pos2 = p2.CY - p1.CY
                addToArray "wash_fast_line2 " & ch1 & " " & pos1 & " " & ch2 & " " & pos2 & " ", instructionSquence()
                Last.CX = Last.CX + pos1
                Last.CY = Last.CY + pos2
                
                If j Mod 2 = 0 And j <> PNum / 2 - 1 Then
                    
                    '拔出
                    step = -depth
                    addToArray "fast_pmove " & ch3 & " " & step & " ", instructionSquence()
            
                    '挪刀
                    p1 = thisScanner(i).SSquence(j + 2)
                    p2 = thisScanner(i).SSquence(j + 1)
                    pos1 = p2.CX - p1.CX
                    pos2 = p2.CY - p1.CY
                    addToArray "find_fast_line2 " & ch1 & " " & pos1 & " " & ch2 & " " & pos2 & " ", instructionSquence()
                    Last.CX = Last.CX + pos1
                    Last.CY = Last.CY + pos2
                
                    '插入
                    step = depth
                    addToArray "fast_pmove " & ch3 & " " & step & " ", instructionSquence()
                    
                End If
                
            Next j

            If j = PNum - 2 And i < UBound(thisScanner) Then
                p1 = p2
                p2 = thisScanner(i + 1).SSquence(0)
                pos1 = p2.CX - p1.CX
                pos2 = p2.CY - p1.CY
                addToArray "find_fast_line2 " & ch1 & " " & pos1 & " " & ch2 & " " & pos2 & " ", instructionSquence()
                Last.CX = Last.CX + pos1
                Last.CY = Last.CY + pos2

            End If

        End If
                   
    Next i
    
    '拔出
    step = -depth
    addToArray "fast_pmove " & ch3 & " " & step & " ", instructionSquence()
    
End Sub
'#############################################################################
'修改邊界坐標以適應邊框
Private Sub modifyBoundary(PSquence() As CoordType, d As Double, layer As Long)
    Dim i As Long
    
    Dim PNum As Long
    PNum = UBound(PSquence) + 1
    
    Dim PGroup As Long
    PGroup = PNum / 2
    
    For i = 0 To PGroup - 1
        PSquence(2 * i).CX = PSquence(2 * i).CX + d
        PSquence(2 * i + 1).CX = PSquence(2 * i + 1).CX - d
    Next i
End Sub
'#############################################################################
'回原點
Private Sub returnOrigin()
    Dim pos1 As Long
    Dim pos2 As Long
    
    pos1 = -Last.CX
    pos2 = -Last.CY
    addToArray "find_fast_line2 " & ch1 & " " & pos1 & " " & ch2 & " " & pos2 & " ", instructionSquence()
    
    Last.CX = 0
    Last.CY = 0
    
End Sub
'#############################################################################
'根據(jù)點的橫坐標把數(shù)組ps中點進行從小到大排序
Private Sub sortPointSquence(ps() As CoordType)
    
    Dim i As Long
    Dim j As Long
    Dim temp As Double
    Dim eleNum As Long
    eleNum = UBound(ps) + 1
    
    For i = 0 To eleNum - 1
        For j = 0 To eleNum - i - 2
            If ps(j).CX > ps(j + 1).CX Then
                temp = ps(j).CX
                ps(j).CX = ps(j + 1).CX
                ps(j + 1).CX = temp
            End If
        Next j
    Next i
    
End Sub
'#############################################################################
'求p1和p2兩點間的距離
Private Function getDistance(p1 As CoordType, p2 As CoordType) As Double
    
    getDistance = Sqr((p1.CX - p2.CX) ^ 2 + (p1.CY - p2.CY) ^ 2)
    
End Function
'#############################################################################
'根據(jù)已知兩點firPoint和secPoint求過這兩點的直線
Private Function getLine(firPoint As CoordType, secPoint As CoordType) As LineType
    
    Dim x1 As Double
    Dim y1 As Double
    Dim x2 As Double
    Dim y2 As Double
    
    getLine.LBegin = firPoint
    getLine.LEnd = secPoint
    
    x1 = firPoint.CX
    y1 = firPoint.CY
    x2 = secPoint.CX
    y2 = secPoint.CY
    
    If Abs(x1 - x2) < 0.001 Then
        getLine.LK = Null
        getLine.LB = x1
    Else
        getLine.LK = (y2 - y1) / (x2 - x1)
        getLine.LB = y1 - getLine.LK * x1
    End If
    
