arc in VBA - any wizzkids out there ?

I'm trying to draw an arc using VBA. However, I DON'T know the arc's center point, nor the radius. I DO know the start angle, end angle and one point on the arc.

Does anyone know how to do this in VBA ??

Thanks a lot !!

Jan

 

Hi Jan,

You have insufficient information to define a unique arc. There are an
infinite number of arcs which pass through a point with the same start an
end angle.

--


Laurie Comerford
CADApps
www.cadapps.com.au

center point, nor the radius. I DO know the start angle, end angle and one
point on the arc.

 

Thanks for your reply, Laurie.
I didn't mention that I am trying to make a sort of fillet tool.
So I have two lines or plines or whatever, and a point.
Now I want to create an arc, that has the same angle as
the line at the start and endpoint.

Do you have any clue how to perform that trick ?

 

Hi,

This may not be acceptable, but simply buy Land Desktop. It has this
command built in.

I don't know a specific algorithm for this, but you could try iterating a
trial radius and using offsets of the lines, comparing the distance to the
intersection of the offset lines to the point.

--

Regards


Laurie Comerford
www.cadapps.com.au

 

Jan,

I hope you've got your Geometry/trig hat firmly affixed. I haven't worked
out the coding, but it should be simple enough.

The basics:

If you have an arc with 3 points on it, (2 ends and 1 point on the arc) the
center point and radius are fairly easy to find. It works out that if you
have 3 points on an arc, the lines perpendicular to the chords intersect at
the center point

Center point:

Given/assumptions: 3 points - I'll assume that by having the start angle,
you also have the start POINT. The same goes for the end POINT

Ax,y - Start angle point (4,4)

Bx,y - End angle point (1,1)

Cx,y - point on arc (1.5,3)

Px,y - Center point of arc

Find the midpoints and angles of the AC and BC chords

Mac = (4+1.5)/2,(4+3)/2 = 2.75,3.5

Mbc = (1+1.5)/2,(1+3)/2 = 1.25,2

Aac = atan((ay-cy)/(ax-cx)) = atan(1/2.5) = 0.380506 (radians) = 21.8014
(deg) Abc = atan((by-cy)/(bx-cx)) = atan(2/0.5) = 1.325828 (rad) = 75.96376
(deg) These angles are NOT absolute. Pay attention to your circle PERFORM
ANGLE REALITY CHECKS!!!!

The math will easily send you in the WRONG DIRECTION!!! And you may not know
until the end of the calcs.

Get the chord length between Mac and Mbc

Lacbc = sqrt(x^2+y^2) = sqrt((2.75-1.25)^2+(3.5-2)^2) = 2.1213

Determine Angle between Mbc and C

This is the angle with point C in the middle and segments CB and CA Abca =
125.838 deg. = 2.196287 (rad)- Note how the 21.8... + 75.9... Values don't
add up to the actual angle if laid out in acad. It has to do with the
movement through the 360deg section of the circle. The 75 deg value becomes
255.964 if reversed. Which equates to a closing angle of 104.036 + the
21.8014 to give the actual angle of 125.838. Rather confusing but mus be
delt with.

Now then, back to trig

Determine inside angles of the triangle defined by Point C, Mbc and Mac Ambc
= 30.964 deg - Had to use obtuse law of sines here due to large (>90) angle
at Point C Amac = 23.199 deg - Had to use obtuse law of sines here due to
large (>90) angle at Point C

So, the angle between the chord of Mbc and Mac and the line from Mbc to P is

180 - 90 (perpendicular) - 30.964 (inside) = 59.036 deg

The angle between the chord of Mbc and Mac and the line from Mac to P is
180 - 90 - 23.199 = 66.801 deg = 1.165897 rad

Next,

Solve for the length of the line from Mbc to P using law of sines Angle P =
180-59.036-66.801 = 54.163 (deg) = 0.945323 (rad) Leg length =
(2.1213*sin( 66.801))/sin(54.163) = 2.4051 Note: Actual degree angle is used
here rather than radian value Leg Mca to P =
(2.1213*sin(59.036))/sin(54.163) = 2.2438 Note: Actual degree angle is used
here rather than radian value

Finally,

Use the POLARPOINT vba function, feeding in

Starting point (Mbc) (1.25,2)

Angle (345.964) 6.038211 radians - derrived from Anglebc (75.964) and then
rotating right 90 deg - again, VALIDATE direction needed to be turned! Why
head off in the wrong direction Distance (2.4051)

This will return a vairant record with your center point.

I would do the same down the other leg to verify that your points agree
within some tolerance as a validity check.

The radius is a simple calc using the pythag therum for a right triangle to
solve for hyp. From P to A,B or C. Your choice

Sorry so messy but that's what it takes given your starting conditions.
Also, error check everywhere! I'm planning on pasting a function up due to
amount of error checking coding alone.

My email is correct if you want to further this conversation offline. I'll
save the labeled acad drawing for your reference and send it offline. It
should clear up a few questions.

Regards,

Thomas Homan

center point, nor the radius. I DO know the start angle, end angle and one
point on the arc.

 

Thomas, I'd love to see the ACAD file myself. Can you send it offline to
me? Jan's problem stuck with me, and I couldn't help plugging away on it
too.

Thanks,
James

 

Wow, Thomas.
I really will have to take a closer look at this one.
I didn't realize there was so much math / trig involved in solving my question. Although my math is quite all right I couldn't figure it out myself right away.

Thanks for your reply !! I will get into it over the weekend and see how it turns out in code.

 

it turns out in code.


Jan,
Please let us know how this problem goes for you, and if you still need help
on it.

James

 

James,

I haven't had time to try it out yet.
I'll post my findings asap.

Jan

 

Are you looking for the code, or the sample drawing representing the math?

Sorry for the long response, I had to go over to Italy for 3 weeks.

Regards,

Tom

 

The sketch, so I could re-read your explanation with it. I had tackled the
problem assuming I didn't know the tangent points of the fillet arc. I got
as far as solving a 4-th order polynomial (found long formulas for its roots
on Google), but then had to put it down. I haven't looked at it in a couple
weeks now. When I find some more free time I'll try to wrap it up and see
if I get any correct answers.

I hope your travel was for fun. I'm jealous.

James