darboux-igph · deformation explorer

DEFORMATION REPLAYER

Shape evolves under information-geometric flow

STATE idle

STEP 0 / 0

KNOT STACKS 0

Spline + target

Deformation view

Blue closed curve: B-spline source. Orange points: target cloud.

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Red dots are control points; the blue closed polyline is the evaluated cubic B-spline at the current step.

Latent topology

Knot intervals + continuity

Heatmap: $\Delta_i = \mathrm{softplus}(\gamma_i)$ per parameter index over time (collapsed = dark, full = bright). Spline color above tracks local continuity: green C², amber C¹, red C⁰ break.

t = 0 t = T

parameter index 0 → index n−1

Heatmap colour scale absolute scale

Δ = 0.00 Δ = 1.50

C² smooth C¹ C⁰ break γ < threshold (stacked)

Run

Method —

Timeline

Playback

Spline curve Control points Target cloud

Latent state

Live metrics

Bound to the current frame.

S_\varepsilon Sinkhorn divergence —

T(p) kinetic energy —

H_d damped Hamiltonian —

\|\nabla_q V\| control-point grad —

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Run header

Choose a run from the dropdown to load its artifact bundle.

Flow law

Hamiltonian gradient with damping. Sinkhorn potential $V = S_\varepsilon(\mu_q, \nu)$ pulls the curve onto the target.

Curve identity

Closed uniform cubic B-spline; control polygon $\{q_i\}_{i=0}^{n-1}$ evolves under the port-Hamiltonian flow.