T2 · 2nd-order spatial fields, Easing & easing-aware interpolation

[wow-miley]

Context. The 2nd-order layer: a {DofId → value} snapshot in four flavors, plus how time flows. Easing & Cycle are in the initial set because they buy legible, alive motion.

Objective. Define the spatial fields, Easing, and easing-aware interpolation.

Changes (:ampere-core)

data class DofValue(val kind: DofKind, val data: FloatArray)   // size == dof.dimensionality
typealias Pose        = Map<DofId, DofValue>   // commanded target
typealias Observation = Map<DofId, DofValue>   // measured (afferent twin); same shape ⇒ Pose − Observation = agency error
data class DofBound(val min: DofValue, val max: DofValue)
typealias Envelope    = Map<DofId, DofBound>   // per-DOF safety bounds — the Breaker, as data
typealias SignalField = Map<DofId, Float>      // per-DOF display intensity — Phosphor's input
fun interface Easing { fun warp(alpha: Float): Float }   // [0,1]->[0,1]; provide Linear, EaseInOut, MinimumJerk
object PoseInterpolator { fun interpolate(a: Pose, b: Pose, alpha: Float, easing: Easing = Easing.Linear): Pose }
fun Envelope.clamp(pose: Pose): Pose

interpolate warps alpha FIRST, then linear for Revolute/Prismatic/Activation, SLERP for Spherical. Activation interpolates linearly but is flagged actuation-space (config↔actuation inverse = a Load concern, deferred).

Validation

Interpolate a 2-keyframe pair per DofKind at α=0.5; assert MinimumJerk ≠ Linear at the same α; assert Spherical uses SLERP (not componentwise lerp); assert Pose − Observation computes (same shape); assert Envelope.clamp bounds an out-of-range pose; assert the arm morphology interpolates on the identical path.

Out of scope

Arc composition; emission; the actuation-space inverse mapping.

Scope ~3–4 pts · Model: Sonnet, medium thinking.