Public Type tagPoint
x As Double
y As Double
z As Double
End Type
Public Type tagLine2D
k As Double 'Slope ,K is the "K" of "y=kx+b"
b As Double 'intercept,B is the "B" of "y=kx+b"
Angle As Double 'arctg(k) '0 to 180 deg
Straightness As Double
RSQ As Double
End Type
Public Type tagLine3D
'3D line's formula is showing as following.
'1)|Ax +By +Z+D =0
' |A1x+B1y+z+D1=0
'2)(x-x0)/m=(y-y0)/n=(z-z0)/p----(x-x0)/m=(y-y0)/n=z/1
'3)x=mt+x0,y=nt+y0,z=pt+z0
'Only point's coordinate is (a+b*Z, c+d*Z,Z),so the line's vector is {b,d,1}
x As Double
y As Double
z As Double
x0 As Double ' Added on Jul.1st,2009
y0 As Double ' Added on Jul.1st,2009
z0 As Double
m As Double '(x-x0)/m=(y-y0)/n=(z-z0)/p ,same as :z=a+bx ,z=c+dy
n As Double
p As Double 'vector s={m,n,p}
Angle As Double
xAn As Double
yAn As Double
zAn As Double
Straightness As Double
MinSt As Double
MaxSt As Double
'A line feature is reported as the projection of the centroid of the data points used to fit the line, which is projected onto the line feature, the direction of measurement measured as an angle, and a measurement of the straightness of the line. If a projection plane (xy, yz, zx) is specified, the data points are projected onto the projection plane and then fitted to a line
'X: The distance from the origin to the centroid, as measured along the x-axis.
'Y: The distance from the origin to the centroid, as measured along the y-axis.
'Z: The distance from the origin to the centroid, as measured along the z-axis
'Angle: The angle between the projection of the line onto the xy-plane and the x-axis of the current coordinate system.
'X-angle: The angle between the line and the x-axis of the current coordinate system. (X-Angle = arc cosine k). The x-angle is a positive number between 0 and 180 degrees.
'Y-angle: The angle between the line and the y-axis of the current coordinate system. (Y-Angle = arc cosine l). The y-angle is a positive number between 0 and 180 degrees.
'Z-angle: The angle between the line and the z-axis of the current coordinate system. (Z-Angle = arc cosine m). The z-angle is a positive number between 0 and 180 degrees.
'Straightness: Straightness is a condition for which an element of a surface or an axis is in a straight line.
'Straightness, in a 3-D definition, is reported as the width of the zone formed by a cylinder with diameter (t) with the constructed line feature as its axis. The zone's width is determined by finding the point that is the maximum distance from the constructed line. A value of zero indicates perfect straightness.
'Straightness, as used in a 2-D definition, is the distance between two closest parallel lines that fully contain the point set used to fit the line feature.
'Straightness (minimum): The distance from the fitted line to the nearest measured point in the point set. See Explanation of Max/Min distance in different cases.
'Straightness (maximum): The distance from the fitted line to the farthest measured point in the point set. See Explanation of Max/Min distance in different cases.
'Angularity: Angularity is a condition for where the line feature must be inclined at a specific angle with respect to a datum plane or datum axis.
'QVPAK reports the angularity of a line as the width of a zone formed when projecting the measured points onto the xy-plane or a z/ref plane. The z/ref plane feature is a plane including the reference line and parallel to (or including) the z-axis. A specified reference feature is also projected onto the plane, and a line feature is constructed inclined at a specified angle relative to the to the projection of the reference feature. The zone's width is determined by finding the distance between two lines which are parallel to the to the constructed line feature. The positions of these two parallel lines are determined by the finding the two projected points which have minimum and maximum distance from the constructed line. The value returned is the distance between the parallel lines. This value indicates the number of measurement units (mm or inches) by which the zone deviates from a straight line at the specified angle with respect to the reference feature.
'Line Angularity
'Parallelism: Parallelism is a special case of angularity, where the specified angle relative to the reference feature is zero (0) degrees.
'Parallelism (minimum): The distance from the referenced line or plane to the point in the point set with the least value (least positive value if all evaluated points are positive, or most negative value if evaluated points include negative values). See Explanation of Max/Min distance in different cases.
'Parallelism (maximum): The distance from the reference line or plane to the point in the point set with the greatest value (most positive value if evaluated points include positive values, or least negative value if all evaluated points are negative). See Explanation of Max/Min distance in different cases.
