Tangency in projected geometry / nonorthogonal planes

[edgemarston]

Hey everyone, I'm trying to figure out a tangency problem that's driving me nuts. The part consists of a circular sweep followed by a loft:

I want it to be a smooth transition in three specific directions. I figured out how to make the front and back rails of the loft perfectly vertical where they touch the sweep, by making them tangent to the intersected body:

However, I can't figure out how to make the side rail of the loft be perfectly tangent to the arc of the sweep:

I've gotten it extremely close by eyeballing it and then tweaking both the angle of the plane that the rail is in and the actual spline itself, but it isn't exact. It's driving me crazy. Is there an obvious way to constrain the model that I'm missing?

I've attached the project.

Thank you!

[davebYYPCU]

The loft rails at the Revolve end are already tangent.

To do the slot end, create a dummy patch body (extrude)

Project > Intersect the patch body to the rail Sketches, and Tangent constrain the rail to the projected article.

Rail 3 went wonky, so I deleted the middle fit point.

Might help....

[edgemarston]

Edit: sorry, I thought this worked, but it looks like I jumped the gun a little. It seemed to work at first but isn't replicating.

To be clear about what I'm having trouble with: in the picture below, I'm focused on the yellow line. When the whole part is viewed from the right (like in that picture), I want the right-most part of the loft to lift off from the end of the rotation at the same angle as the arc where the rotation ends. The rail will go off in a different plane as it approaches the slot, and that's okay, it just needs to be tangent with respect to the perspective I've shown in that picture.

In other words I'm sort of trying to do a reverse projection -- I want to constrain the rail so that, if I were to project the rail into the plane you're looking at in the picture, it would be tangent to the yellow line exactly at the point where the two bodies meet.

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@davebYYPCU, thank you so much! I was actually trying to make smooth tangents where the loft connects to the revolve, not at the slot itself, but I applied your same technique of extruding a dummy patch from the circular edge of the revolve and then intersecting that with each of the 3 planes for the 3 loft rails, and it worked great.

Now I just need to wrap my head around the projective geometry so I understand why it worked 🙂

[laughingcreek · Accepted solution]

Your using the sketch profile instead of the face for your loft.  when you use the face you get the option of tangency or curvature conditions for the loft, so the loft will leave that face exactly tangent to the connecting faces.

see the screen cast.

you can see from the zebra analysis that the loft intersection isn't tangent to begin with.  deleting that loft profile and electing the face instead improves the surface.  Adding the helper body like @davebYYPCU  suggests to the other end and lofting to the face improves it more.

there are more improvements to the rails be had if you want to go to the trouble (they'll be less trouble than what your ding right now).  currently your rails aren't leaving the "small ring" normal to the lofting face.  they may be tangent to your projected curves,but they are traveling at an angle to the normal direction.  if you "split face" of the tube, you can constrain your rails to be tangent to those edges.  that should further improve the loft surface

[laughingcreek]

re-reading the bit about splitting the faces and adding rails tangent to them, it kinda sounds like giberish.

maybe this screen cast will be more clear

more improvements can be had from here to, but may have to go into surfaces environment for that.  that one crease on the top is really bugging me. 

[chrisplyler]

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@edgemarston wrote:

Now I just need to wrap my head around the projective geometry so I understand why it worked 🙂

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It works because projecting in the intersection gives you lines, and then when you draw your rail lines, you can constrain them to be tangent to those projected intersection lines.

Here is a way to ensure tangency without rails at all. You still have to eyeball the SHAPE, but not the tangency.

[edgemarston]

Wow, thank you all so much! I learned a ton from this thread. I really appreciate all the work that went into those screencasts.

@laughingcreek , I hadn't realized the different options presented when choosing a sketch vs a face as a loft profile. That's extremely useful. I went with lofting the face of the rotation tangently, while also using two guide rails. It worked perfectly. Also good call on the zebra analysis. I'd only used curvature analysis in the past.