Fold up Equilateral Triangle to make Tetrahedron with arc tool and guideline

I confess to being a bit bemused here. This question seems to pertain to the philosophical aspects of computing in general and to have nothing to do with SketchUp per-se. That is, SketchUp does the same as essentially all other computer applications: it uses finite-precision binary representations of numbers.

@jimhami42 beat me to the post with more or less the same comment.

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Therefore: I can trust the accuracy of an arc segment inference point, in exactly the same way that I trust the accuracy of a GM edge inference point.

If this is so, the I don’t need to draw the internal rectangles of regular polyhedron to find there vertices. I can use the fold up arc method and obtain the same level floating point accuracy?

Jim

The broad answer is for any practical purpose, “yes”: trust (or distrust) everything about the same.

As always, the devil is in the details.

For example, the tetrahedron inset into a cube method taffgoch showed has the advantage that if you draw the cube aligned with the model axes, SketchUp can use the same (finite-precision) value for the lengths of all the sides. That is, it can copy the value instead of calculating anything. The value may be a finite-precision representation, but it is the same for all corners. Then when you draw diagonals to create the tetrahedron, you are just joining those cube vertices, again without SketchUp having to calculate anything. Note, however, that if you rotate the tetrahedron to align it with axes or rotate the cube, the vertex locations are run through transformation calculations that introduce finite-precision effects.

In contrast for some of the GM-based methods, as you draw a rectangle the inference engine continuously calculates the ratio of the lengths of the sides. When this finite-precision calculation comes close to the GM (also represented using finite-precision) the inference engine offers to snap to the GM. Unlike the tetrahedron in the cube, there are calculations going on that induce finite-precision errors. Neither the side ratio nor the GM is exact.

When you draw a circular arc, SketchUp captures the center point, normal vector, and radius. It then uses the circle formula to calculate the locations of the vertices for the edges representing the circle. Of course, with a circular arc you have to bear in mind that only the vertices are calculated to lie on the circle. Between them are straight edges that only approximate the circle. So, you have to be wary whether other drawing operations hit the circle at one of the vertices or somewhere on an edge. That’s why Dave swung an arc up to where the end landed on the vertical line instead of drawing a full circle and finding an intersection. The inferred location is a point that is simultaneously calculated to be on the line and on the mathematical circle.

Is the circle vertex calculation less precise than the rectangle GM ratio? It’s a more complex calculation, but you’d need a deep analysis such as described in the linked article to find out, and it would probably depend on the specific values involved. In the long run, unless you are OCD, not worth the effort.

I appreciate and agree with all the preceding discussion about theory and precision in SU.

Coming at it from another direction, if all you want to do practically is draw a regular Platonic solid quickly, I wrote a free plugin to do just that. It’s available both from the Sketchup Extension warehouse and the SketchUcation plugin store.

See SketchUp Plugins | PluginStore | SketchUcation or Extension | SketchUp Extension Warehouse

If you want to see more detail of how I set the parameters to use close to the maximum precision possible in SketchUp see the Documentation file on GitHub - polyhedra/DOCUMENTATION.md at master · johnwmcc/polyhedra · GitHub .

And if you want your finished model polyhedra to have thickness (as your uploaded image files suggest), and to dissect into faces with thickness, copy, paste in place, and then scale one of the shapes up (or down) about its centre (press Ctrl [Windows] or Option key [Mac] in the Scale tool) to get the wall thickness and external size you want.

Then turn on X-ray view (menu View/Faces/X-ray). Explode both polyhedra, delete all but one corresponding internal and external face, and draw lines from inner to outer vertices to make a solid single face. Then add locking bumps (looking here at your image for a model cube). Check that the model is solid, then export to STL, and 3D print.

John McC

A Dear Mountain Sages,

Where might you dwell?

In swirling snow topped mountains, far from the crowded streets of my neighborhood.

I hear your calls; yet the mystery of your knowledge remains just beyond my grasp.

I’m left to toil on my own: until I gather the courage to to summon your wisdom again.

Be in peace until then,
Working on Octohedron now : wish me luck
Jim