### Thursday, January 27, 2005

## Going Off on a Tangent

Platform: AutoCAD 2004

Download: DrawInsideTangent.zip

I recently had a problem where I needed to find the inside tangent points between two circles. See the image to the right for clarity. I knew where the two centers were (X and Y) and I knew the radius of both circles...but how to find the tangents. The other problem I had was that I needed a routine that was flexible enough to handle a wide range of values, point X and point Y can vary in position and the two radii can vary. The only thing I knew for sure was that point Y was below point X.

The AutoCAD API didn't have much to help me out so I headed to the web in search of an answer. There was one very descriptive article on how to solve this problem but the solution was written in C++ and was simply too complex to be ported to VB.

In the end a co-worker pointed me down the right path (thanks Mike!). Take a look at the code below; if you have any questions after trying it out, let me know.

Public Const PI = 3.14159265358979 ' 3.1415926535897932384626433832795 or atn(1.0)*4

Public Sub DrawTangent()

Dim objLine As AcadLine

Dim objArc As AcadArc

Dim pt1(0 To 2) As Double

Dim pt2(0 To 2) As Double

Dim pt3 As Variant

Dim pt4 As Variant

Dim rad1 As Double

Dim rad2 As Double

Dim dblLength As Double

Dim dblOffset As Double

Dim dblValue As Double

Dim dblAngle As Double

Dim dblTanAngle As Double

Dim dblStartAngle As Double

' Center of first circle

pt1(0) = 0#

pt1(1) = 0#

' Center of second circle

pt2(0) = 30#

pt2(1) = -3#

' Radius of first circle

rad1 = 10#

' Radius of second circle

rad2 = 1.5

' Distance between two centers (hypotenuse of triangle)

dblLength = GetDistance(pt1, pt2)

' Add both radii (opposite length of triangle)

dblOffset = rad1 + rad2

' Length of the adjacent side of the triangle between centers

dblValue = Sqr((dblLength ^ 2) - (dblOffset ^ 2))

' Angle between hypotenuse and adjacent side

dblTanAngle = Atn(dblOffset / dblValue)

' Add hypotenuse side of triangle

Set objLine = ThisDrawing.ModelSpace.AddLine(pt1, pt2)

' Angle of hypotenuse from zero

dblStartAngle = ThisDrawing.Utility.AngleFromXAxis(pt1, pt2)

' Angle of adjacent from zero

If pt2(1) >= pt1(0) Then

dblAngle = (360# * (PI / 180#)) - Abs(dblStartAngle - dblTanAngle)

Else

dblAngle = dblStartAngle - dblTanAngle

End If

' Find end point of adjacent side

pt3 = ThisDrawing.Utility.PolarPoint(pt1, dblAngle, dblValue)

' Add adjacent side of triangle

Set objLine = ThisDrawing.ModelSpace.AddLine(pt1, pt3)

' Add opposite side of triangle

Set objLine = ThisDrawing.ModelSpace.AddLine(pt3, pt2)

' Angle from zero to first tangent

dblAngle = dblAngle + (90# * (PI / 180#))

' Start of infeed angle

pt3 = ThisDrawing.Utility.PolarPoint(pt1, dblAngle, rad1 + rad2)

' Add start arc

Set objArc = ThisDrawing.ModelSpace.AddArc(pt1, rad1 + rad2, dblAngle, 90# * (PI / 180#))

' Start of end angle

pt4 = ThisDrawing.Utility.PolarPoint(pt2, dblAngle + (180# * (PI / 180#)), rad2)

' Add end arc

Set objArc = ThisDrawing.ModelSpace.AddArc(pt2, rad2, dblAngle + (180# * (PI / 180#)), 270# * (PI / 180#))

' Add line between arcs

Set objLine = ThisDrawing.ModelSpace.AddLine(pt3, pt4)

End Sub

You'll also need the "GetDistance" function. It calculates the distance between two points in all three axis of AutoCAD space.

