refactor!: Move Transform2/Transform3 from Affine to Isometry

[andiwand]

The geometry, navigation and propagation code has always assumed the
linear part of a transform is orthogonal: Surface::freeToBoundJacobian
uses referenceFrame().transpose() as its inverse, and referenceFrame
is typed RotationMatrix3. A scaled or sheared transform therefore
produces a silently wrong Jacobian rather than an error. Make the
assumption part of the type, so that is a compile error instead.

AffineTransform2/AffineTransform3 name the unconstrained form for the
external geometry that legitimately needs it, and
makeTransform3(rotation, translation) replaces the
Translation3 * RotationMatrix3 idiom, which Eigen types as affine.

Picks up #4055 by pbutti.

Co-Authored-By: Pierfrancesco Butti pierfrancesco.butti@gmail.com
Co-Authored-By: Claude Opus 5 (1M context) noreply@anthropic.com

[andiwand]

Why

Surface::freeToBoundJacobian inverts the reference frame with .transpose(), DiscSurface::normal reads matrix column 2 without normalising it, and referenceFrame() is typed RotationMatrix3. Orthogonality is already a hard requirement — it just was not expressed anywhere, so violating it gives a wrong Jacobian instead of an error.

Exactly one place in the repo ever violated it: the beveled endcap disc in CylinderVolumeBounds::orientedSurfaces. #4055 disabled that code; here it is diagnosed instead. Its factor is 2 - 1/cos(bevel) ≈ cos(bevel) where an elliptical cut needs 1/cos(bevel), and it goes singular at 60°. Nothing outside Core constructs bevels, so the disc is now only tilted.

What changed vs #4055

• No runtime throws (that was the open question there). One debug assert inside makeTransform3, and the rest is compile-time.
• Translation3 * RotationMatrix3 is affine in Eigen, so those sites go through makeTransform3(rotation, translation) rather than wrapping in Eigen::Isometry3d(...).
• Transform2 too, plus AffineTransform2/AffineTransform3 for external geometry. Widening Transform3 → AffineTransform3 is implicit, narrowing is a static_assert, so every entry into ACTS geometry is an explicit decision.

Not a perf PR. The isolated inverse() * position is 2.8x faster as a transpose, but #4055 measured no end-to-end gain on ODD 1k events and I have no reason to expect otherwise. The case is correctness.

Review guide

25 files, but only the first is a design decision:

1. Definitions/Algebra.hpp — the four aliases and makeTransform3. Everything else follows mechanically.
2. CylinderVolumeBounds.cpp — the only behaviour change.
3. Plugins/GeoModel/.../GeoTransformConverter.hpp — GeoTrf::Transform3D is Eigen::Affine3d, so this is where external affine meets ACTS rigid.
4. The remaining 22 are call-site rewrites of one idiom.

What breaks for users

Four compile-error classes, all loud, ~23 sites in this repo: building from Translation3 * RotationMatrix3; passing an Eigen::Affine3d; .scale()/Eigen::Scaling; and mutating rotation(), which is now a const block rather than a matrix by value. One hole the type cannot close: linear() = <non-orthogonal> still compiles and then inverse() is wrong.

Notes for maintainers

• Results shift at rounding level (~1e-11 mm over a 3 m lever arm), so root hashes and physmon references need regenerating — same single-bin GSF churn as refactor!: Move Affine to Isometry for Acts::Transform3 #4055.
• The API breaking label will not fire automatically. Everything in Algebra.hpp sits inside a Doxygen @defgroup, and CI/public_api/public_api_surface.py skips compounds whose name does not start with Acts — a group compound is named algebra_types. Running the diff locally reports "No change to the public API surface ✅", which is an artifact. ChargeHypothesis.hpp, ParticleHypothesis.hpp, EstimateTrackParamsFromSeed.hpp and Logger.hpp have the same blind spot. Happy to fix the scanner separately.

Verified: Core + DD4hep/Geant4/GeoModel/Json/Root/ActSVG/EDM4hep + Examples + python bindings build clean, 375/375 ctest with assertions forced on.

[github-actions]

Public API surface diff

No change to the public API surface. ✅

[github-actions]

📊: Physics performance monitoring for 396a6b8

Full contents

physmon summary

• ✅ Particles fatras
• ✅ Particles geant4
• ✅ Particles ttbar
• ✅ Vertices ttbar
• ✅ Truth tracking (KF)
• ✅ Truth tracking (GSF)
• ✅ Truth tracking (GX2F)
• ✅ Truth tracking (KF refit)
• ✅ Truth tracking (GSF refit)
• ✅ CKF finding performance | trackfinding | single muon | truth smeared seeding
• ✅ CKF fitting performance | trackfinding | single muon | truth smeared seeding
• ✅ CKF track summary | trackfinding | single muon | truth smeared seeding
• ✅ Seeding trackfinding | single muon | truth estimated seeding
• ✅ CKF finding performance | trackfinding | single muon | truth estimated seeding
• ✅ CKF fitting performance | trackfinding | single muon | truth estimated seeding
• ✅ CKF track summary | trackfinding | single muon | truth estimated seeding
• ✅ Seeding trackfinding | single muon | default seeding
• ✅ CKF finding performance | trackfinding | single muon | default seeding
• 🔴 CKF fitting performance | trackfinding | single muon | default seeding
• ✅ CKF track summary | trackfinding | single muon | default seeding
• ✅ Seeding trackfinding | single muon | orthogonal seeding
• ✅ CKF finding performance | trackfinding | single muon | orthogonal seeding
• 🔴 CKF fitting performance | trackfinding | single muon | orthogonal seeding
• ✅ CKF track summary | trackfinding | single muon | orthogonal seeding
• ✅ Seeding trackfinding | 4 muon x 50 vertices | default seeding
• ✅ CKF finding performance | trackfinding | 4 muon x 50 vertices | default seeding
• 🔴 CKF fitting performance | trackfinding | 4 muon x 50 vertices | default seeding
• ✅ CKF track summary | trackfinding | 4 muon x 50 vertices | default seeding
• ✅ Ambisolver finding performance | trackfinding | 4 muon x 50 vertices | default seeding
• ✅ IVF notime | trackfinding | 4 muon x 50 vertices | default seeding
• ✅ AMVF gauss notime | trackfinding | 4 muon x 50 vertices | default seeding
• ✅ AMVF grid time | trackfinding | 4 muon x 50 vertices | default seeding
• ✅ Seeding trackfinding | ttbar with 200 pileup | default seeding
• ✅ CKF finding performance | trackfinding | ttbar with 200 pileup | default seeding
• ✅ CKF fitting performance | trackfinding | ttbar with 200 pileup | default seeding
• ✅ CKF track summary | trackfinding | ttbar with 200 pileup | default seeding
• ✅ Ambisolver finding performance | trackfinding | ttbar with 200 pileup | default seeding
• ✅ ML Ambisolver | trackfinding | ttbar with 200 pileup | default seeding
• ✅ AMVF gauss notime | trackfinding | ttbar with 200 pileup | default seeding
• ✅ AMVF grid time | trackfinding | ttbar with 200 pileup | default seeding
• 🔵️ Comparison - Truth tracking (GX2F vs KF)

[sonarqubecloud]

Quality Gate passed

Issues
0 New issues
0 Accepted issues

Measures
0 Security Hotspots
0.0% Coverage on New Code
0.0% Duplication on New Code

See analysis details on SonarQube Cloud