'Perpendicularity: Perpendicularity is a special case of angularity, where the specified angle relative to the reference feature is ninety (90) degrees.
End Type
作者: tmtony 时间: 2012-12-13 10:12
Public Type tagCircle
x As Double
y As Double
z As Double
r As Double
d As Double
Circular As Double '
'Circularity: Circularity is defined as the condition of a surface of revolution (for example, cylinders or cones) for which all points of the surface intersected by any plane perpendicular to the rotation axis are equidistant from the center.
'QVPAK reports circularity as the width of the zone defined by the two closest concentric circles that bound the data points.
End Type
Public Type tagVector
a As Double
b As Double
c As Double
End Type
Type tagPlane
x As Double 'The distance from the origin to the centroid, as measured along the x-axis.
y As Double 'The distance from the origin to the centroid, as measured along the y-axis
z As Double 'The distance from the origin to the centroid, as measured along the z-axis
'Z + A*x + B*y + C =0 z's coefficient is just 1
ax As Double 'coefficient of X
by As Double 'coefficient of Y
cz As Double
d As Double 'Constant C
Angle As Double 'The angle(deg) between the projection of the (fitted) plane's normal vector onto the XY-plane and the X-axis of the current coordinate system
'The fitted plane's normal vector is n1={A,B,1} ,is also line s1
'The XY plane's normal vector is n2={0,0,N}, is also Line s2
'Line s1 is projected on to plane xy-Plane,so Plane n3 = s1*s2 (the multiplication of two vetors)
'the intersect line n4=s1*n3
'the Angle(0,360) s3 =n4* Sxyplane s3(0,180)
'to dicide the line location in which. we should know value of B3 (A3,B3,C3)
'if b3>0 then s2(0,180), b3<0 then (180,360)
xAn As Double 'The angle(deg) between the (fitted) plane's normal vector and the X axis of the current coordinate system.(xAn=arc cosine K). The xAn is a positive number between 0 to 180
yAn As Double 'The angle(deg) between the (fitted) plane's normal vector and the Y axis of the current coordinate system.(xAn=arc cosine K). The yAn is a positive number between 0 to 180
zAn As Double 'The angle(deg) between the (fitted) plane's normal vector and the Z axis of the current coordinate system.(xAn=arc cosine K). The zAn is a positive number between 0 to 180
Flat As Double 'Flatness is ka condition for which an element of a surface is in a plane
'Flatness is reproted as the width of the zone formed by two closest parallel planes that fully contain the point int the point set used to fit the plane feature. A value of zero indicates perfect flatness.
MinFlat As Double 'Flatness(minimum), the distance from the fitted plane to the measured point farthest below--- the fitted plain in the point set. Above and below are determined by the direction of the plane vector
MaxFlat As Double 'Flatness(maximum), the distance from the fitted plane to the measured point farthest above--- the fitted plain in the point set
End Type
作者: tmtony 时间: 2012-12-13 10:12
'*************************************************************
' 函数名：Line3DSet0
' 功能： 求拟合空间直线（相关参数）
' 参数： dataRaw - tagPoint型 自定义点类型(x,y,z)，数组
' nLine - tagLine3D 其值返回为直线相关参数
' 返回值：Long型，失败为0，成功为-1
'*************************************************************
Function Line3DSet0(dataRaw() As tagPoint, nLine As tagLine3D) As Long
'3D line's formula is showing as following.