End Function
'#############################################################################
'求兩條直線firLine和secLine的交點
Private Function getLine_LineIntersection(firLine As LineType, secLine As LineType, Optional mode As Long) As CoordType
    
    Dim p As CoordType
    Dim s As Double
    Dim s1 As Double
    Dim s2 As Double
    
    Dim temp As Double
    
    Dim b1 As Boolean
    Dim b2 As Boolean
    Dim b3 As Boolean
    Dim b4 As Boolean
    
    If IsNull(firLine.LK) And IsNull(secLine.LK) Then
        If Abs(firLine.LB - secLine.LB) <= 0.0001 Then
            p = secLine.LEnd
        End If
    Else
        If IsNull(firLine.LK) Then
            p.CX = firLine.LB
            p.CY = secLine.LK * p.CX + secLine.LB
        Else
            If IsNull(secLine.LK) Then
                p.CX = secLine.LB
                p.CY = firLine.LK * p.CX + firLine.LB
            Else
                If Abs(firLine.LK - secLine.LK) <= 0.0001 Then
                    If Abs(firLine.LB - secLine.LB) <= 0.0001 Then
                        p = firLine.LEnd
                    End If
                Else
                    p.CX = (secLine.LB - firLine.LB) / (firLine.LK - secLine.LK)
                    p.CY = firLine.LK * p.CX + firLine.LB
                End If
            End If
        End If
        
    End If
    
    If mode = 1 Then
        getLine_LineIntersection = p
    Else    '方式0,默認方式
        If firLine.LK - secLine.LK = 0 Then
            getLine_LineIntersection.CX = -1 '約定，當返回值p.cx的值為-1時，掃描無效
            Exit Function
        End If
        
        '判定這一點是否在這條線段內(nèi)
        s = getDistance(firLine.LBegin, firLine.LEnd)
        s1 = getDistance(p, firLine.LBegin)
        s2 = getDistance(p, firLine.LEnd)
            
        temp = s - s1 - s2
        If Abs(temp - 0.0001) < 0.001 Then
            temp = 0
        End If
            
        b1 = p.CX <> firLine.LBegin.CX
        b2 = p.CY <> firLine.LBegin.CY
        b3 = p.CX <> firLine.LEnd.CX
        b4 = p.CY <> firLine.LEnd.CY
            
        If (temp = 0) And (b1 Or b2) And (b3 Or b4) Then
            getLine_LineIntersection = p
        Else
            getLine_LineIntersection.CX = -1
        End If
    End If
        
End Function
'###########################################
'根據(jù)兩點及所夾弧的凸度求這段圓弧的參數(shù)
Private Function getArc(pEty As EntityType, pn As Long) As ArcType
                                                  
    Dim p1 As CoordType
    Dim p2 As CoordType
    
    Dim tempConvex As Double     '由參數(shù)傳遞過來的凸度
    Dim absConvex As Double      '凸度的絕對值
              '包含角的角度制
    Dim radian As Double         '包含角的弧度制
    
    Dim eleNum As Long         '多線段實體中點數(shù)組的上標
    eleNum = pEty.EPnum

    Dim PI As Double
    PI = 3.14159265358979

    p1 = pEty.ECoord(pn)
    getArc.ABegin = p1
    
    If pn < eleNum - 1 Then   '未到達最后一點
        p2 = pEty.ECoord(pn + 1)
    Else                   '到達最后一點
        p2 = pEty.ECoord(0)
    End If
    getArc.AEnd = p2
    
    tempConvex = pEty.EConvex(pn)
    absConvex = Abs(tempConvex)
    angle = 4# * (Atn(absConvex) * 180# / PI)
    
    getArc.AAngle = angle
    If pEty.EConvex(pn) > 0 Then
        getArc.AAngle = -angle
    End If

    radian = 4# * (Atn(absConvex))
    
