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feat(num): N3 selectable scale-floor clamp mode (HardJava | SmoothBarrier)

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The hyper-ideal vertex scale b is floored to keep the geometry valid.  The
original clamp `b<0 → 0.01` mirrors the Java oracle but is only C⁰ (in fact
value-discontinuous at b=0): a Newton step crossing the feasibility boundary
hits a kink that can stall convergence (numerical-stability audit N3).

Rather than replace the Java-faithful behaviour (which would break the golden
parity tests), make the floor a selectable mode so BOTH the Java standpoint
and the clean mathematics are available:

- HyperIdealScaleClamp::HardJava (DEFAULT) — the original snap, bit-for-bit
  faithful to HyperIdealFunctional.java → all parity tests unchanged.
- HyperIdealScaleClamp::SmoothBarrier — C¹ softplus floor
  b ↦ floor + softplus_β(b−floor), β = HYPER_IDEAL_SCALE_SHARPNESS (=100);
  ≈ identity away from the floor, smooth across b=0.  Opt-in.

clamp_hyper_ideal_scale centralises the logic (also folds in the N4 nachzügler:
compute_face_angles used a bare 0.01).  The mode threads with a defaulted
trailing parameter through compute_face_angles, face_angles_from_local_dofs,
evaluate_hyper_ideal, the four hyper_ideal_hessian* variants and
newton_hyper_ideal — so every existing call site keeps HardJava behaviour.

Tests (+4): clamp-function C¹/floor/identity contract, mode-equivalence away
from the boundary, and end-to-end SmoothBarrier convergence to the same Java
golden vector (LawsonHyperIdeal).  296/296 CGAL tests pass.
Documented in doc/math/geometry-modes.md.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
This commit is contained in:
Tarik Moussa
2026-05-31 16:27:48 +02:00
parent b7c7d108b5
commit 186f11b11a
7 changed files with 242 additions and 27 deletions
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24
code/include/hyper_ideal_hessian.hpp
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@@ -64,7 +64,8 @@ inline Eigen::SparseMatrix<double> hyper_ideal_hessian(
ConformalMesh& mesh,
const std::vector<double>& x,
const HyperIdealMaps& m,
double eps = 1e-5)
double eps = 1e-5,
HyperIdealScaleClamp clamp = HyperIdealScaleClamp::HardJava)
{
const int n = hyper_ideal_dimension(mesh, m);
std::vector<Eigen::Triplet<double>> trips;
@@ -77,8 +78,8 @@ inline Eigen::SparseMatrix<double> hyper_ideal_hessian(
xp[sj] = x[sj] + eps;
xm[sj] = x[sj] - eps;
auto Gp = evaluate_hyper_ideal(mesh, xp, m, /*energy=*/false).gradient;
auto Gm = evaluate_hyper_ideal(mesh, xm, m, /*energy=*/false).gradient;
auto Gp = evaluate_hyper_ideal(mesh, xp, m, /*energy=*/false, /*grad=*/true, clamp).gradient;
auto Gm = evaluate_hyper_ideal(mesh, xm, m, /*energy=*/false, /*grad=*/true, clamp).gradient;
xp[sj] = xm[sj] = x[sj]; // restore
@@ -101,9 +102,10 @@ inline Eigen::SparseMatrix<double> hyper_ideal_hessian_sym(
ConformalMesh& mesh,
const std::vector<double>& x,
const HyperIdealMaps& m,
double eps = 1e-5)
double eps = 1e-5,
HyperIdealScaleClamp clamp = HyperIdealScaleClamp::HardJava)
{
auto H = hyper_ideal_hessian(mesh, x, m, eps);
auto H = hyper_ideal_hessian(mesh, x, m, eps, clamp);
Eigen::SparseMatrix<double> Ht = H.transpose();
return (H + Ht) * 0.5;
}
@@ -142,7 +144,8 @@ inline Eigen::SparseMatrix<double> hyper_ideal_hessian_block_fd(
ConformalMesh& mesh,
const std::vector<double>& x,
const HyperIdealMaps& m,
double eps = 1e-5)
double eps = 1e-5,
HyperIdealScaleClamp clamp = HyperIdealScaleClamp::HardJava)
{
const int n = hyper_ideal_dimension(mesh, m);
std::vector<Eigen::Triplet<double>> trips;
@@ -187,9 +190,9 @@ inline Eigen::SparseMatrix<double> hyper_ideal_hessian_block_fd(
vm[j] -= eps;
auto Op = face_angles_from_local_dofs(
vp[0], vp[1], vp[2], vp[3], vp[4], vp[5], v1b, v2b, v3b);
vp[0], vp[1], vp[2], vp[3], vp[4], vp[5], v1b, v2b, v3b, clamp);
auto Om = face_angles_from_local_dofs(
vm[0], vm[1], vm[2], vm[3], vm[4], vm[5], v1b, v2b, v3b);
vm[0], vm[1], vm[2], vm[3], vm[4], vm[5], v1b, v2b, v3b, clamp);
const double Gp[6] = {
Op.beta1, Op.beta2, Op.beta3,
@@ -221,9 +224,10 @@ inline Eigen::SparseMatrix<double> hyper_ideal_hessian_block_fd_sym(
ConformalMesh& mesh,
const std::vector<double>& x,
const HyperIdealMaps& m,
double eps = 1e-5)
double eps = 1e-5,
HyperIdealScaleClamp clamp = HyperIdealScaleClamp::HardJava)
{
auto H = hyper_ideal_hessian_block_fd(mesh, x, m, eps);
auto H = hyper_ideal_hessian_block_fd(mesh, x, m, eps, clamp);
Eigen::SparseMatrix<double> Ht = H.transpose();
return (H + Ht) * 0.5;
}