绘图用到的部分算法（VB）

部分算法(VB语言)

‘******************************************************************************

‘是否在多边形内

‘1表示在多边形内，0表示在多边形外

Private Function IsInner(ByVal pts As MapXLib.Points, ByVal P As MapXLib.Point) As Integer

Dim i As Integer

Dim ret As Integer

Dim sum As Integer

Dim direc As Long

Dim num As Long

Dim px() As New MapXLib.Point

ret = 0

sum = 0

direc = 0

num = pts.Count

If pts.Count < 3 Then

IsInner = 2 ‘

Exit Function

End If

ReDim px(0 To num - 1)

For i = 0 To num - 1

px(i).Set pts.Item(i + 1).x, pts.Item(i + 1).y

Next i

For i = 0 To num - 2

ret = IsCross(px(i), px(i + 1), P)

If ret = 2 Then

IsInner = 2

Exit Function

End If

sum = sum + ret

Next i

ret = IsCross(px(num - 1), px(0), P)

If ret = 2 Then

IsInner = 2 ‘无法判断

Exit Function

End If

sum = sum + ret

If direc Then

IsInner = 1 ‘位于多边形区域内

Exit Function

End If

If sum Mod 2 = 0 Then

IsInner = 0 ‘位于多边形区域外

Else

IsInner = 1

End If

End Function

‘***********************************************************************

‘高飞:2000.10.1

‘输入参数：点p1,p2,p0

‘输出：排序之后的点p1,p2(p1,p2相对于p0作逆时针排序)

Private Sub AntiClockWise(P1 As MapXLib.Point, P2 As MapXLib.Point, ByVal P0 As MapXLib.Point)

Dim a1 As Double ‘a1是P1->P0与水平轴之间的夹角(0~2π)

Dim a2 As Double ‘a2是P2->P0与水平轴之间的夹角(0~2π)

Dim a0 As Double

Dim P11 As New MapXLib.Point

Dim P12 As New MapXLib.Point

a1 = GetAngle(P1, P0)

a2 = GetAngle(P2, P0)

a0 = a2 - a1

If a0 > 0 Then

If a0 < PI_IN_MATH Then

P11.Set P1.x, P1.y

P12.Set P2.x, P2.y

Else

P11.Set P2.x, P2.y

P12.Set P1.x, P1.y

End If

Else

If a0 < PI_IN_MATH Then

P11.Set P2.x, P2.y

P12.Set P1.x, P1.y

Else

P11.Set P1.x, P1.y

P12.Set P2.x, P2.y

End If

End If

P1.Set P11.x, P11.y

P2.Set P12.x, P12.y

End Sub

‘******************************************************************************

‘高飞：2000.10.1

‘判断点与直线的关系

‘输入点的坐标 a(x, y), 直线方程a * x + b * y + c = 0

‘如果点在直线上方 return 1;

‘如果点在直线上   return 0;

‘如果点在直线下方 return -1;

‘////////////////////////////////////////////////////////////

Private Function Jponli(ByVal x As Double, ByVal y As Double, _

ByVal a As Double, ByVal b As Double, ByVal c As Double) As Long

Dim j  As Long, e As Double

j = 1

If (a * x + b * y + c) < 0# Then

j = -1

End If

e = Sqr(a * a + b * b)

If e >= 0.000001 Then

If Abs(a * x + b * y + c) < (0.001 * e) Then

j = 0

End If

End If

‘-------------------

Jponli = j

End Function

‘******************************************************************************

‘高飞: 2000.10.1

‘沿逆时针方向，P2->P0与P1->P0之间的夹角(0~π)

Private Function Get3DAngle(ByVal P1 As MapXLib.Point, ByVal P0 As MapXLib.Point, ByVal P2 As MapXLib.Point) As Double

Dim a0 As Double

a0 = GetAngle(P1, P0) - GetAngle(P2, P0)

