• Login
sketchucation logo sketchucation
  • Login
🤑 SketchPlus 1.3 | 44 Tools for $15 until June 20th Buy Now

Prism problem

Scheduled Pinned Locked Moved SketchUp Discussions
sketchup
38 Posts 14 Posters 2.8k Views 14 Watching
Loading More Posts
  • Oldest to Newest
  • Newest to Oldest
  • Most Votes
Reply
  • Reply as topic
Log in to reply
This topic has been deleted. Only users with topic management privileges can see it.
  • R Offline
    remus
    last edited by 26 May 2008, 00:18

    Good find jim.

    Still quite a way out though 😉

    http://farm4.static.flickr.com/3003/2522211423_ee5c428b5e_o.jpg

    I also tried rotating a copy of the base triangle in to place by the dihedral angle (accurate to 6 decimal places) and that is still quite a way out as well. about 0.7% if i remeber correctly.

    http://remusrendering.wordpress.com/

    1 Reply Last reply Reply Quote 0
    • G Offline
      Gaieus
      last edited by 26 May 2008, 05:54

      Gee Jim,

      That's indeed very simple! 😲

      Gai...

      1 Reply Last reply Reply Quote 0
      • W Offline
        Wo3Dan
        last edited by 26 May 2008, 09:13

        Unfortunately I have not found a solution for this problem in general (i.e. rotate/snap by pure construction), see attachment below.
        For special cases like the one presented here by fruitjelly (a tetrahedron) there always seem to be good workarounds. So next question: How would you solve the rotation in the attached model to get the one and only edge AB?
        (We had this discussion before about creating the perfect buckyball but that's also a special case)


        RotateSnapProblem.skp

        1 Reply Last reply Reply Quote 0
        • G Offline
          Gaieus
          last edited by 26 May 2008, 09:31

          Ah, Wodan,

          I remember this challange. I even have a "no-solution" version of this among my models at the WareHouse: http://sketchup.google.com/3dwarehouse/details?mid=8075be6a6da45be3d2f8fef8fa52eceb

          Actually the exact same problem as here...

          Gai...

          1 Reply Last reply Reply Quote 0
          • F Offline
            fruitjelly
            last edited by 26 May 2008, 15:09

            Jim's image so far best illustrates the easiest way to for that shape. Then again, if ultimately, we want a equilateral triangle with for example 1m on each side.... We have to use maths, such as pythagoras theorem, but the weird never ending figures simply will not produce an accurate shape.

            So do you guys think its ok to say that, as far as complicated geometry are concerned (especially with arcs and curves), sketchup ain't that useful when dealing with accuracy.

            Modeling this tetrahedron had been a real pain, but turns out the solution is a damn cube....

            1 Reply Last reply Reply Quote 0
            • J Offline
              juju
              last edited by 26 May 2008, 15:57

              It's a known fact that SU accuracy isn't the best around, but then again it isn't meant for creating geometry smaller than the feet of a dust mite.

              Save the Earth, it's the only planet with chocolate.

              1 Reply Last reply Reply Quote 0
              • A Offline
                Anssi
                last edited by 26 May 2008, 18:00

                @fruitjelly said:

                Then again, if ultimately, we want a equilateral triangle with for example 1m on each side.... We have to use maths...

                No we don't - we use the Tape measure tool. Make a triangle of any size, measure the side, and type the length you want, and press Enter. SU asks if you eant to resize the model, click OK, and you are done. If you have other things in your model that you don't want resized, group the triangle, and do the trick inside the group.

                Anssi

                securi adversus homines, securi adversus deos rem difficillimam adsecuti sunt, ut illis ne voto quidem opus esset

                1 Reply Last reply Reply Quote 0
                • R Offline
                  remus
                  last edited by 26 May 2008, 20:48

                  Even the cube method isnt entirely accurate, see my previous post.

                  http://remusrendering.wordpress.com/

                  1 Reply Last reply Reply Quote 0
                  • J Offline
                    jeff hammond
                    last edited by 26 May 2008, 21:26

                    @remus said:

                    Even the cube method isnt entirely accurate, see my previous post.

                    really? i did the cube method 3 times and it always worked out perfectly.. every edge was the same length.. or maybe i'm not understanding something?

                    dotdotdot

                    1 Reply Last reply Reply Quote 0
                    • R Offline
                      remus
                      last edited by 27 May 2008, 00:19

                      Hmmm, perhaps i made a mistake when i did it, i'll give it a go when i get home.

                      http://remusrendering.wordpress.com/

                      1 Reply Last reply Reply Quote 0
                      • V Offline
                        Voder Vocoder
                        last edited by 27 May 2008, 02:07

                        As long as we're looking things up on Wikipedia, we can see that it gives the dihedral (included angle between two adjacent faces) of a tetrahedron as 70.528779°. That gives us the following very simple construction:

                        http://saveimage.eu/showoriginal-35/tet.jpg

                        ~Voder

                        1 Reply Last reply Reply Quote 0
                        • J Offline
                          jeff hammond
                          last edited by 27 May 2008, 03:06

                          @voder vocoder said:

                          As long as we're looking things up on Wikipedia, we can see that it gives the dihedral (included angle between two adjacent faces) of a tetrahedron as 70.528779°.

