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Geometry-Based Metrics for Early-Stage Hull-Form Producibility Screening

Andrea Serani, Kevin Maki

arXiv:2609.27544v1cs.CEcs.CG

TL;DR

Early hull-form design can explore hydrodynamic performance without directly assessing geometry-related production complexity. This paper develops and evaluates a representation-aware geometric screening signature; its hull applications show complementary curvature information, including a KCS–DTMB 5415 difference in developability deviation.

  • Problem

    Hydrodynamically attractive hull geometries may still contain production-relevant curvature features, while geometry alone cannot predict fabrication man-hours or cost.

    Source: §1 · pp. 1–2

  • Method

    The framework combines total and signed developability deviation, curvature-class area fractions, distributed fields, and metric-specific validity and representation provenance.

    Source: §8 · p. 21

  • Results

    KCS has approximately 24% greater developability deviation than DTMB 5415; double-curved regions cover 72.9% of KCS's valid surface versus nearly all of DTMB 5415's.

    Source: §8 · p. 21

  • Takeaways & Limitations

    The signature is an initial geometric screening layer for comparing hull forms before detailed production information is available.

    Source: §7.3 · p. 21, §8 · p. 22

    The framework does not predict forming effort, fabrication cost, or process feasibility; correlation and calibration against plate-scale experiments or shipyard production evidence remain future validation needs.

    Source: §7.3 · p. 21, §8 · p. 21

Abstract

from arXiv · show

This paper presents a representation-aware framework for geometry-based screening of hull-form producibility at early design stages. The proposed signature combines dimensionless total and signed developability deviation with curvature-class area fractions, distributed fields, metric-specific validity, and representation provenance. These descriptors characterize surface features relevant to plate forming and developability, but are not calibrated predictors of fabrication cost, forming effort, or process feasibility. Native IGES/STEP boundary representations (BReps) are evaluated through direct differential geometry and trimmed-domain quadrature, whereas triangulated surfaces use discrete curvature recovery and area-weighted aggregation. Analytical and semi-analytical controls verify the formulation, while matched-face BRep-to-mesh tests assess discrete curvature recovery. Application to DTMB 5415, KCS, JBC, and KVLCC2M shows that curvature intensity and areal extent provide complementary information and that derivative-based outcomes can be representation sensitive. KCS, for example, exhibits approximately 24% greater developability deviation than DTMB 5415, while double-curved regions occupy 72.9% of its valid surface versus nearly the entire DTMB valid surface. The resulting quantities provide an early geometric screening layer for subsequent use as objectives, constraints, surrogate responses, or design-space features. HullProd, the companion open-source software, implements the signature, distributed fields, validity, and provenance.

1 Introduction

Early hull optimization can favor hydrodynamic performance without revealing geometry-related production difficulty, while existing production assessments often depend on process-specific information. The paper proposes a normalized, representation-aware geometric signature for early screening, with metric-specific validity and provenance.

1 Introduction

  • Hydrodynamically attractive geometries may still contain extensive double curvature, concentrated curvature, or abrupt shape changes that are difficult to identify when producibility is considered late.Geometry alone cannot predict fabrication man-hours or cost, though it can expose features relevant to forming, fairing, subdivision, and inspection.Source: §1 · pp. 1–2
  • Existing approaches leave a gap for a normalized, representation-aware signature that separates curvature intensity, sign, and areal composition, localizes responses, and qualifies validity.Cost-weighted metrics require process-specific coefficients, while forming models need production information.Source: §1 · p. 2
  • The signature combines global descriptors, distributed fields, and metric-specific validity and provenance rather than collapsing geometry-induced producibility into one universal score.Its intended role is an initial comparison layer before detailed production information is available.Source: §1 · p. 2
  • BRep and triangulated surfaces receive separate numerical realizations, with mesh-resolution, connectivity, boundary, and element-quality effects treated as realization concerns.Validity is assessed individually for each metric and reported with representation provenance.Source: §1 · p. 2
  • Analytical and semi-analytical controls and four public hulls assess the formulation and representation sensitivity, with the retained contract implemented in companion HullProd software.Higher-regularity and section-based quantities were screened but not promoted to the recommended signature after numerical verification.Source: §1 · pp. 2–3
  • The framework characterizes geometry relevant to forming but does not model plate layout, materials, processes, yard practice, cost, labor, or schedule.Those production factors require information beyond the external hull surface.Source: §1 · p. 2, Figure 1 · p. 3

2 Background and relation to ship-production metrics

Geometry-based indicators offer early information about shape-induced complexity, but do not capture the production conditions that determine fabrication effort. This section situates curvature descriptors within that limited role and explains why some candidate descriptors were excluded.

