# Simple 2D shape speed challenge

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Someone in the office today asked me the best/easiest/fastest way to create this 2D shape. I have to say I was a little stumped (being that I've never actually dabbled much in drawing simple 2D shapes). I could make it, obviously, but I'm sure it wasn't in the best and quickest way.

So that's the challenge, what method would a VW guru use to create this polygon in the least number of steps?

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My 2?: First, start with the idea that shape wil be created along the x/y axes, then rotated later. Draw the two circles. Then draw the trapazoid that connects them. Then ADD SURFACE to make one big shape. Next, draw the ellipse (or giant cirlce) that defines the indented sides, place it properly (one copy on either side) then use tham as the CLIPPERS to CLIP SURFACE. Voila!

i agree with peter (mostly), but i would not add surface until after I had placed the two indented sides. That way you can use the snap to tagent to get the giant cicle parts in place.

1) When drawing the trapezoid, how do you know where to meet the circles? Presumably there's a relationship between the two circles, based on their diametres and their distance apart from one another, which tells you the ideal tangent point of each circle.

2) When drawing the giant circles what mode should be used and where do you click 1st, 2nd, etc.?

3) What if you want the indents to be less perfect than circles (i.e a polyline of some description). How would you make the whole polygon then?

57 seconds including rotation.

Oops, posts crossed over. To make the fillets non-arced is more challenging (I would use tangent constraint).

Edited by P Retondo

57 secs! Phew.

How are you drawing the fillet Pete? With the Arc tool?

Fillet tool (keyboard shortcut 7) with "leave other objects in place" mode. Click on one circle, then click on the next.

Ah, Fillet fillet. How did you decide what radius to use? I found I could use your method using the Arc tool too.

Christiaan, actually, the arc tool or tangent constraint has a bug, I think - when joining the arc to the 2nd circle the cursor hint says "tangent" when it isn't really at a tangent point (NNA take note!). I didn't have the geometry constraints obviously, but if you just want to get a notion of what will work I often use arc by three points to do a trial shape.

Okay I did it 46 seconds, as below.

My usual habit is to then convert it to a polygon, but I don't know why I have this habit. I noticed if I leave it as a polyline I can still snap to the centres of the circles, whereas you lose this ability once you convert it to a polygon. Are there any other advantages or disadvantages to keeping as a polyline?

The key to programming this shape is the matching of tangent angles with the angles of arc rotation.

( Note that the example directly above fails this test ).

Inserting a 3 point arc between the circles may look right but is not sufficient

as indicated by the need to "trim" away the circles instead of using the correct arc angles.

Programming this shape requires 2 tangent arcs and two lines of tangent.

Composing is the final step if closure & fill is required.

The key to programming this shape is the matching of tangent angles with the angles of arc rotation.

( Note that the example directly above fails this test ).

Yeah, agreed (that was my question 1 above).

Programming this shape requires 2 tangent arcs and two lines of tangent.

Can you elaborate on the process?

There isn't one correct curve - there are many curves that can be tangential to both initial circles. The only thing they will have in common is their centre will be on a line perpindicular to a straight line tangential to the two circles, and starting from its centre point.

You can do it this way:

- Switch on the Tangent Snap and draw a line that is tangential to both circles.

- From the centre point of this line draw a line perpindicular to it.

- Switch off the Tangent Snap.

- Pick a point on this line which you want to be the centre of your arc.

- Draw lines from this point to the centre points of each of the circles.

- Select the Arc Tool and set it to Two points and Centre mode.

- Draw the arc using the intersection points of the circles with the two lines from their centre points as the end points, and set the arc centre at the previously chosen arc centre point.

- Repeat for the other side.

- Then proceed as per Christiaan's post above.

You need to make a decision about the arc to get the 'correct' solution for what you want to do.

Thanks Mike. 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)??

Looks like my logic is wrong. I'll have to ponder on that one.

I have come up with another quicker solution though.

- Draw your two circles (A and B).

- Draw a circle © with the required radius you want for the arc.

- Select the Constrain Tangent constraint.

- Click on circle C and then on circle A.

- Click on circle C again and then on circle B.

- Use the Trim tool to remove the unwanted portion of circle C.

- Repeat the process for the other side.

- Use the Trim tool to remove the unwanted portions of circles A and B.

- Compose the four arcs.

The only issue with this method is that you need to decide up front what the radius is for the joining arc.

Looks like my logic is wrong. I'll have to ponder on that one.

I'm not much of a mathematician (in fact I'm not one at all), but it seems your problem lies in the fact that the circles have different diametres.

The diameters of the two circles doesn't have an impact as long as they are located such that a tangential connecting arc is possible. The only thing that matters is that the arc centre is located equidistant from both of the circles.

Bit academic anyway as the second method I posted solves the problem, and it is quick.

Christiaan,

I think the required norm (ie the line on which the centre if the "fillet" arc is) for the tangential line connecting the two circles is not the "centre norm" (or whatever you call it in English) but depends on the radius of the fillet. Or something like that.

TBit academic anyway as the second method I posted solves the problem, and it is quick.

I think the required norm for the tangential line connecting the two circles is not the "centre norm" but depends on the radius of the fillet. Or something like that.

Looks like it. Which logically means you can't find the two tangents without first knowing the radius of the fillet?

Yep.

Well that's just inconvenient.

No. That's geometry.

When I was at school I remember thinking geometry was like magic. Now it can just piss off.

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

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