Journal

Spline controls.

Well known problems

I'm rebuilding the mesh tube generator I made a while back. I made it for something else, but ended up using it to generate cables in Vesper. The problem was with the mathematical frame I was using to generate the mesh intersections (The orthonormal basis, or local up/right/forward). It was off somehow, so the cord/tube tended to flatten out and twist strangely where it curved more.

I learned that what I was doing is called a Frenet frame (deriving an orthonormal basis from tangent, normal and binormal at any given point along the curve). In cases where curvature is zero the normal is undefined, and so when the curvature changes sign at inflection points, the normal can flip, causing the bending and twisting and spinning I was seeing. That makes it unstable for mesh extrusion (which is what this is) and it's a well known problem, just not my me - until now.

So now I'm moving to a parallel transport frame (PTF). Instead of computing the normal at each sample point along the curve, we set it at the start and then carry it with is us along the curve, applying the minimal possible amount of twist between sample points. This yields a stable moving orthonormal frame.

[↑] The PTF in action, along with editor-view visualisation of the intersections and orthonormal basis at each sample point. I add a lot of these visualisations along the way, so I can understand what's happening. It takes time, but otherwise I get lost.

[↑] I'm re-building the small space craft where the story of Vesper begins.

Exploration week came and went. Still, I spend a few of the early hours working on the vegetation and the lighting.