Turns out that accessing the texture control maps was instrumental is fixing the problem. That said, it still required quite a bit of fiddling with options because the manual is less than informative. Want to know which options make sense in any particular situation? That's not in the manual. There is a lot of what the buttons and menus are. Much of that is intuitively obvious if only marginally informative. The manual spends a whole 15 lines of text to explain the texture control map dialog and zero words explaining the impact of any changes you might make or when making changes are indicated. Good technical writing addresses the 5 W's and How. Fusion's manual misses out on about half of that.
Think the automatic (default) option will help? Not always. Apparently it's not smart enough to determine that certain aspect ratios call for the linear option.
I was texturing a box, a rather eccentric box, but it still had 6 rectangular sides with the same dimensions on the opposite sides and those parallel to each other. It's an extruded rectangle. The gotcha: its a model of a piece of extruded mesh .080 in. thick. Using the box option I was able to get the texture on the two sides to the same orientation, but no amount of tweaking would overcome a very noticeable offset between the sides. All translations move the texture the same direction the same distance. I'm not sure, but any changes you make appear to be cumulative unless you reset. I can't be positive because the transition values reset to zero with no visible impact on the target texture.
Now the manual says that linear is for 2d planar surfaces. My component is close to 2D, but it's 3D. After trying to get the box option to work for the better part of an hour, I tried linear in desperation. It worked. Apparently it was close enough. Would have been nice if the manual mentioned that. Shucks, that little tidbit would fit in a tooltip.
