Hi,
How needed are auto-orientation fixes to lookat/rivet/path constraints these days?
This (what's shown in the gif attachment) was something I was struggling with for a long time: Setting up an “up vector” to “jump” when the “aim vector” aligned to the same direction, to prevent flipping. This was more of an issure for when I was using Maya, along with custom nodes that calculated rotation using vectors and cross products, although the aim constraints weren't that much more stable, either. The other frustration was that the main way to set up any of these actions was through callbacks and/or triggers that involved a lot of scripting and naming conventions.
I wanted a more geometric approach, though my motivation for such a thing probably stemmed from my brains potentially problimatic free-assoiation between the trig. equations for a circle using sin/cos, the documentation on transformation matrices showing a lot of the same sin/cos functions for the rotation part, and the classic gimbal widget made up of three circles that was driven by a transformation matrix.
From that, my thinking was “what other ‘shapes’ that could be made with sin/cos could be converted into a rotation matrix?” So far, all that has resulted is this: instead of a circlular path for the x-rotation, I used the formula for a superellipse with n1=n2=0, which turned out to be not as literally translatable into a rotation matrix transformation as I thought it should be…
Still, this has led me to consider the possibility of expressing other geometric shapes and paths as rotations…Simply replace the sine and cosine of a transform matrix (per rotation axis) with whatever equation for a 2d circle-derived shape (such as a epicycloid, regular ellipse, spyrograph, etc), and that way you don't have to use extra curve objects and path constraints to achive the same result…
I'm not sure how to convert any closed curve into a rotation matrix…I assume it's mathemetically possible, but I've come to learn in the most frustrating way that computers don't inherently speak “math” the way mathematicians speak it. So it may take some time for me to figure out a working implementation…