If a0 < 0 Then

a0 = a0 + 2 * PI_IN_MATH

End If

‘--------------

Get3DAngle = a0

End Function

‘******************************************************************************

‘高飞：2000.10.1

‘搜索使a0最小的直线

‘输入参数:f0,点P11,点P12,点P22,角度a0,fkey

‘输出:P22,a0,fkey

Private Function SearchNextLine(ByVal f0 As MapXLib.Feature, ByVal P11 As MapXLib.Point, ByVal P12 As MapXLib.Point, P22 As MapXLib.Point, a0 As Double) As Boolean

Dim i As Long

Dim j As Long

Dim ct As Long

Dim PT_S As MapXLib.Points

Dim P1 As MapXLib.Point

Dim P2 As MapXLib.Point

Dim bSearched As Boolean

If f0.Type <> miFeatureTypeLine Then ‘只检查直线

bSearched = False

Exit Function

End If

bSearched = False

ct = f0.Parts.Count

For i = 1 To ct

Set PT_S = f0.Parts.Item(i)

For j = 1 To PT_S.Count - 1

Set P1 = PT_S.Item(j)

Set P2 = PT_S.Item(j + 1)

If IsEqual(P1.x, P12.x) And IsEqual(P1.y, P12.y) Then ‘P1=P12

If Get3DAngle(P11, P12, P2) < a0 Then

a0 = Get3DAngle(P11, P12, P2)

P22.Set P2.x, P2.y

bSearched = True

End If

End If

If IsEqual(P2.x, P12.x) And IsEqual(P2.y, P12.y) Then ‘P2=P12

If Get3DAngle(P11, P12, P1) < a0 Then

a0 = Get3DAngle(P11, P12, P1)

P22.Set P1.x, P1.y

bSearched = True

End If

End If

Next j

Next i

‘return

SearchNextLine = bSearched

End Function

‘******************************************************************************

‘求两线段的交点

‘输入四点的坐标 l1: A(x1, y1)  B(x2, y2)

‘             l2: C(x3, y3)  D(x4, y4)

‘输出交点A(*xx, *yy);

‘如果两线段没有交点, return FALSE, and *xx = *yy = 9e5;

‘否则 return TRUE;

Private Function PlsLs(ByVal x1 As Double, ByVal y1 As Double, _

ByVal x2 As Double, ByVal y2 As Double, _

ByVal x3 As Double, ByVal y3 As Double, _

ByVal x4 As Double, ByVal y4 As Double, _

xx As Double, yy As Double) As Boolean

Dim a1 As Double, b1 As Double, c1 As Double ‘第一条直线方程的系数a1*x + b1*y + c1=0

Dim a2 As Double, b2 As Double, c2 As Double ‘第二条直线方程的系数a2*x + b2*y + c2=0

Dim i1 As Long, i2 As Long

Dim j1 As Long, j2 As Long

Dim bb1 As Double, bb2 As Double

Dim cc1 As Double, cc2 As Double

xx = 0.00001

yy = xx

‘判断四点中是否有两点是相同的

‘如果A、C为一点

If (IsEqual(x1, x3) And IsEqual(y1, y3)) = True Then

xx = x1

yy = y1

PlsLs = True

Exit Function

End If

‘如果A、D为一点

If (IsEqual(x1, x4) And IsEqual(y1, y4)) = True Then

xx = x1

yy = y1

PlsLs = True

Exit Function

End If

‘如果B、C为一点

If (IsEqual(x2, x3) And IsEqual(y2, y3)) = True Then

xx = x2

yy = y2

PlsLs = True

Exit Function

End If

‘如果B、D为一点

If (IsEqual(x2, x4) And IsEqual(y2, y4)) = True Then

xx = x2

yy = y2

PlsLs = True

Exit Function

End If

‘---------------------------------------------------------------------

If CoEff1(x1, y1, x2, y2, a1, b1, c1) = False Then

PlsLs = False

Exit Function

End If

If CoEff1(x3, y3, x4, y4, a2, b2, c2) = False Then

PlsLs = False

Exit Function

End If

i1 = Jponli(x1, y1, a2, b2, c2)

i2 = Jponli(x2, y2, a2, b2, c2)

j1 = Jponli(x3, y3, a1, b1, c1)

j2 = Jponli(x4, y4, a1, b1, c1)

