Extrusion With Precision (Blender)

[Devriv]

Hello Everyone :matte-motes-big-grin:,

I’d like to extrude all the top edges of the mesh below inward exactly 25 centimeters, so that any point on the extruded edges is at a distance of exactly 25 centimeters from the original edge.



I’ve done everything I could think of, experimented with transformation orientations and various pivot centres, even resorting to the solidify modifier (hehe) and add-ons, but the extrusions are still uneven.  The add-on that I tried is the “Offset Edges” add-on which is not a precision tool (I cannot input 25 centimeters). I also wanted to try the newer “Perfect Shape” addon to see if that would help but I cannot install it on 2.77a. 



The idea here does not seem complex to me, so I must be overlooking something.  How best to extrude those edges inward exactly a certain amount?  :matte-motes-nerdy:

[Imnotgoing Sideways]

What you got was effectively geometrically correct.  For example, the corner you have highlighted at 42.4cm is actually 21.2cm measured at a 45 degree angle.  To force that angle to have a constant depth, the outer corner (inner wall) would have to have a radius... Which would make it more of a bend than a corner. ()

EDIT: Something to consider: zoom the model until the grid is at centimeter scale, edit all the vertices at 45 and 90 degree angles and Ctrl+S snap to grid.  Sadly, it won't work on curves. (._.)

[Drongle McMahon]

Here's a diagram. First, the shape was made by Alt-selecting the top edge, typing F to make a face, then typing i0.25 to inset the face, then deleting the central face. You get exactly the same geometry if you use the solidify tool with thickness 0.25. The lower inset show why the radial edges are not 0.25. It's because that is the radial distance between the middle of the inner and outer edges. Because the segments are trapezoid, not curved, the actual edges have to be slightly longer. At the corners, the diagonal edge is sqrt(2)*0.25=0.3536 (sqrt(2)=sin(pi/4)) because it's a 45 degree diagonal.



[Devriv]

“What you got was effectively geometrically correct”

Thank you Immy, that particular 42cm extrusion seemed so way off (by 12 cm!) the mark and seeing the other irregularities it didn’t occur to me that it was correct. I mistakenly used .3 as input, here I used the .25:



So, getting the exact extrusions on all edges would require a) that the polygon be convex and b) that its angles be congruent?  I do get the exact measure with the two met, but not with this one.

Equiangular convex polygon:



Not Equiangular:

 

[Devriv]

Thank you for that explanation Drongle.  I used the insert faces method this time, and now I see that I get the same extrusions using it, the solidify modifier or the add-on. I understand now why the radial edges are more than 25cm. Are the edges on the arc section behaving as expected too?

[Drongle McMahon]

Yes. Here's another picture. They are exactly what's expected from the angle of the trapezium. HGaven't checked the ones transtioning to the straight edges though.



ETA: The angle between the straight sides and the last segment is exactly half of the angle between two segments. The 0.2503 edge is what's expected when that is divided by 2. So again, ity's what is expected. Just another consequence of the fact that curves are approximated by straight-line segments.

[Devriv]

Thank you again Drongle, and sorry for the inconvenience.  It’s an issue I’ve had since the very beginning with similar shapes…with visual thinking, I see now, superseding the logical (geometrical).  Very much appreciated

[Drongle McMahon]

It might be worth noting how the deviation of length decreases with the increase in accuracy of the curve by increasing the number of segments in the full circle. 8->0.2706; 16->0.2549; 32->0.2512; 64->0.2503; 128->0.2501; 256->0.2500.