@V state element (aka $ in ABOP) isn't rendering out correctly

[heckj]

Fundamentally, the example trees rendered with the L-systems taken directly from The Algorithmic Beauty of Plants aren't resulting the same visualizations as described in the book. They're close, but there's complication - I think - around a specific symbol and what it's doing: @V in the implementation research paper, and $ in the book itself.

As an example, compare the results for the following sympodial and monopodial trees:

I suspect part of the core of this issue is that what I'm doing to create the rotations for the $ symbol is resulting in a rotation that is far too vertically oriented.

I thought perhaps I had confused basic transforms and headings, but in reviewing the relevant code (https://github.com/heckj/Lindenmayer/blob/main/Sources/Lindenmayer/SceneKitRenderer.swift#L181-L214), I seem to have accounted for the corrected heading.

Since I've been mentally confusing directions, I suspect that I need to add a debugging view (#26), as well as potentially tests, to generate the relevant objects and then interrogate them to verify rotations, translations, etc.

[heckj]

It's still not 100% to what the results from the book show, but it's notably better - so committing this as the fix for the @V symbol.

[heckj]

well darnit. The fix is notably improved, but needs more work. While iterating on a debugging view of the Sympodial trees, it appears to be over-rotating just slightly, meaning that something in the calculated angle that is applied to "roll vertical" is incorrect.

State 119 of the basic sympodial structured tree at 4 iterations illustrates this:

The starting point is:

And after application of the "rollUpToVertical" (position 120), the state is:

[heckj]

Initial value:

simd_float4x4(
    simd_float4(-1.1513867, -0.12829041, 2.2153668, 0.0),
    simd_float4(2.173691, 0.43699712, 1.155033, 0.0),
    simd_float4(-0.44651538, 2.458165, -0.08971556, 0.0),
    simd_float4(4.4409075, 13.833499, 8.220964, 1.0),
)

After transforms applied:

simd_float4x4(
    simd_float4(-1.0507754, -0.5739607, 2.194639, 0.0),
    simd_float4(2.173691, 0.43699712, 1.155033, 0.0),
    simd_float4(-0.64879775, 2.3936589, 0.315371, 0.0),
    simd_float4(4.4409075, 13.833499, 8.220964, 1.0),
)

[heckj]

fully resolved. example with sympodial trees

and monopodial trees

[heckj]

fully resolved by #32