'1)|Ax +By +Z+D =0
' |A1x+B1y+z+D1=0
'2)(x-x0)/m=(y-y0)/n=(z-z0)/p
'3)x=mt+x0,y=nt+y0,z=pt+z0
'Only point's coordinate is (a+b*Z, c+d*Z,Z),so the line's vector is {b,d,1}
Dim SumX, SumY, SumZ, SumXZ, SumYZ, SumZ2
Dim TolN As Long, i As Long, j As Long, lb As Long, ub As Long
Dim d, d1, d2
Dim VecLine As tagVector
Dim xLine As tagVector '{1,0,0}
Dim yLine As tagVector '{0,1,0}
Dim zLine As tagVector '{0,0,1}
Dim maxS As Double, minS As Double, tmpD As Double
xLine.a = 1: xLine.b = 0: xLine.c = 0
yLine.a = 0: yLine.b = 1: yLine.c = 0
zLine.a = 0: zLine.b = 0: zLine.c = 1
'Dim AvgX As Double, AvgY As Double
lb = LBound(dataRaw): ub = UBound(dataRaw)
If ub < 2 Then
Line3DSet0 = 0
Exit Function
End If
TolN = ub - lb + 1
For i = lb To ub
With dataRaw(i)
SumX = SumX + .x
SumY = SumY + .y
SumZ = SumZ + .z
SumXZ = SumXZ + .x * .z
SumYZ = SumYZ + .y * .z
SumZ2 = SumZ2 + .z ^ 2
End With
Next i
d = TolN * SumZ2 - SumZ ^ 2
d1 = SumX * SumZ2 - SumZ * SumXZ
d2 = TolN * SumXZ - SumX * SumZ
With nLine
.p = 1
.x0 = d1 / d
.m = d2 / d
VecLine.a = .m: VecLine.b = .n: VecLine.c = 0
.Angle = Intersect(VecLine, xLine) '(xLine.A * SLine.A + xLine.A * SLine.B + xLine.C * SLine.C)
If VecLine.b < 0 Then .Angle = 360 - .Angle
VecLine.a = .m: VecLine.b = .n: VecLine.c = .p
.xAn = Intersect(VecLine, xLine)
.yAn = Intersect(VecLine, yLine)
.zAn = Intersect(VecLine, zLine)
For i = lb To ub
Call PointToLine(dataRaw(i), nLine, tmpD)
If i = lb Then
maxS = tmpD
minS = tmpD
Else
If tmpD > maxS Then maxS = tmpD
If tmpD < minS Then minS = tmpD
End If
'Cells(i + 1, 15) = tmpD
Next i
.MaxSt = maxS
.MinSt = minS
.Straightness = 2 * maxS
End With
Line3DSet0 = -1
End Function
'*************************************************************
' 函数名：Line3DSet
' 功能： 求拟合空间直线（相关参数）
' 参数： dataRaw - tagPoint型 自定义点类型(x,y,z)，数组
' nLine - tagLine3D 其值返回为直线相关参数
' 返回值：Long型，失败为0，成功为-1
'*************************************************************
Public Function Line3DSet(dataRaw() As tagPoint, nLine As tagLine3D) As Long
'3D line's formula is showing as following.
'1)|Ax +By +Z+D =0
' |A1x+B1y+z+D1=0
'2)(x-x0)/m=(y-y0)/n=(z-z0)/p
'3)x=mt+x0,y=nt+y0,z=pt+z0
'Only point's coordinate is (a+b*Z, c+d*Z,Z),so the line's vector is {b,d,1}
Dim TolN As Long, i As Long, j As Long, lb As Long, ub As Long
Dim VecLine As tagVector
Dim xLine As tagVector '{1,0,0}
Dim yLine As tagVector '{0,1,0}
Dim zLine As tagVector '{0,0,1}
Dim maxS As Double, minS As Double, tmpD As Double
Dim a(1, 1) As Double, b(1, 1) As Double, c(1, 1) As Double
xLine.a = 1: xLine.b = 0: xLine.c = 0
yLine.a = 0: yLine.b = 1: yLine.c = 0
zLine.a = 0: zLine.b = 0: zLine.c = 1
Dim SumXZ, SumX, SumYZ, SumY, SumZ2, SumZ
lb = LBound(dataRaw): ub = UBound(dataRaw)
TolN = ub - lb + 1
If ub < 2 Then
Line3DSet = 0
Exit Function
End If
For i = lb To ub
With dataRaw(i)
SumXZ = SumXZ + .x * .z
SumYZ = SumYZ + .y * .z
SumX = SumX + .x
SumY = SumY + .y
SumZ = SumZ + .z
SumZ2 = SumZ2 + .z ^ 2
End With
Next i
a(0, 0) = SumXZ: a(0, 1) = SumX: a(1, 0) = SumYZ: a(1, 1) = SumY