Public Function GetDistance(distPnt1 As Variant, distPnt2 As Variant) As Double

Dim Xval As Double

Dim Yval As Double

Dim Zval As Double

Xval = distPnt1(0) - distPnt2(0) 'Difference between x values

Yval = distPnt1(1) - distPnt2(1) 'Difference between y values

Zval = distPnt1(2) - distPnt2(2) 'Difference between z values

' Calc distance using Pythagorean Theorum

GetDistance = Sqr((Sqr((Xval ^ 2) + (Yval ^ 2)) ^ 2) + (Zval ^ 2))

End Function

Try copying both functions into VBA and run the "DrawTangent" routine you should see two arcs with a perfect tangent between them. It also draws the triangle we needed to calculate the tangent points. If you need to draw tangents in other directions, the angles will have to be modified to suit but the theory above will work for any two circles as long as they don't overlap.

Download: DrawInsideTangent.zip

I recently had a problem where I needed to find the inside tangent points between two circles. See the image to the right for clarity. I knew where the two centers were (X and Y) and I knew the radius of both circles...but how to find the tangents. The other problem I had was that I needed a routine that was flexible enough to handle a wide range of values, point X and point Y can vary in position and the two radii can vary. The only thing I knew for sure was that point Y was below point X.

The AutoCAD API didn't have much to help me out so I headed to the web in search of an answer. There was one very descriptive article on how to solve this problem but the solution was written in C++ and was simply too complex to be ported to VB.

In the end a co-worker pointed me down the right path (thanks Mike!). Take a look at the code below; if you have any questions after trying it out, let me know.

Public Const PI = 3.14159265358979 ' 3.1415926535897932384626433832795 or atn(1.0)*4

Public Sub DrawTangent()

Dim objLine As AcadLine

Dim objArc As AcadArc

Dim pt1(0 To 2) As Double

Dim pt2(0 To 2) As Double

Dim pt3 As Variant

Dim pt4 As Variant

Dim rad1 As Double

Dim rad2 As Double

Dim dblLength As Double

Dim dblOffset As Double

Dim dblValue As Double

Dim dblAngle As Double

Dim dblTanAngle As Double

Dim dblStartAngle As Double

' Center of first circle

pt1(0) = 0#

pt1(1) = 0#

' Center of second circle

pt2(0) = 30#

pt2(1) = -3#

' Radius of first circle

rad1 = 10#

' Radius of second circle

rad2 = 1.5

' Distance between two centers (hypotenuse of triangle)

dblLength = GetDistance(pt1, pt2)

' Add both radii (opposite length of triangle)

dblOffset = rad1 + rad2

' Length of the adjacent side of the triangle between centers

dblValue = Sqr((dblLength ^ 2) - (dblOffset ^ 2))

' Angle between hypotenuse and adjacent side

dblTanAngle = Atn(dblOffset / dblValue)

' Add hypotenuse side of triangle

Set objLine = ThisDrawing.ModelSpace.AddLine(pt1, pt2)

' Angle of hypotenuse from zero

dblStartAngle = ThisDrawing.Utility.AngleFromXAxis(pt1, pt2)

' Angle of adjacent from zero

If pt2(1) >= pt1(0) Then

dblAngle = (360# * (PI / 180#)) - Abs(dblStartAngle - dblTanAngle)

Else

dblAngle = dblStartAngle - dblTanAngle

End If

' Find end point of adjacent side

pt3 = ThisDrawing.Utility.PolarPoint(pt1, dblAngle, dblValue)

' Add adjacent side of triangle

Set objLine = ThisDrawing.ModelSpace.AddLine(pt1, pt3)

' Add opposite side of triangle

Set objLine = ThisDrawing.ModelSpace.AddLine(pt3, pt2)

' Angle from zero to first tangent

dblAngle = dblAngle + (90# * (PI / 180#))

