planarity (developability) loss

[giorgioangel]

This PR adds a planarity/developability prior that encourages each 2×2 quad patch of the reconstructed surface to be locally planar. The loss is implemented as a Ceres cost with two residuals per quad (one per opposite triangle), integrated into both the local and global optimization paths. It is wrapped with a Huber loss.

Weight term

Right now the weight is set to 0.1f. Setting it to 0 disables the loss. We should wait for the metrics to be ready or do some tests to assess whether this loss helps.

Motivation

• Reduce local twisting (possibly leading to fewer sheet jumps?)
• Complement existing distance and straightness terms with a rotation-invariant planarity prior.

Formulation

For a quad with vertices:

(p00) -- (p01)
  |        |
(p10) -- (p11)

we define two signed point-to-plane distances:

• Plane of triangle (p00,p01,p10), distance of p11 to that plane:

  • n0 = (p01−p00) × (p10−p00)
  • d0 = n0 · (p11−p00) / ‖n0‖

• Plane of triangle (p11,p01,p10), distance of p00 to that plane:

  • n1 = (p01−p11) × (p10−p11)
  • d1 = n1 · (p00−p11) / ‖n1‖

Residuals:

r = sqrt(w) * [ d0, d1 ]

Two opposite triangles avoid bias and keep good gradients even when one triangle is nearly degenerate.

Integration points

• Local/centered losses:

  • emptytrace_create_centered_losses(...) now calls
    add_quad_planarity_loss_3D(state, loc, p, problem, flags, nullptr, planarity_weight_3D);

• Global/“missing” losses:

  • emptytrace_create_missing_centered_losses(...) dedups via a loss_status bit (bit 12) using:

    int conditional_planarity_loss(int bit=12, ...);

• Surftracking graph:

  • Local add: surftrack_add_local(...) includes planarity when LOSS_3D_INDIRECT is set.

  • Global graph: surftrack_add_global(...) includes a dedupbed planarity residual with a unique type id 20 via:

    int cond_surftrack_planarity_3D(int type=20, ...);