‘如果两直线重合

If (i1 = 0 And i2 = 0 And j1 = 0 And j2 = 0) Then

PlsLs = False

Exit Function

End If

‘如果有一点在另一条直线上

If ((i1 * i2 * j1 * j2) = 0) Then

‘如果A在l2上

If (i1 = 0) Then

‘如果C、D在l1两侧

If ((j1 * j2) <= 0) Then

xx = x1

yy = y1

PlsLs = True

Exit Function

End If

PlsLs = False

Exit Function

End If

‘如果B在l2上

If (i2 = 0) Then

‘如果C、D在l1两侧

If ((j1 * j2) <= 0) Then

xx = x2

yy = y2

PlsLs = True

Exit Function

End If

PlsLs = False

Exit Function

End If

‘如果C在l1上

If (j1 = 0) Then

‘如果A、B在l2两侧

If ((i1 * i2) <= 0) Then

xx = x3

yy = y3

PlsLs = True

Exit Function

End If

PlsLs = False

Exit Function

End If

‘如果D在l1上

If (j2 = 0) Then

‘如果A、B在l2两侧

If ((i1 * i2) <= 0) Then

xx = x4

yy = y4

PlsLs = True

Exit Function

End If

PlsLs = False

Exit Function

End If

Else ‘如果没有一点在另一条直线上

‘如果两线段相互交叉

If ((i1 * i2 + j1 * j2) = -2) Then

bb1 = b1 * a2

bb2 = b2 * a1

cc1 = c1 * a2

cc2 = c2 * a1

If IsEqual(bb1, bb2) = True Then

PlsLs = False

Exit Function

End If

yy = -(cc1 - cc2) / (bb1 - bb2)

cc1 = c1 * b2

cc2 = c2 * b1

xx = -(cc1 - cc2) / (bb2 - bb1)

PlsLs = True

Exit Function

End If

PlsLs = False

Exit Function

End If

‘--------------

PlsLs = False

End Function

‘******************************************************************************

‘两点确定一条直线

‘输入两点坐标A(x1, y1) B(x2, y2)

‘输出直线方程l: *a*x + *b*y + *c = 0

‘如果是同一点 return FALSE, *a = *b = *c = 0

‘成功 return TRUE

Private Function CoEff1(ByVal x1 As Double, ByVal y1 As Double, _

ByVal x2 As Double, ByVal y2 As Double, _

a As Double, b As Double, c As Double) As Boolean

If IsEqual(x1, x2) And IsEqual(y1, y2) Then ‘如果是同一点

a = 0#

b = 0#

c = 0#

CoEff1 = False

End If

‘-------------------

a = y2 - y1

b = x1 - x2

c = -x1 * a - y1 * b

CoEff1 = True

End Function

‘******************************************************************************

Private Function IsCross(ByVal P1 As MapXLib.Point, ByVal P2 As MapXLib.Point, ByVal P As MapXLib.Point) As Integer

Dim xt As Integer

Dim direc As Long

If (P.y > P1.y And P.y > P2.y) Or (P.y < P1.y And P.y < P2.y) Then

IsCross = 0                      ‘不相交

Exit Function

End If

If P2.y = P1.y Then

If P.y = P1.y Then

If (P.x > P1.x And P.x > P2.x) Then

IsCross = 2 ‘无法判断

Else

If (P.x < P1.x And P.x < P2.x) Then

IsCross = 0

Else

direc = 1 ‘热点坐标正好位于多边形的边界

End If

End If

Else

IsCross = 0

End If

Exit Function

End If

xt = P1.x + 1# * (P2.x - P1.x) * (P.y - P1.y) / (P2.y - P1.y)

If xt > P.x Then

IsCross = 0

Else

If xt = P.x Then

direc = 1

Else

If (P.y = P1.y Or P.y = P2.y) Then

IsCross = 2

Else

IsCross = 1 ‘相交

End If

End If

End If

End Function

‘******************************************************************************

‘是否在多边形内

‘1表示在多边形内，0表示在多边形外

Private Function IsInner(ByVal pts As MapXLib.Points, ByVal P As MapXLib.Point) As Integer

