Update User Stories
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@ -9,3 +9,13 @@ Brief summaries of activities one might try/problems one might solve with dyna3.
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- A slightly farfetched one: put three or more "pins" in a plane (or in space). Constrain an additional point in the plane as the "pencil" such that the length of a string looped around the pins and the pencil in some way (there are multiple configurations) has constant length. Find the locus of positions of the pencil. (Generalizations of ellipse-drawing; note James Clerk Maxwell considered these loci in his youth and apparently wrote an article or report of some kind on his findings.)
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- Somewhat less farfetched, another natural generalization of ellipse-drawing: find the locus of a point P such that the surface area of tetrahedron $ABCP$ is a constant. (In the plane, an ellipse is the locus of a point $P$ such that the perimeter of $ABP$ is constant.)
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A thing I am trying/needing to do right now:
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Understand the configuration space of http://levskaya.github.io/polyhedronisme/?recipe=aaaD but with: each trapezoid a congruent rectangle and each pentagon constrained to be regular (and hence planar) and each rhombus constrained to be planar. In particular, is it realizable with an arbitrary aspect ratio of rectangle, and if so, for a given ratio, what similarity type of rhombus arises? Actually, in real life, the rectangles will each be a face of a box, so bonus points if we can actually make them part of a rectangular solid.
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I am trying out solvespace to understand how things go in that setting for doing this. So here's something of a log of my efforts, in case that provides useful background for Dyna3 work.
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- I decided to start with the rectangular panels, as they are individually rigid, and connecting them with the appropriate constraints creates the entire polyhedron.
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- It is very easy to draw one such a rectangle in SolveSpace: activate the current planar sketch (actually in starts activated in a new drawing), use the Rectangle tool, and then constrain the W and H to the desired dimensions. And the bonus points come easily, too: you can just hit the extrude button and it makes a rectangular solid with one face being the rectangle, and then constrain the third dimension of that solid.
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- Now I just want to make more boxes. Unfortunately, it does not seem that SolveSpace has a "free copy" operation that will let me just duplicate this box, except with the ability to rotate/translate arbitrarily in space as a rigid body. However, there does appear to be a contributed branch that adds such an operation, so I am going to try to compile from source and then go onto that branch.
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