' Start of infeed angle

pt3 = ThisDrawing.Utility.PolarPoint(pt1, dblAngle, rad1 + rad2)

' Add start arc

Set objArc = ThisDrawing.ModelSpace.AddArc(pt1, rad1 + rad2, dblAngle, 90# * (PI / 180#))

' Start of end angle

pt4 = ThisDrawing.Utility.PolarPoint(pt2, dblAngle + (180# * (PI / 180#)), rad2)

' Add end arc

Set objArc = ThisDrawing.ModelSpace.AddArc(pt2, rad2, dblAngle + (180# * (PI / 180#)), 270# * (PI / 180#))

' Add line between arcs

Set objLine = ThisDrawing.ModelSpace.AddLine(pt3, pt4)

End Sub

You'll also need the "GetDistance" function. It calculates the distance between two points in all three axis of AutoCAD space.

Public Function GetDistance(distPnt1 As Variant, distPnt2 As Variant) As Double

Dim Xval As Double

Dim Yval As Double

Dim Zval As Double

Xval = distPnt1(0) - distPnt2(0) 'Difference between x values

Yval = distPnt1(1) - distPnt2(1) 'Difference between y values

Zval = distPnt1(2) - distPnt2(2) 'Difference between z values

' Calc distance using Pythagorean Theorum

GetDistance = Sqr((Sqr((Xval ^ 2) + (Yval ^ 2)) ^ 2) + (Zval ^ 2))

End Function

Try copying both functions into VBA and run the "DrawTangent" routine you should see two arcs with a perfect tangent between them. It also draws the triangle we needed to calculate the tangent points. If you need to draw tangents in other directions, the angles will have to be modified to suit but the theory above will work for any two circles as long as they don't overlap.

### Wednesday, January 26, 2005

## Welcome

Hello to new friends and old. This is my second attempt at a blog focusing on creating custom code for AutoCAD and Inventor by Autodesk. For the next little while, most articles will focus on AutoCAD, as that is what I'm currently working in. If things go well, I'll be joining the ADN later this year and then the real fun will begin. (insert evil laughter here). If you have any bits of code you're having trouble with or ideas for posts, let me know. I'll try to post something every couple of days (or more) but no guarantees.

And now a bit about me: I've been working in drafting/CAD since 1998. Like a few others here, I started out on paper and moved to CAD as quickly as possible. A few systems I've worked with over the years are AutoCAD (r9 to current), SolidWorks, Inventor, ACAD MDT, ACAD Mechanical, ACAD Electrical, ADH800 (no mouse required, don't even ask!), VisionAEL, ME10 and One Space Designer.

Despite the list above, my true love is programming... still not sure why I went for Mech. Eng. in college. I program in numerous languages (16 last time I counted) and have been customizing and extending various CAD systems for more than a decade.

I've worked in a wide range of industries including (but not limited to) automotive, beef processing, telecommunications, safe/vault manufacturing and was even an AE for an Autodesk VAR for a stint before I was enticed back into the real world to automate conveyor systems.

If anyone is interested, I am available for after-hours freelance work/training/etc.

And now a bit about me: I've been working in drafting/CAD since 1998. Like a few others here, I started out on paper and moved to CAD as quickly as possible. A few systems I've worked with over the years are AutoCAD (r9 to current), SolidWorks, Inventor, ACAD MDT, ACAD Mechanical, ACAD Electrical, ADH800 (no mouse required, don't even ask!), VisionAEL, ME10 and One Space Designer.

Despite the list above, my true love is programming... still not sure why I went for Mech. Eng. in college. I program in numerous languages (16 last time I counted) and have been customizing and extending various CAD systems for more than a decade.

I've worked in a wide range of industries including (but not limited to) automotive, beef processing, telecommunications, safe/vault manufacturing and was even an AE for an Autodesk VAR for a stint before I was enticed back into the real world to automate conveyor systems.

If anyone is interested, I am available for after-hours freelance work/training/etc.