The 2300 year old geometry primer begins with definitions for point, line and plane surface establishing these concepts which will be used virtually unchanged even in modern cad applications. A point has no parts, it says. Later geometers will add it only has position but no dimension. A line has only length, no width, only one dimension. A plane surface has both length and width, two dimensions. 17th century mathematicians added XYZ variables to locate position. Euclid constructed, stated (“I say that…”), and proved elementary facts of geometry by starting with the most basic usable definitions and with virtual or real tools of straightedge and compass, that only allowed lines and circles to be constructed, made a textbook of geometry theorems that all depend on previous constructions for the proof of their canonic accuracy. His very first theorem constructs an equilateral triangle, a triangle with all sides and all angles equal, from a single random line.

Euclid has been criticized by moderns because he included no previous definition, postulate or axiom that two circles overlapping intersect in a single point. I thought finding that intersection point would be the hardest part of programming it, but there is a dedicated method, Intersectwith, for nearly every autocad object which returns a single dimension array of x, y and z values for all intersections. Here I just choose the first one. I use a random number generator to create the seed line.

Sub prime_pr1() 'given lineAB call proposition1 Connect_Acad Dim ptA(0 To 2) As Double Dim ptB(0 To 2) As Double Dim Ax As Double, Ay As Double Dim Bx As Double, By As Double Ax = rnddbl(0, 10) Ay = rnddbl(0, 10) Bx = rnddbl(11, 20) By = rnddbl(0, 10) Call pt(ptA, Ax, Ay, 0) Call pt(ptB, Bx, By, 0) Call pr1(ptA, ptB) acadApp.Update End Sub Sub pr1(ptA() As Double, ptB() As Double) Dim lineAB As AcadLine, lineAC As AcadLine, lineBC As AcadLine Dim circD As AcadCircle, circE As AcadCircle Dim ptC(0 To 2) As Double Dim r As Double Dim intpts As Variant Set lineAB = acadDoc.ModelSpace.AddLine(ptA, ptB) r = distance(ptA, ptB) Set circD = acadDoc.ModelSpace.AddCircle(ptA, r) r = distance(ptB, ptA) Set circE = acadDoc.ModelSpace.AddCircle(ptB, r) intpts = circD.IntersectWith(circE, acExtendNone) Call intpts_eval(intpts) 'going to take positive y value 'keeps traditional illustrations upright If ptG1(1) > ptG2(1) Then ptC(0) = ptG1(0) ptC(1) = ptG1(1) ptC(2) = ptG1(2) Else ptC(0) = ptG2(0) ptC(1) = ptG2(1) ptC(2) = ptG2(2) End If Set lineAC = acadDoc.ModelSpace.AddLine(ptA, ptC) Set lineBC = acadDoc.ModelSpace.AddLine(ptB, ptC) End Sub

helper functions

Option Explicit Public num_int_pts As Integer Public ptG1(0 To 2) As Double Public ptG2(0 To 2) As Double 'to evaluate the output array of the Intersectwith method 'loads up to two points in a global variable 'the calling program has to decide which one to use 'the core loop here taken directly out of autocad vba help for Intersectwith method Sub intpts_eval(intpts As Variant) Dim i As Integer, j As Integer, k As Integer Dim str As String If VarType(intpts) <> vbEmpty Then For i = LBound(intpts) To UBound(intpts) str = "Intersection Point[" & k & "] is: " & intpts(j) & "," & intpts(j + 1) & "," & intpts(j + 2) Debug.Print str str = "" i = i + 2 j = j + 3 k = k + 1 Next End If Debug.Print LBound(intpts) Debug.Print UBound(intpts) 'global var num_int_pts = k Select Case k Case Is = 0 ptG1(0) = 0: ptG1(1) = 0: ptG1(2) = 0 ptG2(0) = 0: ptG2(1) = 0: ptG2(2) = 0 Case Is = 1 Call pt(ptG1, (intpts(0)), (intpts(1)), (intpts(2))) ptG2(0) = 0: ptG2(1) = 0: ptG2(2) = 0 Case Is = 2 Call pt(ptG1, (intpts(0)), (intpts(1)), (intpts(2))) Call pt(ptG2, (intpts(3)), (intpts(4)), (intpts(5))) Case Is > 2 MsgBox "thats a lot of points" End Select End Sub Sub pt(ByRef ptn() As Double, x As Double, y As Double, z As Double) ptn(0) = x: ptn(1) = y: ptn(2) = z End Sub Function rnddbl(upr As Double, lwr As Double) As Double Randomize rnddbl = CDbl((upr - lwr + 1) * Rnd + lwr) End Function ' straight out of autocad vba help ' Calculate distance between two points Function distance(sp As Variant, ep As Variant) As Double Dim x As Double Dim y As Double Dim z As Double x = sp(0) - ep(0) y = sp(1) - ep(1) z = sp(2) - ep(2) distance = Sqr((Sqr((x ^ 2) + (y ^ 2)) ^ 2) + (z ^ 2)) End Function