Logic with arcs (mini-challenge?)

jeff hammond

hey gruff.. your method does in fact work out to be accurate if you divide some of the arcs into 500 or so segments.. and actually, that's a really nice way to see it.. i like it .. i think it'd be better to do in layout or something that draws true arcs because snapping to intersections would be easier than hyper-divided segmented arcs in SU.

so cool, 2 different approaches now!

[hoping TIG adds the 3rd and final ]

jeff hammond

@gruff said:

Of course they also had filleting (Corner Curves) which could easily solve your problem in one step. All could create a fillet between two lines, arc and line, or two arcs.
In your case it would be between the left arc and the horizontal line at the bottom right.

that's the ruby request to TIG in the picture above.. the idea came from a cad program.

@unknownuser said:

All that said I wonder about your need for accuracy in this case. In the real world everything has a tolerance and not suprisingly when you start to build things over 6 to 10 feet your measuring tools start to throw their own errors into the mix.
For instance how accruate do you think a tape measure is? Sag, flex, temperature, material and other factors add to the issue. This is why in building construction an error of 1/8 inch is an everyday occurance.

the need for accuracy is more to do with adjoining pieces in SU rather than real world.. if i draw a piece that's almost correct and butt it with a piece that is correct, i end up with holes in surfaces that are basically impossible to fix.. so i have to draw the incorrect piece first and copy/move it around the drawing for the next few weeks and draw everything else with the same error just so the finished drawing will line up.. 1/128" errors in SU are the biggest pain because for one, they're very hard to detect and usually even harder to fix..

i know it's possible to draw it very accurately and easily so why not strive to do so?

as to real world tolerances, i deal with them everyday and it's no big deal.. tapes have errors sure.. or 7' on one tape isn't the same 7' on the other.. the lumber i work with can vary by 1/4" thickness etc.. foundations with dips in them.. moisture expansion/contraction working differently on the separate types of materials i use.. all of it.

that said, i definitely try not to compound the errors.. a small error on top of another small one can add up to something bigger than the sum of the two.. surely you can understand this and i think you'd agree that it's not the smartest thing in the world to make a bad drawing just because you know there will be some +/- on the site..

anyway -- i've finally arrived at a method for doing the drawing to 100% accuracy while being able to choose the radius of both arcs.. it's pretty simple to do and a definite hand/head moment considering how many times i've fought this in the past.. i'll draw up a little tut in a bit for anyone interested..

(btw, i build skateboard ramps if you're wondering what these curves are for.. there are 3-4 situations i use these convex/concave tangents for.. this ramp shows two of those situations)

jeff hammond

For anyone interested, i'm attaching a tutorial showing how i'll be doing this from now on. (well, unless TIG adds it to TrueTangents )

fwiw, it's a mismash of methods suggested by mac1 and gruff in this thread.. thanks dudes.

ARCS_TUT.skp

TIG

http://forums.sketchucation.com/viewtopic.php?p=160780#p160780 'filletarc' now added.

Adds radiused fillet helpers to a selected arc/circle and line/cline to a radius given in a dialog...

TIG

http://forums.sketchucation.com/viewtopic.php?p=192769#p192769 'tangentialarcs'

Doesn't quite do what your tutorial shows... it makes the tangential arcs from the arc/line selected... I'll do another version that is more a 'fillet' arc to line tool - you select an arc and a line, the tool asks for a radius in a dialog and it creates the center/tangent-points etc need to construct the arc fillet to suit... Watch this space...

Gruff

Jeff,

I can see the faceting of curves in Sketchup as being a big issue. It is to me as well.
My background is mechanical engineering and I have used many different CAD systems over the years. All of them used true arc and circles so this was never an issue.

Of course they also had filleting (Corner Curves) which could easily solve your problem in one step. All could create a fillet between two lines, arc and line, or two arcs.
In your case it would be between the left arc and the horizontal line at the bottom right.

All that said I wonder about your need for accuracy in this case. In the real world everything has a tolerance and not suprisingly when you start to build things over 6 to 10 feet your measuring tools start to throw their own errors into the mix.
For instance how accruate do you think a tape measure is? Sag, flex, temperature, material and other factors add to the issue. This is why in building construction an error of 1/8 inch is an everyday occurance.

Aerospace is the only industry I know of that has addressed the problem with any success.
They are starting to use a new technology called indoor GPS.
This uses infraRed lasers mounted around the ceiling with the receiver in a hand held measuring tool. The user takes hits on the object to be measured and the 3D coordinate data gathered is uploaded and overlaid on the original CAD model. Boeing developed it.