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Simple 2D shape speed challenge

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Do you gentlemen have jobs...or is it as for me, this forum is just more fun? wink.gif

Geometry "FUN"?? You would make Euclid turn in his grave! Gytis: The Harmony of the Spheres is a very, very spiritual matter, and not to be trifled with!


Besides which, if you're designing "product" rather than buildings, tangents to circles is a fundamental part of life. It's also something where the VW -sometimes-I'll-work-and-sometimes-I-won't tangent snaps are a real pain.


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To estimate your fillet radius, draw a 3 point arc between the circles which sort of looks tangent to both circles and read its radius in the OIP. Then in the fillet tool assign a fillet radius value close to your estimate and create the fillet. Adjust the fillet radius in the fillet tool and create new fillets until you get the look you are after. Or use Mike m Oz's method: draw a circle or arc that looks about right, drag it close and use constraints or parametric constraints to place it tangent to both. Trim.

It would be great if you could use parametric tangent constraints to keep the fillet tangent to both circles, and then move the arc center or change its radius in the OIP to adjust the fillet config. Unfortunately, VW moves the circles and the arc to keep everything tangent. Adding parametric distance constaint between the circles to keep them in place crashes VW when arc radius is adjusted (well, the beach ball of doom spun longer than my patience allowed). Locking the circles to keep them in place does not work either. VW dissallows changing radius of tangent constrained arc, and will not allow constraints on locked objects.

So where is the center of any tangent arc/fillet? Draw a bunch of fillets and note that chords of all these fillets are not parallel. They sort of fan out. Therefore, the centers of all possible fillets lie on a curve. Some smarty pants out there can give us a mathematical description of that curve (not me!), if it seems important to prelocate the center. Me, I'm just glad VW can calculate the fillets tangent to both circles.

And, yes please, could we get that tangent constraint and tangent arc tool fixed so we can make arcs tangent to objects at both ends during creation.


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Christiaan, try reading the instructions again - it really is quite simple. Your two circles are circles A and B. The fillet arc is circle C - as you apply the constraints circle C will move to match the constraint conditions.

Once you have the three circles constrained together you can adjust the size of circle C by dragging on its perimeter handle. Be warned though that it is now circle C which will stay still and circles A an B will both move.

I trust you do inform others in your office where you have obtained many of the answers to their questions from, and that you are not just using our goodwill for your persona gain.

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Christiaan, why sweat it? Let VW do the geometry. For another piddly 11 seconds, you can use the fillet tool, which automatically creates fillet arcs that are tangent to both circles. You can set the radius of the fillets to whatever value is within range. If you have other constraints, then maybe you'd have to go the hard way and construct a custom arc.

As pointed out, the 3 point arc tool can give you something approaching tangency at the intersection points, but will not be exact unless you are incredibly lucky.

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Christiaan - I think Pete wins hands down. The big question though is what you are going to reward him with? 50 Euros sound about right.

Christiaan's help to everyone on this forum gives him plenty of credit with me!

Islandmon, I believe that for two arcs to be mutually tangent, the two centers and the point of coincidence have to lie on a line. Your lower tangent point doesn't seem to meet that requirement.

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I've found the method of estimating the radius with a circle then 2 Fillets, Trim, Compose to be the quickest method. 26 seconds to be precise.

So thanks for everyone's input; it'll help with many other shapes too I'm sure.

By the way, does anyone know the answer to my query about the advantages and disadvantages of converting it into a polygon? One disadvantage is that you lose the snap centres of the circles.

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I can't for the life of me figure out what I'm doing wrong though. When I get to the point where I draw the arc it never meets the assumed centre line (see dotted line)??


It is because the center of the arc is only on your assumed center line when the radius of the arc is infinite. Notice you started with a line tangential to both circles. That is equivalent to an arc of infinite radius. When the radius is less than infinite, the center point of the arc falls to one side of your assumed center line, namely, it falls to the side of the smaller circle.

The path of all possible centers traces an hyperbola and one asymptote is the line you drew. The exception is when both circles are of equal radii, then the expected path of center points is vertical and bisects the line connecting the two closest points on the circles.

Plotting the family of possible curves is quite beautiful. Perhaps Islandmon will post a picture if I send him the scratch file I've been using.


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ej, thank you. You've made it look exceptional. The renderings in your gallery - even more so.


One thing that did not show up in the picture above are the markers along the green line that correspond to the centers of the displayed fillets. The centers of all possible fillets lie on the green line and the green line gets closer to the red asymptote as the fillet radius increases, but never crosses it.

In the file I sent ej the fillet centers were marked with Loci, which obviously did not print/render. I was expecting a screen shot, but I got a work of art. I really should have expected this, considering the source.

Thanks again, ej.


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