2 Background and relation to ship-production metrics

  • Geometry-based descriptors can support early design comparisons, but the same surface may imply different effort under different materials, plate subdivisions, processes, tolerances, and facilities.They indicate shape-induced complexity rather than directly estimating work content.Source: §2 · p. 3

2.1 Developability, curvature class, and plate forming

  • Gaussian curvature and principal-curvature signs provide forming-relevant geometric descriptors; the proposed formulation retains normalized total and signed measures, curvature-class area fractions, localization, validity, and provenance.Unlike relative fabrication-weight metrics, the present work does not assign universal cost coefficients.Source: §2.1 · p. 3

2.2 Scope relative to cost and process models

  • The framework uses the external hull surface before production inputs are specified, but geometry alone cannot infer fabrication effort, cost, labor, or schedule.HullProd reports geometry quantities without process-specific weights or a calibrated shipyard cost model.Source: §2.2 · p. 4

2.3 Screened descriptors and representation diagnostics

  • Higher-regularity and section-based descriptors were excluded because robust general hull-level values were not established across the considered public CAD representations.Mesh-local normal variation remains a representation-quality diagnostic because it depends on resolution, connectivity, and local element quality.Source: §2.3 · p. 4

3 Geometry-based producibility framework

The framework characterizes hull geometry through complementary measures of double-curvature intensity, sign, and areal extent, retaining distributed fields and validity rather than collapsing them into a universal score. These geometry-based descriptors are not calibrated measures of forming effort or fabrication cost.

3 Geometry-based producibility framework

  • Mean curvature describes local average bending, while Gaussian curvature distinguishes developable, elliptic, and saddle-type local geometry.Vanishing Gaussian curvature throughout a sufficiently regular region is the local differential condition for developability; pointwise K = 0 alone does not establish a finite patch is developable.Source: §3 · pp. 4–5

3.1 Developability deviation

  • ID measures area-averaged double-curvature intensity, while signed components distinguish elliptic from saddle or reverse contributions.ID = 0 is the developable limit, but ID is not a calibrated scale of forming effort or fabrication cost.Source: §3.1 · pp. 5–6

3.2 Curvature-class area distribution

  • Curvature-class area fractions describe surface-type extent, complementing intensity and sign to distinguish hulls with different distributions of double curvature.The classes use dimensionless quasi-zero tolerances, not manufacturing criteria or forming limits.Source: §3.2 · pp. 6–7

3.3 Geometry-based producibility signature

  • The signature combines global and distributed descriptors with metric-specific validity and representation provenance, without a universal weighted score.Global values support compact comparisons, while distributed fields locate responses; downstream use requires physical or process-specific calibration.Source: §3.3 · p. 7, Figure 2 · p. 8

4 Representation-aware numerical realization

Native BReps and triangle meshes are treated as distinct numerical realizations of the same descriptors, with no silent conversion between representations. Each path reports metric-specific validity and provenance so that unresolved or representation-sensitive values remain explicit.

4.1 Native BRep backend

  • Native BReps use parametric surface derivatives and integrate over trimmed face domains, with adaptive quadrature and explicit convergence evidence.Failure to meet tolerance is retained as unresolved evidence rather than hidden by reporting the last finite quadrature value.Source: §4 · p. 8, §4.1 · p. 9

4 Representation-aware numerical realization

  • The two representations evaluate the same conceptual descriptors through separate numerical paths rather than converting one geometry into the other.Native CAD derivatives describe continuous geometry; mesh curvature must be reconstructed from discrete positions, connectivity, and face orientation.Source: §4 · p. 8

4.2 Triangle-mesh backend

  • Triangle meshes reconstruct curvature tensors from discrete normal variations, aggregate vertex quantities by area, and exclude open-boundary vertices from retained Gaussian-curvature aggregation.Boundary samples are marked invalid rather than assigned zero curvature; mesh-resolution and quality diagnostics are retained but are not part of the recommended signature.Source: §4.2 · pp. 10–11

4.3 Metric-specific validity

  • Validity is assigned per metric, distinguishing established values from convergent improper integrals, unresolved results, divergence, and mesh sensitivity.A finite value that cannot be established as meaningful or resolved is reported as null rather than accepted from a finite-depth computation.Source: §4.3 · pp. 11–12

5 Verification and benchmark protocol

The protocol uses analytical and semi-analytical controls before testing matched-face curvature recovery, whole-hull mesh-resolution sensitivity, and representation sensitivity. It applies the descriptors to four public hulls while retaining metric-specific validity and representation provenance.

