Defining points in 3d space

Hi guys, I can hear the groans when I mention geometry, but how else are you gonna solve this problem

Take 3 sides of a triangle with sides say 3.5,4.5,5.5 unit lengths.

Try to draw that in su and most know, you cant, because of the limitations of segmented arcs when trying intersect the sides. Even using the highest resolution 960segment per circle it wont join properly with accurate sides.

You can’t for example create a polygon with a defined side length. Try drawing a pentagon with unit side length

AFAIK this limitation is the same for 2016 and this is not a criticism, its the nature of the beast.

Some years ago I put together the algebra equations to solve this problem (groans), intersection of 2 circles (2d) and 3 spheres (3d) and made it all work on excel. Complex and fiddly but just high school maths

So I punted this to the community asking for someone to help turn my equation written in simple pseudo code into a Ruby app for everyones’ benfit, but got no offers

I’m hoping in 2016, given the amount of clever extensions out there that someone will see the value of this little tool

As we all know, accuracy is essential in su, you can’t be near enough, its not good enough and erros left in your model have a habit of propagating and you cant get faces to fill properly. Trying to fix these minute errors in an advanced model retrospectively is a ball breaking task

So guys, any Ruby wizards willing to collaborate?

Robin

These may be of interest…

Skema Survey — Extension Warehouse

Didier Bur: Trilateration v1.1x — SketchUcation PluginStore

TIG: TrueTangents v3.0 — SketchUcation PluginStore

Good links, for 2d triangles but cant make a solid eg a pyramid let alone a dodecahedron made with pentagons

I did it by finding ways to draw lines with lengths made from irrational numbers eg 3/5^1/2 or 3/sqrt(5) in pseudocode

i havent tested these tools yet but 2mlw bw (bw? Buddha willing)

Cheers

Robin

This is history since SU2015. The ‘Pie’ tool allows for precise intersection to create your triangle.

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i haven’t got a pie tool, pls advise

You do have it if you are using SU2015 or SU2016. It’s in the Drawing toolbar.

Also in the Draw menu under Arcs.

Menu Draw > Arcs > Pie
Or the icon as one of the arc tools.

OK, I get it, thanks!

Sorry guys but the arc tool is the same old segmented circle and wont give the right point of intersection for a true circle and this is where you can be caught out. Note I have measured the true length of the sides, not the radius of the arc tool (3.5 and 4.5)

tried trilateration, but its buggy doesn’t work for me though I did find the manual eventually, uses cosine law and , if it worked, may not be accurate to 13 places?

TIG true tangents doesn’t do anything, no instructions

SUCCESS! After going thru the fiendishly difficult process of creating a Trimble account, I was finally able to download the Skema survey app

and it seems to work great simple to use and seems accurate AFAIK

the perfect tetrahedron. If anyone can tell me how to post a .skp file here I’ll be glad to share. (wonder why Trimble doesn’t want us sharing models?)

Each of the 6 sides is exactly 1.000000
It was done using Skema

If anyone is interested I’ll post details, but it involve constructing the height triangle (using Skema)

to get the height line then moving it to the centroid of the base. The rest is done by copy base and rotate (see the height line I made at the top of the pic

thanx to Geo for the recommendation

Enjoy

Robin

Use the Upload button in the message window

Anssi

I’ll try, i thought it was only for pixtetrahedron.skp (112.0 KB)

OMG, what a klutz, shows what OD-ing on SU does to your brain:grinning:

Thanx 10^6

Robin

You might also try the plugin for parametric regular polyhedra:
http://sketchucation.com/plugin/879-polyhedra

That draws the five regular Platonic solids, specified by either edge length or radius of enclosing sphere. You can edit the size subsequently as well.

Is this not one of the purposes of the 3DWarehouse?

2 Likes

[quote=“robint, post:10, topic:30797”]
TIG true tangents doesn’t do anything, no instructions
[/quote] That’s somewhat disingenuous…
You didn’t look very far, did you !?
http://sketchucation.com/pluginstore?pln=TrueTangents
Click on More Info… that sends you to:
http://sketchucation.com/forums/viewtopic.php?p=160780#p160780
which has lots of info on the first page and more in responses…
That first page also has a clear link to even more detail…
http://sketchucation.com/plugin/771-truetangents

What more do you need ?

2 Likes

Hre is link showing some of Paul Bourke’s work Starting on page five is on intersection of a line and sphere ( or circle) you should find helpful. http://paulbourke.net/geometry/circlesphere/

thanx Mac, that link has pages 8,9 which show the algebraic equations for the intersection of 2 spheres and gives a circle, then use intersection of 2 circles on that to get 2 +/- points in space for the point in space required from 3 vertices intersecting, qed.

I am sure I ought to be able to do this with the Skema tool, will revert

Robin

Hmm; I just clicked the link above, it does not show page# but when you try to print it shows 28 pages. The part I though you would find of interest is the line 3 d sphere part but was not expecting any action on your part just FYI. It was published in 1992 and can be useful for problems like you noted.