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microsoft-visualbasic-runtime/Extensions/Image/Math/GeometryMath.vb

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update file headers
2018-09-08 01:26:45 +08:00
#Region "Microsoft.VisualBasic::d686d36337a9031e2e78af7daadb163a, Microsoft.VisualBasic.Core\Extensions\Image\Math\GeometryMath.vb"
update directory
2018-09-08 00:34:19 +08:00
' Author:
'
' asuka (amethyst.asuka@gcmodeller.org)
' xie (genetics@smrucc.org)
' xieguigang (xie.guigang@live.com)
'
' Copyright (c) 2018 GPL3 Licensed
'
'
' GNU GENERAL PUBLIC LICENSE (GPL3)
'
'
' This program is free software: you can redistribute it and/or modify
' it under the terms of the GNU General Public License as published by
' the Free Software Foundation, either version 3 of the License, or
' (at your option) any later version.
'
' This program is distributed in the hope that it will be useful,
' but WITHOUT ANY WARRANTY; without even the implied warranty of
' MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
' GNU General Public License for more details.
'
' You should have received a copy of the GNU General Public License
' along with this program. If not, see <http://www.gnu.org/licenses/>.
' /********************************************************************************/
' Summaries:
' Module GeometryMath
'
' Function: GetLineIntersection, (+4 Overloads) IntersectionOf, (+2 Overloads) QuadrantRegion
'
' Enum QuadrantRegions
'
' LeftBottom, LeftTop, RightBottom, RightTop, XLeft
' XRight, YBottom, YTop
'
'
'
'
'
' Enum Intersection
'
' Containment, Intersection, None, Tangent
'
'
'
'
'
'
' /********************************************************************************/
#End Region
Imports System.Drawing
Imports System.Runtime.CompilerServices
Imports sys = System.Math
Namespace Imaging.Math2D
''' <summary>
''' https://stackoverflow.com/questions/30080/how-to-know-if-a-line-intersects-a-plane-in-c-basic-2d-geometry
'''
''' 与几何相关的辅助类
''' </summary>
Public Module GeometryMath
''' <summary>
''' 判断线段与多边形的关系
''' </summary>
''' <param name="line"></param>
''' <param name="polygon"></param>
''' <returns></returns>
'''
<Extension>
Public Function IntersectionOf(line As Line, polygon As Polygon) As Intersection
If polygon.Length = 0 Then
Return Intersection.None
End If
If polygon.Length = 1 Then
Return IntersectionOf(polygon(0), line)
End If
Dim tangent As Boolean = False
For index As Integer = 0 To polygon.Length - 1
Dim index2 As Integer = (index + 1) Mod polygon.Length
Dim intersection As Intersection = IntersectionOf(line, New Line(polygon(index), polygon(index2)))
If intersection = Intersection.Intersection Then
Return intersection
End If
If intersection = Intersection.Tangent Then
tangent = True
End If
Next
Return If(tangent, Intersection.Tangent, IntersectionOf(line.P1, polygon))
End Function
''' <summary>
''' 判断点与多边形的关系
''' </summary>
''' <param name="point"></param>
''' <param name="polygon"></param>
''' <returns></returns>
Public Function IntersectionOf(point As PointF, polygon As Polygon) As Intersection
Select Case polygon.Length
Case 0
Return Intersection.None
Case 1
If polygon(0).X = point.X AndAlso polygon(0).Y = point.Y Then
Return Intersection.Tangent
Else
Return Intersection.None
End If
Case 2
Return IntersectionOf(point, New Line(polygon(0), polygon(1)))
End Select
Dim counter As Integer = 0
Dim i As Integer
Dim p1 As PointF
Dim n As Integer = polygon.Length
p1 = polygon(0)
If point = p1 Then
Return Intersection.Tangent
End If
For i = 1 To n
Dim p2 As PointF = polygon(i Mod n)
If point = p2 Then
Return Intersection.Tangent
End If
If point.Y > sys.Min(p1.Y, p2.Y) Then
If point.Y <= Math.Max(p1.Y, p2.Y) Then
If point.X <= Math.Max(p1.X, p2.X) Then
If p1.Y <> p2.Y Then
Dim xinters As Double = (point.Y - p1.Y) * (p2.X - p1.X) / (p2.Y - p1.Y) + p1.X
If p1.X = p2.X OrElse point.X <= xinters Then
counter += 1
End If
End If
End If
End If
End If
p1 = p2
Next
Return If((counter Mod 2 = 1), Intersection.Containment, Intersection.None)
End Function
''' <summary>
''' 判断点与直线的关系
''' </summary>
''' <param name="point"></param>
''' <param name="line"></param>
''' <returns></returns>
Public Function IntersectionOf(point As PointF, line As Line) As Intersection
Dim bottomY As Single = sys.Min(line.Y1, line.Y2)
Dim topY As Single = Math.Max(line.Y1, line.Y2)
Dim heightIsRight As Boolean = point.Y >= bottomY AndAlso point.Y <= topY
'Vertical line, slope is divideByZero error!