5.2 Public-hull campaign and representation verification

  • Matched-face BRep-to-mesh tests isolate curvature-recovery and connectivity effects, while separate campaigns assess whole-hull mesh-resolution and representation sensitivity.The frozen coarse, medium, and fine tessellations are used for the resolution assessment.Source: §5 · p. 12, §5.2 · p. 13

5.1 Analytical and semi-analytical controls

  • Plane, sphere, cylinder, saddle, torus, and half-Wigley controls exercise zero, positive, single, negative, spatially varying, and open hull-like curvature properties.The first four and the torus have exact reference quantities; the half-Wigley hull has independent semi-analytical references.Source: §5.1 · pp. 12–13, Figure 3 · p. 12

5.2 Public-hull campaign and representation verification

  • The four benchmark geometries are DTMB 5415, KCS, JBC, and KVLCC2M, spanning naval and commercial forms rather than serving as a hull-type ranking.The campaign records source representation and scale; assessed-surface composition depends on which surfaces are included.Source: §5.2 · pp. 13–14, Table 3 · p. 14
  • Curvature-recovery accuracy compares recovered and direct-BRep H and K at identical vertices over a common valid interior mask.A global sign is selected for recovered H; the global-norm denominator avoids unstable pointwise relative division near zero.Source: §5.2 · p. 13
  • Native results use Lref = Lpp and bounded global-refinement evidence; quantities unresolved at maximum depth 6 remain reported as unresolved.For retained ID, final and prior relative changes must not exceed 2% and 3%, respectively.Source: §5.2 · p. 13
  • Changes in curvature-class composition between mesh levels are summarized as the sum of absolute changes across the four class fractions.This accompanies the frozen coarse, medium, and fine whole-hull tessellation assessment.Source: §5.2 · p. 13

6 Results

The results verify the signature on analytical controls and public hulls, show that developability intensity and curvature-class area are complementary, and demonstrate sensitivity to geometric representation. They interpret the outputs as geometric descriptors whose validity and numerical provenance must accompany their use.

6.1 Analytical and semi-analytical verification

  • Plane, cylinder, sphere, saddle, and torus controls recover expected classes or references; half-Wigley native-BRep results have approximately 1.5 × 10^-6 relative error and 3.64 × 10^-4 maximum class-component error.The class-vector error is absolute; the scalar-reference error is relative.Source: Table 4 · p. 15, §6.1 · p. 15

6.2 Public-hull global signatures

  • DTMB and KCS are nearly balanced in elliptic and saddle/reverse intensity; KVLCC2M is positive-dominant and JBC negative-dominant, with double-curved area fractions of 43.5% and 34.4%, respectively.Intensity, sign, and areal composition provide related but distinct information.Source: §6.2 · p. 16
  • KCS has approximately 24% greater developability deviation than DTMB 5415, while double-curved regions cover 72.9% of KCS's valid surface versus essentially all of DTMB 5415's.These global signatures are reported for native BRep and frozen fine-STL representations, without combining components into a universal score.Source: Table 5 · p. 16, §6.2 · p. 16

6.4 Representation sensitivity: native BRep versus triangulated geometry

  • Fine-STL developability deviations differ from native BRep by −16.0% for KVLCC2M to +24.3% for JBC, with signed components and class fractions also redistributed.These are representation differences, not isolated curvature-estimator errors.Source: Table 5 · p. 16, §6.4 · p. 19

6.3 Distributed localization of the main descriptors

  • Figures 5 and 6 localize developability intensity and curvature classes across the hulls; the fields identify contributions around the bow, stern, bilge, keel, and CAD patches.Curvature-class fractions describe represented-valid-area composition; isolated singular sets carry zero represented area.Source: Figure 5 · p. 17, §6.3 · pp. 17–18, Figure 6 · p. 18

6.2 Public-hull global signatures

  • Across the threshold study, total double-curved area fraction and its cross-hull ordering remain stable, although individual flat and single-curvature fractions can be more threshold-sensitive.Changes from the smallest to largest thresholds range from approximately 0.05% for DTMB 5415 to 5.0% for JBC.Source: §6.2 · p. 17

6.4 Representation sensitivity: native BRep versus triangulated geometry

  • At 48 × 48, matched-face relative L2 errors range from 0.7–4.3% for mean curvature and 1.4–8.2% for Gaussian curvature; all error ratios versus 12 × 12 are below one.These tests assess curvature recovery and connectivity sensitivity, not full-hull BRep-to-mesh convergence.Source: Table 6 · p. 19, §6.4 · p. 19
  • Coarse-to-fine developability changes are 16.7–21.9%, versus 2.5–10.3% from medium to fine; JBC's poor campaign tessellations contrast with its ordinary matched-face recovery errors.The campaign meshes are not a controlled convergence-to-native-BRep study.Source: §6.4 · p. 19

7 Discussion

The discussion treats the signature as an ordered set of geometric descriptors, not a universal producibility score. It emphasizes metric-specific validity and representation provenance, and limits the current contribution to early geometric screening pending process-specific validation.

