.X + spacing, Me.Point2.Y + spacing), New LineData(Me.Point1.X + spacing, Me.Point1.Y + spacing, Me.Point2.X - spacing, Me.Point2.Y + spacing))
            End If
        ElseIf Double.IsNaN(Me.Slope) Then # Vertical Line
            If pos = ParallelPosition.Above OrElse pos = ParallelPosition.Left Then : Return If(Me.Point2.Y > Me.Point1.Y, New LineData(Me.Point1.X - spacing, Me.Point1.Y - spacing, Me.Point2.X - spacing, Me.Point2.Y + spacing), New LineData(Me.Point1.X - spacing, Me.Point1.Y + spacing, Me.Point2.X - spacing, Me.Point2.Y - spacing))
            Else : Return If(Me.Point2.Y > Me.Point1.Y, New LineData(Me.Point1.X + spacing, Me.Point1.Y - spacing, Me.Point2.X + spacing, Me.Point2.Y + spacing), New LineData(Me.Point1.X + spacing, Me.Point1.Y + spacing, Me.Point2.X + spacing, Me.Point2.Y - spacing))
            End If
        Else #Sloped Line
            Dim verticalshift As Double = Math.Abs(spacing / Math.Cos(-Me.Angle))
            Dim horizontalshift As Double = Math.Abs(spacing / Math.Sin(-Me.Angle))
            If Math.Sign(Me.Slope) = -1 Then
                If Me.Point2.X > Me.Point1.X Then
                    If pos = ParallelPosition.Above OrElse pos = ParallelPosition.Left Then : Return New LineData(Me.Point1.X - horizontalshift, Me.Point1.Y, Me.Point2.X, Me.Point2.Y - verticalshift)
                    Else : Return New LineData(Me.Point1.X, Me.Point1.Y + verticalshift, Me.Point2.X + horizontalshift, Me.Point2.Y)
                    End If
                Else
                    If pos = ParallelPosition.Above OrElse pos = ParallelPosition.Left Then : Return New LineData(Me.Point1.X, Me.Point1.Y - verticalshift, Me.Point2.X - horizontalshift, Me.Point2.Y)
                    Else : Return New LineData(Me.Point1.X + horizontalshift, Me.Point1.Y, Me.Point2.X, Me.Point2.Y + verticalshift)
                    End If
                End If
            Else
                If Me.Point2.X > Me.Point1.X Then
                    If pos = ParallelPosition.Above OrElse pos = ParallelPosition.Right Then : Return New LineData(Me.Point1.X, Me.Point1.Y - verticalshift, Me.Point2.X + horizontalshift, Me.Point2.Y)
                    Else : Return New LineData(Me.Point1.X - horizontalshift, Me.Point1.Y, Me.Point2.X, Me.Point2.Y + verticalshift)
                    End If
                Else
                    If pos = ParallelPosition.Above OrElse pos = ParallelPosition.Right Then : Return New LineData(Me.Point1.X + horizontalshift, Me.Point1.Y, Me.Point2.X, Me.Point2.Y - verticalshift)
                    Else : Return New LineData(Me.Point1.X, Me.Point1.Y + verticalshift, Me.Point2.X - horizontalshift, Me.Point2.Y)
                    End If
                End If
            End If
        End If
    End Function

    Public Function CalculateX(y As Double) As Double
        If Me.Slope = 0 Then # Horizontal Line
            If y = Me.Point1.Y OrElse y = Me.Point2.Y Then Return 0 Else Return Double.NaN
        ElseIf Double.IsNaN(Me.Slope) Then # Vertical Line
            Return Me.Point1.X
        Else
            Return (y - Me.YIntercept) / Me.Slope
        End If
    End Function
    Public Function CalculateY(x As Double) As Double
        If Me.Slope = 0 Then # Horizontal Line
            Return Me.Point1.Y
        ElseIf Double.IsNaN(Me.Slope) Then # Vertical Line
            If x = Me.Point1.X OrElse x = Me.Point2.X Then Return 0 Else Return Double.NaN
        Else
            Return Me.Slope * x + Me.YIntercept
        End If
    End Function

    Public Function GetIntersection(ln As LineData) As Point
        If Me.Slope = ln.Slope OrElse (Double.IsNaN(Me.Slope) AndAlso Double.IsNaN(ln.Slope)) Then : Return Nothing
        Else
            If Double.IsNaN(Me.Slope) Then : Return New Point(Me.Point1.X, ln.CalculateY(Me.Point1.X))
            ElseIf Double.IsNaN(ln.Slope) Then : Return New Point(ln.Point1.X, Me.CalculateY(ln.Point1.X))
            ElseIf Me.Slope = 0 Then : Return New Point(ln.CalculateX(Me.Point1.Y), Me.Point1.Y)
            ElseIf ln.Slope = 0 Then : Return New Point(Me.CalculateX(ln.Point1.Y), ln.Point1.Y)
            Else
                Dim x As Double = (Me.YIntercept - ln.YIntercept) / (ln.Slope - Me.Slope)
                Return New Point(x, Me.CalculateY(x))
            End If
        End If
    End Function

    Public Function GetLine() As Line
        Dim templine As New Line
        templine.X1 = Me.Point1.X
        templine.Y1 = Me.Point1.Y
        templine.X2 = Me.Point2.X
        templine.Y2 = Me.Point2.Y
        Return templine
    End Function
End Class

Public Enum ParallelPosition As Byte
    Above
    Below
    Left
    Right
End Enum