Dim i As Integer

Dim ret As Integer

Dim sum As Integer

Dim direc As Long

Dim num As Long

Dim px() As New MapXLib.Point

ret = 0

sum = 0

direc = 0

num = pts.Count

If pts.Count < 3 Then

IsInner = 2 ‘

Exit Function

End If

ReDim px(0 To num - 1)

For i = 0 To num - 1

px(i).Set pts.Item(i + 1).x, pts.Item(i + 1).y

Next i

For i = 0 To num - 2

ret = IsCross(px(i), px(i + 1), P)

If ret = 2 Then

IsInner = 2

Exit Function

End If

sum = sum + ret

Next i

ret = IsCross(px(num - 1), px(0), P)

If ret = 2 Then

IsInner = 2 ‘无法判断

Exit Function

End If

sum = sum + ret

If direc Then

IsInner = 1 ‘位于多边形区域内

Exit Function

End If

If sum Mod 2 = 0 Then

IsInner = 0 ‘位于多边形区域外

Else

IsInner = 1

End If

End Function

‘******************************************************************************

‘求出(x1,y1)到(x2,y2)之间的距离

Public Function GetDistance(ByVal x1 As Double, ByVal y1 As Double, ByVal x2 As Double, ByVal y2 As Double) As Double

Dim xx As Double

Dim yy As Double

xx = Abs(x1 - x2)

yy = Abs(y1 - y2)

GetDistance = Sqr(xx * xx + yy * yy)

End Function

‘******************************************************************************

Public Function SnapNewPoints(ByVal pts As MapXLib.Points, curX As Double, curY As Double, Range) As Boolean

Dim pt As MapXLib.Point

Dim nstPoint As UPoint ‘最近点：MAP坐标

Dim nstDistance As Double ‘最短的距离

Dim calDistance As Double ‘计算出来的距离

‘Initialize the Data

nstPoint.x = curX

nstPoint.y = curY

nstDistance = Range

‘-------------------------------------

For Each pt In pts

‘计算距离

calDistance = GetDistance(pt.x, pt.y, nstPoint.x, nstPoint.y)

If calDistance < nstDistance Then

nstPoint.x = pt.x

nstPoint.y = pt.y

nstDistance = calDistance

End If

Next

‘return the value

curX = nstPoint.x

curY = nstPoint.y

If nstDistance < Range Then

SnapNewPoints = True

Else

SnapNewPoints = False

End If

End Function

‘******************************************************************************

‘--------------------------------------------------

‘直角坐标与极坐标相互转换

‘flag:1-------极坐标 → 直角坐标

‘     0-------直角坐标 → 极坐标

‘参数中：angle的单位为弧度

‘--------------------------------------------------

Public Sub REC2POLAR(ByVal x1 As Double, ByVal y1 As Double, x2 As Double, y2 As Double, dist As Double, angle As Double, ByVal flag As Long)

If flag = 1 Then ‘极坐标 → 直角坐标

x2 = x1 + dist * Cos(angle)

y2 = y1 + dist * Sin(angle)

Exit Sub

End If

‘直角坐标 → 极坐标

‘求(x2,y2)到(x1,y1)之间的距离

dist = Sqr((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1))

If dist = 0 Then

angle = 0

Exit Sub

End If

‘----------------------

angle = Acos((x2 - x1) / dist)

If y2 < y1 Then

If x2 > x1 Then

angle = 2 * PI_IN_MATH - angle

Else

angle = 2 * PI_IN_MATH - angle

End If

End If

End Sub

‘******************************************************************************

‘反余弦函数

‘返回值是弧度

Public Function Acos(ByVal x As Double) As Double

Select Case x

Case 1

Acos = 0

Case -1

Acos = PI_IN_MATH

Case Else

Acos = Atn(-x / Sqr(-x * x + 1)) + 2 * Atn(1)

