Unfortunately, this is something I don't understand very well -- I have no mathematical or engineering basis to analyze a structure and determine if it would be rigid. However, I have some ideas, and I used these to guide my own design of the Desert Nose. Since I haven't actually built the nose yet, I don't know if these concepts are correct or not.

• Convex three-dimensional curves do not need extra bracing.

• Concave three dimensional curves require extra bracing in the form of extra triangles to form a truss which is rigid and extends from one edge of the concavity to the other.

• Avoid long struts unless they are always under tension (not compression). Long struts under compression are more likely to bend. "Long" for 3/4" conduit begins at about 4'.

• There can only be triangles in the structure. Any other shape will create a weakness. The nostrils in the Desert Nose are such weaknesses. That was one reason for the strong column between the nostrils. Still, vertex 8 is liable to be forced toward the central column when weight is applied down on vertex 14. It might be applied down on vertex 14 as a result of weight being distributed through the entire nose tip structure.

• The more struts connecting at the same vertex, the harder it will be to make that vertex actually be solid. The Desert Nose has one vertex, dubbed the "Booger Joint" (vertex 23) at which 14 struts meet. Will a carriage bolt be adequate for this joint?

• Struts must always be straight, but you can build your model with some curves in the struts for your own convenience. When you measure your model, you're going to ignore everything except the positions of the verticies.

• Forces will transfer through your structure and focus on the area(s) where there is a weakness. To repair a weakness, add more struts. These must form new triangles, and you must add enough to form pyramids to reinforce the weakness.

I recommend building a model and applying some pressure to various places to see how the model flexes. Better to break the model than build something full-size which is going to break.

I built my model of the Desert Nose by soldering copper ground wire together. Another approach would be to use 1/8" dowels and 1/8" inside diameter vinyl tubing. The latter material is better suited to showing the effects of stress. The copper model is more durable.

A model could start as a real-world object, like a shoe. (There was an old woman who lived in a shoe...".) You could draw some dots on the shoe with a grease pencil or some safe kind of marker (is there such a thing for shoes?). You'd just place the dot's in a way that you can draw triangles with the dots as the verticies.

Then you could take an initial set of measurements from the dots. You'd have to secure some graph paper under the shoe and measure the X, Y and Z coordinates of each dot. You'd want to label each dot (vertex) and each line connecting them (each strut).

You could build a model from just that, but you might want to apply the above concepts first and anticipate where you'll need some trusswork to stupport a convex curve, such as the one over the top of the foot. You could use a new color pen or grease pencil to represent vertexes "inside" the shoe as opposed to on its skin, and draw the struts which connect to these interior trusswork vertexes in the same or other colors. Then you can estimate coordinates for these interior vertices, since you can't actually measure them.

One of the important considerations when laying out the dots (verticies) for your model is how big the final structure will be. You want to lay things out so that the final struts are between 1 and 4 feet long, with the majority in the 2 to 3 foot range. You can use longer struts but your project will be weaker and more pointy and flat -- less curvy. Shorter struts make a project more curvy, but it increases the weight and effort needed to build the structure and its parts. It takes a lot more shorter struts to build a structure than longer struts.

So, if you were scaling a boot 1' tall to be a 10' tall boot structure, then a 1" strut drawn on the would be 1/12 * 10 = 0.8 feet (9.6") -- too short. A 2" strut would be 1' 7.2" -- that would be OK. But take a look at how the structure might look with straight lines between the vertecies. Again, shorter struts make the structure look more curved, longer struts make it look more angular and flat.

If you need a door you can plan for three struts which are at least 3' in length to meet in a triangle. You can get in through a hole that large. A larger hole will be easier to get in through. If you want a non-triangular door then you'll need some trusswork behind it to support wherever there aren't exclusively triangles.

You might want to position some of the vetecies strategically. For example, the Desert Nose has an interior deck. I adjusted all the vertexes so they were all at the same height (Z value) so the deck would be flat.

If you wanted to build a shelf you could position two neighbor vertexes at the same Z value and use them as anchor points for the table.

If you needed mounting points for speakers or lights or to hold a sign, etc. and you can anticpate where those locations are, rearrange your struts so there are vertexes there. Then use longer carriage bolts at those vertexes. Let the longer threaded end point inside if you need an inside connection, or outside if you need an outside connection.

The idea is that within reason, you can move struts around the surface of your model and it won't drastically affect the shape of the model or the strength of the final structure, as long as struts don't get too long or short and as long as there is adequate trusswork for convex curves.