If line.X1 = line.X2 Then
If point.X = line.X1 AndAlso heightIsRight Then
Return Intersection.Tangent
Else
Return Intersection.None
End If
End If
Dim slope As Single = (line.X2 - line.X1) / (line.Y2 - line.Y1)
Dim onLine As Boolean = (line.Y1 - point.Y) = (slope * (line.X1 - point.X))
If onLine AndAlso heightIsRight Then
Return Intersection.Tangent
Else
Return Intersection.None
End If
End Function
''' <summary>
''' 判断直线与直线的关系
''' </summary>
''' <param name="line1"></param>
''' <param name="line2"></param>
''' <param name="i">可以从这个参数取得交点</param>
''' <returns></returns>
'''
<Extension>
Public Function IntersectionOf(line1 As Line, line2 As Line, Optional ByRef i As PointF = Nothing) As Intersection
' Fail if either line segment is zero-length.
If line1.Length = 0R OrElse line2.Length = 0R Then
Return Intersection.None
End If
If (line1.X1 = line2.X1 AndAlso line1.Y1 = line2.Y1) OrElse
(line1.X1 = line2.X2 AndAlso line1.Y1 = line2.Y2) Then
i = line1.P1
Return Intersection.Intersection
ElseIf (line1.X2 = line2.X1 AndAlso line1.Y2 = line2.Y1) OrElse
(line1.X2 = line2.X2 AndAlso line1.Y2 = line2.Y2) Then
i = line1.P2
Return Intersection.Intersection
Else
Return GetLineIntersection(
line1.X1, line1.Y1, line1.X2, line1.Y2,
line2.X1, line2.Y1, line2.X2, line2.Y2,
i:=i
)
End If
End Function
''' <summary>
''' + [(<paramref name="AX"/>, <paramref name="AY"/>), (<paramref name="BX"/>, <paramref name="BY"/>)]
''' + [(<paramref name="CX"/>, <paramref name="CY"/>), (<paramref name="DX"/>, <paramref name="DY"/>)]
''' </summary>
''' <param name="AX!"></param>
''' <param name="AY!"></param>
''' <param name="BX!"></param>
''' <param name="BY!"></param>
''' <param name="CX!"></param>
''' <param name="CY!"></param>
''' <param name="DX!"></param>
''' <param name="DY!"></param>
''' <param name="i">可以从这个参数取得交点</param>
''' <returns></returns>
''' <remarks>
''' https://stackoverflow.com/questions/563198/how-do-you-detect-where-two-line-segments-intersect/565282#
''' </remarks>
Public Function GetLineIntersection(AX!, AY!, BX!, BY!, CX!, CY!, DX!, DY!, Optional ByRef i As PointF = Nothing) As Intersection
Dim s02_x As Single
Dim s02_y As Single
Dim s10_x As Single
Dim s10_y As Single
Dim s32_x As Single
Dim s32_y As Single
Dim s_numer As Single
Dim t_numer As Single
Dim denom As Single
Dim t As Single
s10_x = BX - AX
s10_y = BY - AY
s32_x = DX - CX
s32_y = DY - CY
denom = s10_x * s32_y - s32_x * s10_y
If denom = 0 Then
' Collinear(平行或共线)
Return Intersection.None
End If
Dim denomPositive As Boolean = denom > 0
s02_x = AX - CX
s02_y = AY - CY
s_numer = s10_x * s02_y - s10_y * s02_x
If (s_numer < 0) = denomPositive Then
' 参数是大于等亿且小于等亿的，分子分母必须同号且分子小于等于分毿
Return Intersection.None
End If
t_numer = s32_x * s02_y - s32_y * s02_x
If (t_numer < 0) = denomPositive Then