End Select

End Function

‘******************************************************************************

‘反正弦函数，返回值单位是弧度

Public Function Asin(ByVal x As Double) As Double

Select Case x

Case 1

Asin = PI_IN_MATH / 2

Case -1

Asin = -PI_IN_MATH / 2

Case Else

Atn (x / Sqr(-x * x + 1))

End Select

End Function

‘******************************************************************************

‘求(x1,y1)——(x2,y2)与

‘  (x3,y3)——(x4,y4）两条直线的交点

‘以上有向线段

Public Sub GetIntersetPt(ByVal x1 As Double, ByVal y1 As Double, _

ByVal x2 As Double, ByVal y2 As Double, _

ByVal x3 As Double, ByVal y3 As Double, _

ByVal x4 As Double, ByVal y4 As Double, _

x0 As Double, y0 As Double)

Dim dlt12 As Double

Dim dlt34 As Double

Dim CosA1 As Double

Dim CosA2 As Double

Dim flag As Long ‘1,2,3,4

‘求余弦平方

flag = -1

CosA1 = (x1 - x2) * (x1 - x2) / ((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2))

CosA2 = (x3 - x4) * (x3 - x4) / ((x3 - x4) * (x3 - x4) + (y3 - y4) * (y3 - y4))

‘1:平行或在同一条直线上

If CosA1 = CosA2 Then

flag = 1

Else

‘2:

If (CosA1 = 1) And (CosA2 <> 1) Then

flag = 2

End If

‘3:

If (CosA1 <> 1) And (CosA2 = 1) Then

flag = 3

End If

‘4:

If (CosA1 <> 1) And (CosA2 <> 1) Then

If (CosA1 = 0) And (CosA2 <> 0) Then

flag = 4

End If

If (CosA1 <> 0) And (CosA2 = 0) Then

flag = 5

End If

If (CosA1 <> 0) And (CosA2 <> 0) Then

flag = 6

End If

End If

End If

‘-------------------

Select Case (flag)

Case 1

x0 = (x2 + x4) / 2

y0 = (y2 + y4) / 2

Case 2

y0 = y2

dlt34 = (x3 - x4) / (y3 - y4)

x0 = x3 - (y3 - y0) * dlt34

Case 3

y0 = y4

dlt12 = (x1 - x2) / (y1 - y2)

x0 = x1 - (y1 - y0) * dlt12

Case 4

x0 = x2

dlt34 = (x3 - x4) / (y3 - y4)

y0 = y3 - (x3 - x0) / dlt34

Case 5

x0 = x4

dlt12 = (x1 - x2) / (y1 - y2)

y0 = y1 - (x1 - x0) / dlt12

Case 6

dlt12 = (x1 - x2) / (y1 - y2)

dlt34 = (x3 - x4) / (y3 - y4)

x0 = ((y3 * dlt12 * dlt34 - x3 * dlt12) - (y1 * dlt12 * dlt34 - x1 * dlt34)) / (dlt34 - dlt12)

y0 = y1 - (x1 - x0) / dlt12

End Select

End Sub

‘******************************************************************************

‘求点到线集的最近距离、线在线集中的位置，

‘并给出点在线集的侧向

‘返回值：1表示逆时针

‘       0表示顺时针

‘(x,y)多边形外一点

‘pts 点集

Public Function IsClockWise(ByVal x As Double, ByVal y As Double, ByVal pts As MapXLib.Points) As Long

Dim min As Double

Dim irec As Long

Dim ct As Long

Dim i As Long

Dim pt() As UPoint

Dim R As Double

Dim dd As Double

ct = pts.Count

If ct <= 1 Then

IsClockWise = -1

Exit Function

End If

‘-------------------------------------

ReDim pt(1 To ct)

For i = 1 To ct

pt(i).x = pts.Item(i).x

pt(i).y = pts.Item(i).y

Next i

R = 0

‘求(x,y)到第一个点的距离

min = Sqr((x - pt(1).x) * (x - pt(1).x) + (y - pt(1).y) * (y - pt(1).y))

