Posted by Jerud Crandall on December 20, 2000 at 10:10:28:In Reply to: We are having some trouble posted by shane on December 20, 2000 at 06:05:57:
Shane:
Watch the post from a few days ago ("Help - Need 3D Geodesic Dome House Model") regarding geodesic issues. It sounds like you're having the very same problem Tom and i are (except i'm not working against an Xmas deadline 8). Mike Wheeler has posted one response and it may help you out, although it's not working for me at this moment (which may or may not be due to my own errors). Hopefully this can be cleared up soon enough to help you out.
You'd probably like a backup plan though. Okay, here it is, but you're not going to like it. Since you say you're only acting on one roof panel (or at worst, a few of them), this is feasible, but since i'm trying to make a whole dome, i'm not willing to do these calculations for each of my triangles!
1) Select the triangle panel you're interested in. Might help to hide everything but it, but not necessary. You will want to leave this triangle in place until the very end, because you'll want to use it to position your new roof panel.
2) Space-jump to each of the three vertices, and write down the xyz coordinates of each. You might want to adjust your units preferences to make this more workable (ie. instead of having your basic unit be feet&inches, which you can't enter directly into a calculator, set units to just plain feet, or just inches, so you get decimals).
3) With three coordinates, you have nine calculations to do by hand. You need to find the dimensions of the triangle in it's own plane, so you need the angle at each vertex and the length of each side. Then you need to find the angles which describe the rotated plane in which the triangle lies. This is the part that sucks. I hope you love trig. I'm very rusty on this sort of thing, although i definitely remember doing it back in the day.
a) I think the way to go about it is by creating two vectors, originating at the same vertex and terminating at each of the remaining two (ie. vectors AB and AC). Using the properties of dot products(A dot B = |A|*|B| cos (theta)), you can find the angle between these two. Now repeat this at one of the other vertices (vectors BA and BC, for example). Don't do it a third time -- you can find the angle at vertex C by subtracting the other two from 180. Simple application of the distance formula, d=sqrt([x2-x1]^2+[y2-y1]^2+[z2-z1]^2) will give you the length of each side of the triangle.
b) Now you need the angles of the plane in which the triangle lies. Pick one of your vector pairs (AB and AC, for example), then take the cross product of them, which yields the normal vector of the plane in which the triangle lies. From here, it should be straightforward trig to get the x, y, and z angles. BTW, a TI-85 or similar graphics calculator can handle the vector operations for you, provided you're familiar w/ setting it up. It might behoove you to seek the assistance of one of the math teachers, since vectors are annoying.4) Now that you have all your dimensions, you can create your own triangle from scratch. In the xy plane, use the polyline tool to draw a triangle with the dimensions you calcluated in 3a). It will be useful to just type the coordinates directly into the xyz boxes along the bottom of the screen. See the user's manual if you're not familiar with doing that. Extrude it to whatever thickness you want your roof to be. Now use the rotate tool in conjunction with the working orientations to rotate this new triangle slab by the x,y,z angles you found in 3b). You may want to drag it over on top of the original triangle to see how well it matches up (using snap-to-handles). In fact, definitely do that, because i haven't had a chance to try any of this stuff myself, and i'm not entirely positive it will be correct. But if you drag the result on top of the original and they at least come very close to coinciding w/ each other, then you're in business. Don't forget to delete the old triangle once the new one is in place.
Hope that helps. Although i hope much more that there's an easier way that we can discover soon enough to prevent all that icky math. Rather, to let DW do that icky math for us.
jerud