    If (radian - PI) > 0 Then
        radian = 2# * PI - radian
    End If
                    
    If Abs(p1.CX - p2.CX) < 0.00002 Then
                
        If Abs(absConvex - 1) < 0.00001 Then
            getArc.ACentre.CX = p1.CX
        Else
            If (((p2.CY > p1.CY) And (absConvex > 1#) And (tempConvex > 0#)) _
                Or ((p2.CY > p1.CY) And (absConvex < 1#) And (tempConvex < 0#)) _
                Or ((p2.CY < p1.CY) And (absConvex > 1#) And (tempConvex < 0#)) _
                Or ((p2.CY < p1.CY) And (absConvex < 1#) And (tempConvex > 0#))) Then
                getArc.ACentre.CX = p1.CX + Abs(p1.CY - p2.CY) / (2# * (Tan(radian / 2#)))
            Else
                getArc.ACentre.CX = p1.CX - Abs(p1.CY - p2.CY) / (2# * (Tan(radian / 2#)))
            End If
        End If
        
        getArc.ACentre.CY = (p1.CY + p2.CY) / 2#
            
    Else
                
        If absConvex = 1# Then
            getArc.ACentre.CY = (p1.CY + p2.CY) / 2#
        Else
            If (((p1.CX > p2.CX) And (absConvex > 1#) And (tempConvex > 0#)) _
                Or ((p1.CX > p2.CX) And (absConvex < 1#) And (tempConvex < 0#)) _
                Or ((p1.CX < p2.CX) And (absConvex > 1#) And (tempConvex < 0#)) _
                Or ((p1.CX < p2.CX) And (absConvex < 1#) And (tempConvex > 0#))) Then
                getArc.ACentre.CY = ((p1.CY + p2.CY) / 2#) + Abs(p1.CX - p2.CX) / (2# * Tan(radian / 2#))
            Else
                getArc.ACentre.CY = ((p1.CY + p2.CY) / 2#) - Abs(p1.CX - p2.CX) / (2# * Tan(radian / 2#))
            End If
        End If
                    
        getArc.ACentre.CX = (p1.CX + p2.CX) / 2# + (p2.CY - p1.CY) * (getArc.ACentre.CY - (p1.CY + p2.CY) / 2#) / (p1.CX - p2.CX)
                    
    End If
    
    getArc.ARadius = getDistance(p1, getArc.ACentre)
    
End Function
'###########################################
'求直線和圓弧的交點
Private Function getLine_ArcIntersection(ln As LineType, arc As ArcType, Optional mode As Long) As Variant
    
    Dim r As Double
    Dim x0 As Double
    Dim y0 As Double                  '弧的參數(shù)
    Dim k As Variant
    Dim b As Double                   '直線方程的參數(shù)
    Dim p1 As CoordType
    Dim p2 As CoordType               '兩個交點的坐標
    
    Dim l As Double
    Dim M As Double
    Dim N As Double
    Dim Q As Double                   '一些用于中途計算的宏
    Dim temp As Double
    Dim approximation As Double
    
    Dim kb As Variant                   '起始點與圓心所成直線的斜率
    Dim ke As Variant                   '終點與圓心所成直線的斜率
    
    Dim ab As Double
    Dim ae As Double
    
    Dim ap1 As Double
    Dim ap2 As Double
    
    
    '先以圓方程計算，求得可能存在的交點
    k = ln.LK
    b = ln.LB
    
    r = arc.ARadius
    x0 = arc.ACentre.CX
    y0 = arc.ACentre.CY
    
    If mode = 1 Then
    
        If IsNull(k) Then
        
            p1.CX = b
            p2.CX = b
            
            approximation = r ^ 2 - (b - x0) ^ 2
            If approximation < 0.0001 Then
                approximation = 0
            End If
            If approximation >= 0 Then
                p1.CY = y0 + Sqr(approximation)
                p2.CY = y0 - Sqr(approximation)
            End If
            getLine_ArcIntersection = Array(p1.CX, p1.CY, p2.CX, p2.CY)
            
        Else
        
            l = k ^ 2 + 1
            M = 2 * k * (b - y0) - 2 * x0
            N = x0 ^ 2 + (b - y0) ^ 2 - r ^ 2
            Q = M ^ 2 - 4 * l * N
        
            If Q <= 0.0001 Then
                Q = 0
            End If
            
            p1.CX = (-M + Sqr(Q)) / (2 * l)
            p2.CX = (-M - Sqr(Q)) / (2 * l)
            
            p1.CY = k * p1.CX + b
            p2.CY = k * p2.CX + b

            getLine_ArcIntersection = Array(p1.CX, p1.CY, p2.CX, p2.CY)

        End If
        
    Else        '方式0，默認方式
        If IsNull(k) Then
        
            p1.CX = b
            p2.CX = b
            
            approximation = r ^ 2 - (b - x0) ^ 2
            If approximation < 0.0001 Then
                approximation = 0
            End If
            
            If approximation >= 0 Then
                p1.CY = y0 + Sqr(approximation)
                p2.CY = y0 - Sqr(approximation)
                getLine_ArcIntersecti