7.1 Engineering hierarchy of the signature

  • Total developability, its signed components, and curvature-class fractions describe intensity, type, and areal extent, answering different production-related geometric questions rather than forming uncalibrated weights.KCS has approximately 24% greater developability deviation than DTMB 5415, while double-curved regions cover 72.9% versus essentially all of the valid surface.Source: §7.1 · p. 20

7.2 Validity and representation provenance

  • Validity must be reported per metric: the same geometry can impose different regularity or integrability requirements, and a finite value at one quadrature depth or mesh resolution does not establish convergence.The DTMB 5415 absolute-Gaussian-curvature developability is a convergent improper integral.Source: §7.2 · p. 20

7.3 Initial screening layer and validation gap

  • The signature exposes geometric features before production details are known, but it does not establish cost, man-hours, or a forming route; validation against experiments or shipyard evidence remains necessary.The stated validation targets include forming effort, distortion, rework, and inspection outcomes.Source: §7.3 · p. 21
  • Once calibrated, individual descriptors or distributed fields may serve as design objectives, constraints, surrogate responses, or dimensionality-reduction features; those downstream workflows are not demonstrated here.The present contribution is the interpretable signature and its validity/provenance contract.Source: §7.3 · p. 21

8 Conclusions

The framework provides representation-aware geometric screening descriptors for hull-form producibility, not calibrated manufacturing predictions. Tests and four-hull applications establish complementary geometric information while identifying representation sensitivity and the need for production-relevant calibration.

8 Conclusions

  • The signature combines total and signed developability deviation, curvature-class area fractions, distributed fields, metric-specific validity, and representation provenance for early-stage geometric screening.It is not a universal score or calibrated predictor of forming effort, fabrication cost, labor, process selection, or manufacturing feasibility.Source: §8 · p. 21
  • Analytical and semi-analytical controls and matched-face BRep-to-mesh comparisons verify geometric definitions and assess discrete curvature recovery, but not end-to-end convergence of the mesh signature.The tests quantify accuracy, refinement behavior, and connectivity sensitivity within the adopted verification protocol.Source: §8 · p. 21
  • KCS exhibits approximately 24% greater developability deviation than DTMB 5415, while double-curved regions cover approximately 72.9% of KCS’s valid surface versus essentially all of DTMB 5415’s.Across the four hulls, intensity, sign, and areal composition provide related but non-redundant information; distributed fields locate the global contributions.Source: §8 · p. 21
  • Derivative-based descriptors can vary materially with geometric representation and mesh resolution, so native BRep and mesh outputs are distinct realizations rather than interchangeable values.Higher-regularity surface and section-based quantities were excluded because robust hull-level behavior was not established across the considered public CAD representations.Source: §8 · p. 21
  • Physical validation requires independent production evidence before descriptor magnitudes or classification thresholds can be interpreted quantitatively as process-specific forming difficulty, manufacturing effort, or cost.Examples include plate-scale forming experiments, deformation or strain measures, rework, inspection data, and shipyard production records.Source: §8 · pp. 21–22
  • Individual components may serve as optimization objectives or constraints, surrogate-model responses, or design-space features, but these downstream applications were not evaluated in the proof of concept.Their use requires appropriate problem-specific interpretation and validation.Source: §8 · p. 22
  • The companion HullProd implementation exposes the recommended global descriptors, distributed fields, validity information, and representation provenance through a common interface.Source: §8 · p. 22

Data and code availability

The HullProd implementation used in the study is publicly available as version 1.0.1 through GitHub and PyPI, with an archived release on Zenodo.

Data and code availability

  • HullProd version 1.0.1 is available through GitHub and the Python Package Index, with an archived software release on Zenodo.Source: Data and code availability · p. 22
  • The versioned implementation, benchmark configurations, and machine-readable provenance support reproducibility; externally sourced hull geometries remain subject to their providers’ access and redistribution terms.Source: Data and code availability · p. 22
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