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Message - Re: double-rotation blues

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Posted by  Jerud Crandall on March 22, 2001 at 12:45:24:

In Reply to:  Re: double-rotation blues posted by Jeff on March 22, 2001 at 07:23:46:

If you were to find the coordinates of the two ends of that cap using space-jumping, you should be able to figure out the angles you need to do a normal elevation rotation and then plan rotation. Let's say the coordinates are (x,y,z) A=(0,0,0), B=(10,5,10). First, you want the angle AB makes with just the x-axis, which is:

arctan[(By-Ay)/(Bx-Ax)] = arctan[(5-0)/(10-0)] = 26.57deg.
call this angle theta.

Then you need the angle that AB makes in the vertical plane which is oriented at 26.57deg. This is found by:

arctan[(Bz-Az)/sqrt((By-Ay)^2+(Bx-Ax)^2)]
= arctan[(10-0)/sqrt((5-0)^2+(10-0)^2)] = arctan[10/sqrt(125)]
= 41.81deg.
call this angle phi.

So now, start off with your ridge cap level and oriented N-S. In East elevation view, set the angle to 'phi' degrees. Then in plan view, set the angle to -(90-'theta') degrees. At this point the cap should be properly oriented in space, you just have to align it to the ridgeline and maybe tweak it with the arrow keys a few times. BTW, instead of guessing on the length of the cap, use:

L = sqrt[(Bz-Az)^2+(By-Ay)^2+(Bx-Ax)^2+]

To find the length of the ridgeline.

I just sat down and followed my own advice, and it works. A few notes though: 1) depending on the direction in which you drew your objects (ie. drag N-S or S-N), you may need a positive angle where i said negative, or a 90+theta rather than 90-theta. This should be pretty intuitive to figure out, if only by trial and error. 2) If you ever need to 'reset' the orientation of an object, do a 'fake group', as i call it. Select the object and nothing else, and do a group on it. The orientation should reset to 0 degrees. This is the same trick for making certain rectlinear cuts in objects with no sides parallel to the xyz plane. You'll have to do a 'fake group' after doign the elevation rotate before you can rotate in plan view.

It's not too much math, and if your building has suitable symmetry, you should only have to do it once. I hope this helps!

Jerud

P.S. The arbitrary working orientation tool sure *would* make this job easier though, wouldn't it?

 


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