c(0, 0) = SumZ2: c(0, 1) = SumZ: c(1, 0) = SumZ: c(1, 1) = TolN
Call sMInverse(b, c) ' to inverse matrix
Call sMMult(c, a, b) 'to multiple two matrix
'{m,x0}
'{n,y0}
For i = lb To ub
Call PointToLine(dataRaw(i), nLine, tmpD)
If i = lb Then
maxS = tmpD
minS = tmpD
Else
If tmpD > maxS Then maxS = tmpD
If tmpD < minS Then minS = tmpD
End If
' Cells(i + 1, 15) = tmpD
Next i
.MaxSt = maxS
.MinSt = minS
.Straightness = 2 * maxS
Line3DSet = -1
Debug.Print "Totol Number", TolN
Debug.Print ".x: ", .x
Debug.Print ".y: ", .y
Debug.Print ".z: ", .z
Debug.Print ".x0: ", .x0
Debug.Print ".y0: ", .y0
Debug.Print ".m: ", .m
Debug.Print ".n: ", .n
Debug.Print ".p: ", .p
Debug.Print ".Angle: ", .Angle
Debug.Print ".xAn: ", .xAn
Debug.Print ".yAn: ", .yAn
Debug.Print ".zAn: ", .zAn
Debug.Print "Straightness", .Straightness, .MaxSt, .MinSt
End With
End Function 作者: tmtony 时间: 2012-12-13 10:12
Public Function Intersect(v1 As tagVector, v2 As tagVector, Optional LinePlane As Long = 0) As Double
'LinePlane 0 :line -line ,1:line --Plane
Dim tmp As Double, tmpSqr1 As Double, tmpSqr2 As Double
tmp = (v1.a * v2.a + v1.b * v2.b + v1.c * v2.c)
'MsgBox tmp
tmpSqr1 = Sqr(v1.a ^ 2 + v1.b ^ 2 + v1.c ^ 2)
tmpSqr2 = Sqr(v2.a ^ 2 + v2.b ^ 2 + v2.c ^ 2)
If tmpSqr1 <> 0 Then
If tmpSqr2 <> 0 Then
tmp = tmp / tmpSqr1 / tmpSqr2
Else
tmp = tmp / tmpSqr1
End If
Else
If tmpSqr2 <> 0 Then
tmp = tmp / tmpSqr2
Else
tmp = 0
End If
End If
If LinePlane <> 0 Then
tmp = Abs(tmp)
End If
If -tmp * tmp + 1 <> 0 Then
tmp = Atn(-tmp / Sqr(-tmp * tmp + 1)) + 2 * Atn(1)
tmp = tmp / PI * 180
Else
tmp = 90
End If
Intersect = tmp
End Function
'*************************************************************
' 函数名：PointToPlane
' 功能： 求点到平面的距离
' 参数： dataRaw - tagPoint型 自定义点类型(x,y,z)
' Plane - tagPlane Double
' RtnDistance -Double 其值为点到直线的距离.
' AbsDist -Long ０：点到平面距离（有正有负），其它值：点到平面距离（绝对值）
' 返回值：Long型，失败为0，成功为-1
'*************************************************************
Public Function PointToPlane(dataRaw As tagPoint, plane As tagPlane, rtnDistance As Double, Optional AbsDist As Long = 0) As Long
Dim i As Long, lb As Long, ub As Long, tmp As Double
With plane
tmp = (.ax * dataRaw.x + .by * dataRaw.y + .cz * dataRaw.z + .d) _
/ Sqr(.ax ^ 2 + .by ^ 2 + .cz ^ 2)
If AbsDist <> 0 Then
tmp = Abs(tmp)
End If
End With
rtnDistance = tmp
End Function
'*************************************************************
' 函数名：PointToLine
' 功能： 求点到直线的距离
' 参数： dataRaw - tagPoint型 自定义点类型(x,y,z)
' nLine3D - tagLine3D Double
' RtnDistance -Double 其值为点到直线的距离.
' 返回值：Long型，失败为0，成功为-1
'*************************************************************
Public Function PointToLine(dataRaw As tagPoint, nLine3D As tagLine3D, rtnDistance As Double) As Long
Dim tmp As Double, d As Double, t As Double
Dim Dataraw0 As tagPoint
With nLine3D
'直线{m,n,1}为平面:ax+by+z+d=0的法线,所以平面法线向量{a,b,1}={m,n,1}
'点(dataRaw)过平面:ax+by+z+d=0, 求出d
d = -.m * dataRaw.x - .n * dataRaw.y - .p * dataRaw.z '.p=1
'直线与平面相交,将(x-xo)/m=(y-y0)/n=z=t ' x=m*t+x0 ; y=n*t+yo z=t 代入平面, 求得t
, 是网友问, 就帮他解决