# Help - I'm still doing math

Question asked by Tyler D. on Aug 28, 2017
Latest reply on Aug 29, 2017 by Bjorn Sorenson

Hi, I'm still learning some basics and have found I'm doing math more than I feel I should be, which makes me think I'm not being efficient at modelling.  I came up with a couple simple examples I'll post to see if I can get some advice on how to do it more efficiently.

Case 1: (Compound) miter cuts

Let's pretend this is something like a roof truss made out of 2x4 lumber (and lets pretend a 2x4 measures 2" x 4").  There's a horizontal beam, then a joist that meets it 30 deg below horizontal (just a single miter for now).  If I just make the 30 deg miter cut and butt joint the cut face to the beam, it's taller, as the vert. dimension of the cut surface is: L = 4" / cos 30 = 4.62".

So, if I want the cut surface to be flush with both top and bottom of the horizontal beam, I'd need to cut down the width of the 2x4 first.  So I could do math: 4*cos(30) = 3.46", draw a beam as 2" x 3.46" then cut the miter.

But I figured this is easier:  Draw 2x4 profile on front plane, draw a sweep path on the right plane 30 deg below horizontal, then do a swept boss/base, then finally square off the free end such that it isn't mitered.  This also gives me a width of 3.46".  This seems to work whether I select the Profile orientation to be "Follow Path" or "Keep Normal Constant", so I suppose I'll have to read in to the difference between these scenarios to understand better.

Now this is where I get stumped.  Now say this is a compound miter cut: 30 deg below horizontal, and 45 deg back.  Now say I still want the cut surface to be flush with top and bottom of the horizontal beam (so I'll need to wind up with the width of the beam to be 3.46") but I want to maintain the full 2" depth of the beam as it still fits fine.  E.g. I do not want the depth to become 2*cos(45)= 1.41"

So the only ways I can figure it out is I either do math manually to get the 3.46" dimension, draw a beam then make a new plane to perform the compound miter cut.

OR

I do math manually to figure out the projected depth 2/cos(45) = 2.83", then draw a profile 2.83" x 4", make a new plane to draw a sweep path on, then sweep along the path resulting in beam dimensions of 3.46" x 2".

Is there a way to be able to get this shape without having to do any math manually?

(I have another example I'll post in a separate post in this thread)

As a preemptive thank you, I really appreciate how willing people are to help beginners on this forum.  I do more asking than contributing, but hopefully that changes sooner rather than later as I get more proficient.

Thanks