[转帖]构建Delaunay三角网的VB源程序

yfy2003 · 发表于 2004-5-14 23:57

Dim tPoints As Integer 'Variable for total number of points (vertices) Private Sub Form_Load()
'Initiate total points to 1, using base 0 causes problems in the functions
tPoints = 1
End Sub Private Sub Picture1_MouseDown(Button As Integer, Shift As Integer, x As Single, y As Single) 'variable to hold how many triangles are created by the triangulate function
Dim HowMany As Integer

'Set Vertex coordinates where you clicked the pic box
Vertex(tPoints).x = x
Vertex(tPoints).y = y

'Perform Triangulation Function if there are more than 2 points
If tPoints > 2 Then
'Clear the Picture Box
Picture1.Cls
'Returns number of triangles created.
HowMany = Triangulate(tPoints)
Else
'Draw a circle where you clicked so it does something
Picture1.Circle (Vertex(tPoints).x, Vertex(tPoints).y), 50, vbBlack
End If

'Increment the total number of points
tPoints = tPoints + 1

'Display the total points and total triangles
lblPoints.Caption = "Points: " & tPoints
lblTris.Caption = "Triangles: " & HowMany

'Draw the created triangles
For i = 1 To HowMany
Picture1.Line (Vertex(Triangle(i).vv0).x, Vertex(Triangle(i).vv0).y)-(Vertex(Triangle(i).vv1).x, Vertex(Triangle(i).vv1).y)
Picture1.Line (Vertex(Triangle(i).vv1).x, Vertex(Triangle(i).vv1).y)-(Vertex(Triangle(i).vv2).x, Vertex(Triangle(i).vv2).y)
Picture1.Line (Vertex(Triangle(i).vv0).x, Vertex(Triangle(i).vv0).y)-(Vertex(Triangle(i).vv2).x, Vertex(Triangle(i).vv2).y)
Next i End Sub

yfy2003 · 发表于 2004-5-15 00:00

Option Explicit

'Points (Vertices)

ublic Type dVertex x As Long y As Long z As Long End Type

'Created Triangles, vv# are the vertex pointers

ublic Type dTriangle vv0 As Long vv1 As Long vv2 As Long End Type

'Set these as applicable

ublic Const MaxVertices = 500

ublic Const MaxTriangles = 1000

'Our points

ublic Vertex(MaxVertices) As dVertex

'Our Created Triangles

ublic Triangle(MaxTriangles) As dTriangle

Private Function InCircle(xp As Long, yp As Long, x1 As Long, y1 As Long, x2 As Long, y2 As Long, x3 As Long, y3 As Long, ByRef xc, ByRef yc, ByRef r) As Boolean 'Return TRUE if the point (xp,yp) lies inside the circumcircle 'made up by points (x1,y1) (x2,y2) (x3,y3) 'The circumcircle centre is returned in (xc,yc) and the radius r 'NOTE: A point on the edge is inside the circumcircle Dim eps As Double Dim m1 As Double Dim m2 As Double Dim mx1 As Double Dim mx2 As Double Dim my1 As Double Dim my2 As Double Dim dx As Double Dim dy As Double Dim rsqr As Double Dim drsqr As Double eps = 0.000001 InCircle = False If Abs(y1 - y2) < eps And Abs(y2 - y3) < eps Then MsgBox "INCIRCUM - F - Points are coincident !!" Exit Function End If If Abs(y2 - y1) < eps Then m2 = -(x3 - x2) / (y3 - y2) mx2 = (x2 + x3) / 2 my2 = (y2 + y3) / 2 xc = (x2 + x1) / 2 yc = m2 * (xc - mx2) + my2 ElseIf Abs(y3 - y2) < eps Then m1 = -(x2 - x1) / (y2 - y1) mx1 = (x1 + x2) / 2 my1 = (y1 + y2) / 2 xc = (x3 + x2) / 2 yc = m1 * (xc - mx1) + my1 Else m1 = -(x2 - x1) / (y2 - y1) m2 = -(x3 - x2) / (y3 - y2) mx1 = (x1 + x2) / 2 mx2 = (x2 + x3) / 2 my1 = (y1 + y2) / 2 my2 = (y2 + y3) / 2 xc = (m1 * mx1 - m2 * mx2 + my2 - my1) / (m1 - m2) yc = m1 * (xc - mx1) + my1 End If dx = x2 - xc dy = y2 - yc rsqr = dx * dx + dy * dy r = Sqr(rsqr) dx = xp - xc dy = yp - yc drsqr = dx * dx + dy * dy If drsqr <= rsqr Then InCircle = True End Function

rivate Function WhichSide(xp As Long, yp As Long, x1 As Long, y1 As Long, x2 As Long, y2 As Long) As Integer 'Determines which side of a line the point (xp,yp) lies. 'The line goes from (x1,y1) to (x2,y2) 'Returns -1 for a point to the left ' 0 for a point on the line ' +1 for a point to the right Dim equation As Double equation = ((yp - y1) * (x2 - x1)) - ((y2 - y1) * (xp - x1)) If equation > 0 Then WhichSide = -1 ElseIf equation = 0 Then WhichSide = 0 Else WhichSide = 1 End If

End Function

yfy2003 · 发表于 2004-5-15 00:02

Public Function Triangulate(nvert As Integer) As Integer
'Takes as input NVERT vertices in arrays Vertex()
'Returned is a list of NTRI triangular faces in the array
'Triangle(). These triangles are arranged in clockwise order.