Return Intersection.None
End If
If ((s_numer > denom) = denomPositive) OrElse ((t_numer > denom) = denomPositive) Then
Return Intersection.None
End If
' Collision detected
t = t_numer / denom
i = New PointF With {
.X = AX + (t * s10_x),
.Y = AY + (t * s10_y)
}
Return Intersection.Intersection
End Function
''' <summary>
''' 获取角度所指向的象限位置
''' </summary>
''' <param name="degree"></param>
''' <returns></returns>
<Extension>
Public Function QuadrantRegion(degree As Double) As QuadrantRegions
If degree > 360 Then
degree = degree Mod 360
ElseIf degree < -360 Then
degree = degree Mod 360
End If
If (degree >= -90 AndAlso degree < 0) OrElse (degree >= 270 AndAlso degree < 360) Then
Return QuadrantRegions.RightTop
ElseIf (degree >= -180 AndAlso degree < -90) OrElse (degree >= 180 AndAlso degree < 270) Then
Return QuadrantRegions.LeftTop
ElseIf (degree >= -270 AndAlso degree < -180) OrElse (degree >= 90 AndAlso degree < 180) Then
Return QuadrantRegions.LeftBottom
Else
Return QuadrantRegions.RightBottom
End If
End Function
''' <summary>
''' 获取坐标点相对于原点<paramref name="origin"/>的象限位置
''' </summary>
''' <param name="origin"></param>
''' <param name="p"></param>
''' <returns></returns>
<Extension>
Public Function QuadrantRegion(origin As PointF, p As PointF) As QuadrantRegions
If p.X > origin.X AndAlso p.Y < origin.Y Then
Return QuadrantRegions.RightTop
ElseIf p.X = origin.X AndAlso p.Y < origin.Y Then
Return QuadrantRegions.YTop
ElseIf p.X < origin.X AndAlso p.Y < origin.Y Then
Return QuadrantRegions.LeftTop
ElseIf p.X < origin.X AndAlso p.Y = origin.Y Then
Return QuadrantRegions.XLeft
ElseIf p.X < origin.X AndAlso p.Y > origin.Y Then
Return QuadrantRegions.LeftBottom
ElseIf p.X = origin.X AndAlso p.Y > origin.Y Then
Return QuadrantRegions.YBottom
ElseIf p.X > origin.X AndAlso p.Y > origin.Y Then
Return QuadrantRegions.RightBottom
ElseIf p.X > origin.X AndAlso p.Y = origin.Y Then
Return QuadrantRegions.XRight
Else
Return QuadrantRegions.Origin
End If
End Function
End Module
''' <summary>
''' 请注意，视图上面的象限的位置和计算机之中的象限是反过来的
''' </summary>
Public Enum QuadrantRegions
''' <summary>
''' 重叠在一起
''' </summary>
Origin = 0
''' <summary>
''' quadrant 1 = 0,90 ~ -90,0 ~ 270,360
''' </summary>
RightTop
YTop
''' <summary>
''' quadrant 2 = 90,180 ~ -180,-90 ~ 180,270
''' </summary>
LeftTop
XLeft
''' <summary>
''' quadrant 3 = 180,270 ~ -270,-180 ~ 90,180
''' </summary>
LeftBottom
YBottom
''' <summary>
''' quadrant 4 = 270,360 ~ -270, -360 ~ 0, 90
''' </summary>
RightBottom
XRight
End Enum
''' <summary>
''' 几何体之间的关系类型
''' </summary>
Public Enum Intersection As Byte
None
''' <summary>
''' 正切
''' </summary>
Tangent
''' <summary>
''' 相交
''' </summary>
Intersection
''' <summary>
''' 包围
''' </summary>
Containment
End Enum
End Namespace