Share your Arc / Circle construction challenges

[Tom_P]

Many times my students fight with constructing Arcs and Circles with given constraints.
This is one of those little challenges - Do you have similar ones - please share them here.

The trapped Arc

Given:

• a horizontal Line.
• At the start of the Line a tangential Circle with R25 (D50)
  Searched:
  An Arc with R5 (green) that is tangent to the Circle and perpendicular to the line.
  (I will post 2 solutions later, if others don’t post them earlier)

looking forward to see your solutions - and other challenges. kind regards - tom

[Gijs (Gijs de Zwart)]

I’d do this:
trapped_arc.3dm (162.1 KB)

[Gijs (Gijs de Zwart)]

As for other arc/circle issues: you should be able to find many here

[Tom_P]

@Gijs

I’d do this:
trapped_arc.3dm (162.1 KB)

… great - different to mine.

[jim]

@Tom_P

At the start of the Line a Circle with R25 (D50)

Seems to me that there are an infinite number of solutions depending on what the phrase “At the start of the Line a Circle” means.
Did you mean the center of the circle is perpendicular to the line or will any 25 unit circle that touches the end of the line do?

[Helvetosaur]

• Offset circle 5 to the outside
• Circle r5 at the intersection of the line and the offset
• Trim what isn’t necessary (for me the fastest)

Or if you really want to draw the arc directly…

• Arc center, start, end
• Pick the intersection of the offset and line as center
• With Cen Osnap, hover over the circle so center snap is active, then Tab to set direction lock
• Come back to the r25 circle and pick the start point
• Snap to the line to finish

[maje90 (Riccardo Majewski)]

This one from the 4th post is interesting:

Curve between two points and a tangent curve

How about this case - I struggle to have ideas: [image] I want the black arc to use the start and end points of the purple curve, and have one tangent with the orange.

[vcruzdesigns (Vince)]

This is my solution:

• Circle via 2 pts to set the 5mm rad
• Line tangent to R25 circle and intersecting with center of R5 circle
• Rotate both circles such that the smaller circle’s center intersects with the horizontal line

Otherwise, I would have just used Pascal’s MoveToTangent script but it throws an error:

[Helvetosaur]

Here’s a variable GH solution based on what I posted above…

FilletCircle.gh (15.7 KB)

[Tom_P]

ok here is the collection of posted approaches - and 2 more:

draw dislocated and move

construct with mirror

construct with D30 or _offset D5

(posted by @Gijs and described by @Helvetosaur

draw dislocated and rotate

@vcruzdesigns approach

(@jim updated the initial description - sorry for being imprecise, the circle is tangent to the horizontal line)

Circle_Challenge_01_trappedArc.3dm (1.7 MB)

[adel.albloushi]

i like the offset d5 version, and it was among the first coming to mind as i saw your problem statement.

but there’s even the trigonometric version. SSA triangle, with S1 = 25, S2 = 25+5, A = pi/2

[adel.albloushi]

i think a quicker trig solution is
the distance of the d5 center from the line-circle intersection is given by:
(d25+d5) * sin ( arccos( d25 / (d25+d5) )

[ThomasE (Thomas Evans)]

1 fixed Circle + 2 constrained Circles along Lines.
Big Circle with thickness tangent to the 3 circles.

I thought it was a challenge until I modelled it in Rhino…
Anyway, it would be interesting to see it with Rhino Constraints feature.
cc @Joshua_Kennedy.