Dim Complete(MaxTriangles) As Boolean
Dim Edges(2, MaxTriangles * 3) As Long
Dim Nedge As Long

'For Super Triangle
Dim xmin As Long
Dim xmax As Long
Dim ymin As Long
Dim ymax As Long
Dim xmid As Long
Dim ymid As Long
Dim dx As Double
Dim dy As Double
Dim dmax As Double

'General Variables
Dim i As Integer
Dim j As Integer
Dim k As Integer
Dim ntri As Integer
Dim xc As Double
Dim yc As Double
Dim r As Double
Dim inc As Boolean

'Find the maximum and minimum vertex bounds.
'This is to allow calculation of the bounding triangle
xmin = Vertex(1).x
ymin = Vertex(1).y
xmax = xmin
ymax = ymin
For i = 2 To nvert
If Vertex(i).x < xmin Then xmin = Vertex(i).x
If Vertex(i).x > xmax Then xmax = Vertex(i).x
If Vertex(i).y < ymin Then ymin = Vertex(i).y
If Vertex(i).y > ymax Then ymax = Vertex(i).y
Next i
dx = xmax - xmin
dy = ymax - ymin
If dx > dy Then
dmax = dx
Else
dmax = dy
End If
xmid = (xmax + xmin) / 2
ymid = (ymax + ymin) / 2

'Set up the supertriangle
'This is a triangle which encompasses all the sample points.
'The supertriangle coordinates are added to the end of the
'vertex list. The supertriangle is the first triangle in
'the triangle list.

Vertex(nvert + 1).x = xmid - 2 * dmax
Vertex(nvert + 1).y = ymid - dmax
Vertex(nvert + 2).x = xmid
Vertex(nvert + 2).y = ymid + 2 * dmax
Vertex(nvert + 3).x = xmid + 2 * dmax
Vertex(nvert + 3).y = ymid - dmax
Triangle(1).vv0 = nvert + 1
Triangle(1).vv1 = nvert + 2
Triangle(1).vv2 = nvert + 3
Complete(1) = False
ntri = 1

'Include each point one at a time into the existing mesh
For i = 1 To nvert
Nedge = 0
'Set up the edge buffer.
'If the point (Vertex(i).x,Vertex(i).y) lies inside the circumcircle then the
'three edges of that triangle are added to the edge buffer.
j = 0
Do
j = j + 1
If Complete(j) <> True Then
inc = InCircle(Vertex(i).x, Vertex(i).y, Vertex(Triangle(j).vv0).x, Vertex(Triangle(j).vv0).y, Vertex(Triangle(j).vv1).x, Vertex(Triangle(j).vv1).y, Vertex(Triangle(j).vv2).x, Vertex(Triangle(j).vv2).y, xc, yc, r)
'Include this if points are sorted by X
'If (xc + r) < Vertex(i).x Then
'complete(j) = True
'Else
If inc Then
Edges(1, Nedge + 1) = Triangle(j).vv0
Edges(2, Nedge + 1) = Triangle(j).vv1
Edges(1, Nedge + 2) = Triangle(j).vv1
Edges(2, Nedge + 2) = Triangle(j).vv2
Edges(1, Nedge + 3) = Triangle(j).vv2
Edges(2, Nedge + 3) = Triangle(j).vv0
Nedge = Nedge + 3
Triangle(j).vv0 = Triangle(ntri).vv0
Triangle(j).vv1 = Triangle(ntri).vv1
Triangle(j).vv2 = Triangle(ntri).vv2
Complete(j) = Complete(ntri)
j = j - 1
ntri = ntri - 1
End If
'End If
End If
Loop While j < ntri

'Tag multiple edges
'Note: if all triangles are specified anticlockwise then all
'interior edges are opposite pointing in direction.
For j = 1 To Nedge - 1
If Not Edges(1, j) = 0 And Not Edges(2, j) = 0 Then
For k = j + 1 To Nedge
If Not Edges(1, k) = 0 And Not Edges(2, k) = 0 Then
If Edges(1, j) = Edges(2, k) Then
If Edges(2, j) = Edges(1, k) Then
Edges(1, j) = 0
Edges(2, j) = 0
Edges(1, k) = 0
Edges(2, k) = 0
End If
End If
End If
Next k
End If
Next j

'Form new triangles for the current point
'Skipping over any tagged edges.
'All edges are arranged in clockwise order.
For j = 1 To Nedge
If Not Edges(1, j) = 0 And Not Edges(2, j) = 0 Then
ntri = ntri + 1
Triangle(ntri).vv0 = Edges(1, j)
Triangle(ntri).vv1 = Edges(2, j)
Triangle(ntri).vv2 = i
Complete(ntri) = False
End If
Next j
Next i

'Remove triangles with supertriangle vertices
'These are triangles which have a vertex number greater than NVERT
i = 0
Do
i = i + 1
If Triangle(i).vv0 > nvert Or Triangle(i).vv1 > nvert Or Triangle(i).vv2 > nvert Then
Triangle(i).vv0 = Triangle(ntri).vv0
Triangle(i).vv1 = Triangle(ntri).vv1
Triangle(i).vv2 = Triangle(ntri).vv2
i = i - 1
ntri = ntri - 1
End If
Loop While i < ntri

Triangulate = ntri
End Function

yfy2003 · 发表于 2004-5-15 00:05

原程序下载:

莫名 · 发表于 2004-5-18 13:04

好东西！

myfreemind · 发表于 2004-5-18 23:56

Y兄继续~~：）

yeats · 发表于 2004-5-27 10:11

太好了！

不知道怎么来感谢楼主

quanguang · 发表于 2004-6-8 01:01

谢谢，楼主真是大好人！！楼主有什么需要帮忙的，尽管问，小弟一定尽力而为

z954134 · 发表于 2004-7-16 15:48

感谢啊

lmh · 发表于 2004-10-28 13:12

无私的人!好东西!

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[转帖]构建Delaunay三角网的VB源程序

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