For i = 1 To ct - 1

dd = PtDist2Line(x, y, pt(i).x, pt(i).y, pt(i + 1).x, pt(i + 1).y)

If dd <= min Then

min = dd

R = i

End If

Next i

‘-----------------

min = (x - pt(R + 1).x) * (x - pt(R + 1).x) + (y - pt(R + 1).y) * (y - pt(R + 1).y)

dd = (x - pt(R).x) * (x - pt(R).x) + (y - pt(R).y) * (y - pt(R).y)

‘----------------------

If min > dd Then

irec = R

Else

irec = R + 1

End If

‘-----------------------

dd = (pt(R + 1).y - pt(R).y) * (x - pt(R).x) - (pt(R + 1).x - pt(R).x) * (y - pt(R).y)

If dd < 0 Then

IsClockWise = 1

Else

IsClockWise = 0

End If

End Function

‘******************************************************************************

‘求点到线段的最近距离

Public Function PtDist2Line(ByVal x As Double, ByVal y As Double, _

ByVal x1 As Double, ByVal y1 As Double, _

ByVal x2 As Double, ByVal y2 As Double) As Double

Dim dist01 As Double

Dim dist02 As Double

Dim dist12 As Double

Dim d As Double

Dim dx As Double

Dim dy As Double

‘dist p - p1

dy = y - y1

dx = x - x1

dist01 = dy * dy + dx * dx

‘dist p-p2

dy = y - y2

dx = x - x2

dist02 = dy * dy + dx * dx

‘dist p1-p2

dy = y1 - y2

dx = x1 - x2

dist12 = dy * dy + dx * dx

If (((dist01 + dist12) > dist02) And ((dist02 + dist12) > dist01)) Then ‘余弦定理: p1角<90 并且 p2角<90

d = Abs(-dy * (x - x2) + dx * (y - y2)) / Sqr(dist12)    ‘ dist p - line(p1-p2)

Else

If dist01 < dist02 Then

d = Sqr(dist01)

Else

d = Sqr(dist02)

End If

End If

PtDist2Line = d

End Function

‘******************************************************************************

‘------------------------------------------------------

‘返回有向线段Pt1-->pt2与水平线之间的夹角(0～2π)

‘-----------------------------------------------------------

Public Function GetAngle(ByVal pt1 As MapXLib.Point, ByVal pt2 As MapXLib.Point) As Double

Dim a As Double ‘夹角

Dim l As Double ‘弦长

Dim pt0 As UPoint ‘pt2相对于pt1的相对坐标

l = Sqr((pt1.x - pt2.x) * (pt1.x - pt2.x) + (pt1.y - pt2.y) * (pt1.y - pt2.y))

a = Acos((pt2.x - pt1.x) / l)

pt0.x = pt2.x - pt1.x

pt0.y = pt2.y - pt1.y

If pt0.y < 0 Then

a = 2 * PI_IN_MATH - a

End If

‘---------------------

GetAngle = a

End Function

‘******************************************************************************

‘-------------------------------------------------

‘参数

‘Pt1,pt2,pt3

‘根据pt3在有向线段pt1->pt2的侧向，来判断是

‘优弧(1)还是劣弧(0)

‘----------------------------------------------------------------

Public Function IsYouHu(ByVal pt1 As MapXLib.Point, ByVal pt2 As MapXLib.Point, ByVal pt3 As MapXLib.Point) As Long

Dim a12 As Double ‘角度

Dim a13 As Double ‘角度

Dim b As Double ‘角度

Dim L13  As Double

Dim p3y As Double

a12 = GetAngle(pt1, pt2)

b = 2 * PI_IN_MATH - a12

a13 = GetAngle(pt1, pt3)

L13 = Sqr((pt3.x - pt1.x) * (pt3.x - pt1.x) + (pt3.y - pt1.y) * (pt3.y - pt1.y))

‘-----------

p3y = L13 * Sin(a13 + b)

‘---------

If p3y > 0 Then

IsYouHu = 0

Else

IsYouHu = 1

End If

End Function

时间： 2024-08-25 00:42:19

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