                          i think the challenge is to build the shape entirely using sketchup tools and locks.. the cube method makes this possible.. your solution uses math (albeit you went straight for the answer but 70.52....deg is a solution for an equation)..
                          here's an easy method for drawing an equilateral triangle without entering any numbers... [edit] - using this same method should work for for the entire shape but i'm having weird snap to problems.. i'll mess around with it tomorrow.. goodnight..


                          triangle.skp

                          dotdotdot

                          1 Reply Last reply Reply Quote 0
                          • R Offline
                            remus
                            last edited by 27 May 2008, 10:29

                            I must have been doing something weird when i tried that cube method originally, works like a charm now.

                            http://remusrendering.wordpress.com/

                            1 Reply Last reply Reply Quote 0
                            • W Offline
                              Wo3Dan
                              last edited by 27 May 2008, 15:59

                              @remus said:

                              I must have been doing something weird when i tried that cube method originally, works like a charm now.

                              Okay Remus, a beer or two now for you or anyone else with %(#FF0000)[a correct method 💭 with only SU, no math, to solve the problem attached to my previous post. No trial and error though,] I did that already.

                              1 Reply Last reply Reply Quote 0
                              • V Offline
                                Voder Vocoder
                                last edited by 27 May 2008, 17:23

                                Wo3Dan, by what means did you place the guide point? What do you mean by "this could be endpoint A"?

                                ~Voder

                                1 Reply Last reply Reply Quote 0
                                • B Offline
                                  Bep
                                  last edited by 27 May 2008, 19:29

                                  Jims wikipedia way to contruct the piramide. 👍construct piramide.skp

                                  greeting,

                                  Bep van Malde

                                  "History is written by the winners"

                                  1 Reply Last reply Reply Quote 0
                                  • W Offline
                                    Wo3Dan
                                    last edited by 27 May 2008, 19:37

                                    @voder vocoder said:

                                    Wo3Dan, by what means did you place the guide point? What do you mean by "this could be endpoint A"?

                                    ~Voder

                                    Voder, interested in the beer, right?!! 👊
                                    I just placed a guidepoint (A’) on the vertical line, measured A’B and moved A’ up and/or down till I got the right length AB= 2102,833625??? mm From now on A’ is called A.
                                    So this was done by trial and error, so to speak. And A is “only” accurate 6 decimals. Thereby it could be THE point A, the one I'm after.

                                    I want the red and yellow plane dimensions unchanged after rotation while they now have a common edge length AB=2102,833625xxx mm

                                    But to be honest, I’m not really interested in being this precise. What I’m after is a decent
                                    way to do a rotation/snap in any situation, something SU unfortunately seems to lack.
                                    So a rotate/snap solely for the reason of better/easier 3D constructing.
                                    Not everything is as regular as a tetrahedron.

                                    Wo3Dan

                                    1 Reply Last reply Reply Quote 0
                                    • J Offline
                                      jeff hammond
                                      last edited by 27 May 2008, 20:13

                                      @unknownuser said:

                                      But to be honest, I’m not really interested in being this precise.

                                      if you don't need super precision, you can use a heavily divided radius and it will get you pretty damn close if not right on the money..
                                      2000 segments per circle here and the radii do in fact intersect..


                                      RotateSnapProblem_jh.skp

                                      dotdotdot

                                      1 Reply Last reply Reply Quote 0
                                      • V Offline
                                        Voder Vocoder
                                        last edited by 27 May 2008, 22:16

                                        @wo3dan said:

                                        Not everything is as regular as a tetrahedron.

                                        True, including me, I'm afraid. But that's for a different forum.

                                        @unknownuser said:

                                        if you don't need super precision, you can use a heavily divided radius and it will get you pretty damn close if not right on the money.
                                        2000 segments per circle here and the radii do in fact intersect.

                                        Jeff, I have taken your previous admonition to heart and agree that the purpose of these construction exercises is not just to get the job done by whatever means, but to work within the constraints of SU's tools and, by applying them in an ingenious and elegant manner, solve the construction problem. The tetrahedron-in-the-cube is such a solution, although no one here can take credit for it beyond finding it in Wikipedia. On the other hand, using a 2000-segment circle is not particularly elegant; rather, it's more of a brute force approach, wouldn't you agree?

                                        Wo3Dan's problem is indeed vexing.

                                        ~Voder

                                        1 Reply Last reply Reply Quote 0
                                        • V Offline
                                          Voder Vocoder
                                          last edited by 27 May 2008, 22:43

                                          Update: Acknowleding that it's really the same kind of brute force approach as the 2000-segment circle (and with a nod and smile to Jeff), dividing the vertical edge containing point A into 1000 segments yields fairly accurate results with the Rotate tool (although you have to Zoom way in to see the best fit). Rotate doesn't seem to have any problem with inferencing an endpoint to another endpoint, only to On Edge.

                                          ~Voder

                                          1 Reply Last reply Reply Quote 0
                                          • 1
                                          • 2
                                          • 2 / 2
                                          2 / 2
                                          • First post
                                            24/38
                                            Last post
                                          Buy SketchPlus
                                          Buy SUbD
                                          Buy WrapR
                                          Buy eBook
                                          Buy Modelur
                                          Buy Vertex Tools
                                          Buy SketchCuisine
                                          Buy FormFonts

                                          Advertisement