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ITS3: add cylinder parameterisation preserving zero gaussian curvature (#15260)
* ITS3: exploit symmetric matrices for interpolation Signed-off-by: Felix Schlepper <felix.schlepper@cern.ch> * ITS3: cleanup code Signed-off-by: Felix Schlepper <felix.schlepper@cern.ch> * ITS3: alignment for inextionsial surfaces Signed-off-by: Felix Schlepper <felix.schlepper@cern.ch> * ITS3: harmonize study and alignment wfx for misalignment Signed-off-by: Felix Schlepper <felix.schlepper@cern.ch> --------- Signed-off-by: Felix Schlepper <felix.schlepper@cern.ch>
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‎Detectors/Upgrades/ITS3/alignment/CMakeLists.txt‎

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o2_add_library(ITS3Align
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TARGETVARNAME targetName
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SOURCES src/AlignmentHierarchy.cxx
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src/AlignmentDOF.cxx
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src/AlignmentMath.cxx
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src/MisalignmentUtils.cxx
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src/AlignmentSensors.cxx
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src/AlignmentParams.cxx
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src/AlignmentTypes.cxx

‎Detectors/Upgrades/ITS3/alignment/README.md‎

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"calib": { "type": "legendre", "order": 1, "fix": [0, 2] }
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}
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]
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}```
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}
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```
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## In-existensional modes
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```json
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{
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"defaults": { "rigidBody": "fixed" },
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"rules": [
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{
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"match": "ITS3Layer1/ITS3CarbonForm0",
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"calib": {
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"type": "inextensional",
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"order": 2,
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"free": ["a_2", "b_2", "c_2", "d_2", "alpha", "beta"]
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}
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}
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]
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}
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```
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```json
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[
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{
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"id": 2,
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"inextensional": {
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"modes": {
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"2": [0.0008, -0.0005, 0.0006, -0.0007]
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},
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"alpha": 0.0004,
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"beta": -0.0003
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}
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}
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]
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```

‎Detectors/Upgrades/ITS3/alignment/include/ITS3Align/AlignmentDOF.h‎

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// Copyright 2019-2026 CERN and copyright holders of ALICE O2.
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// See https://alice-o2.web.cern.ch/copyright for details of the copyright holders.
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// All rights not expressly granted are reserved.
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//
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// This software is distributed under the terms of the GNU General Public
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// License v3 (GPL Version 3), copied verbatim in the file "COPYING".
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//
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// In applying this license CERN does not waive the privileges and immunities
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// granted to it by virtue of its status as an Intergovernmental Organization
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// or submit itself to any jurisdiction.
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#ifndef O2_ITS3_ALIGNMENT_DOF_H
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#define O2_ITS3_ALIGNMENT_DOF_H
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#include <algorithm>
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#include <cstdint>
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#include <format>
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#include <stdexcept>
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#include <string>
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#include <vector>
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#include <Eigen/Dense>
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struct DerivativeContext {
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int sensorID{-1};
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int layerID{-1};
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double measX{0.};
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double measAlpha{0.};
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double measZ{0.};
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double trkY{0.};
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double trkZ{0.};
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double snp{0.};
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double tgl{0.};
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double dydx{0.};
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double dzdx{0.};
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};
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// Generic set of DOF
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class DOFSet
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{
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public:
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enum class Type : uint8_t {
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RigidBody,
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Legendre,
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Inextensional
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};
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virtual ~DOFSet() = default;
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virtual Type type() const = 0;
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int nDOFs() const { return static_cast<int>(mFree.size()); }
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virtual std::string dofName(int idx) const = 0;
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virtual void fillDerivatives(const DerivativeContext& ctx, Eigen::Ref<Eigen::MatrixXd> out) const = 0;
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bool isFree(int idx) const { return mFree[idx]; }
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void setFree(int idx, bool f) { mFree[idx] = f; }
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void setAllFree(bool f) { std::fill(mFree.begin(), mFree.end(), f); }
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int nFreeDOFs() const
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{
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int n = 0;
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for (bool f : mFree) {
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n += f;
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}
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return n;
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}
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protected:
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DOFSet(int n) : mFree(n, true) {}
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std::vector<bool> mFree;
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};
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// Rigid body set
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class RigidBodyDOFSet final : public DOFSet
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{
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public:
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// indices for rigid body parameters in LOC frame
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enum RigidBodyDOF : uint8_t {
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TX = 0,
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TY,
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TZ,
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RX,
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RY,
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RZ,
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NDOF,
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};
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static constexpr const char* RigidBodyDOFNames[RigidBodyDOF::NDOF] = {"TX", "TY", "TZ", "RX", "RY", "RZ"};
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RigidBodyDOFSet() : DOFSet(NDOF) {}
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// mask: bitmask of free DOFs (bit i = DOF i is free)
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explicit RigidBodyDOFSet(uint8_t mask) : DOFSet(NDOF)
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{
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for (int i = 0; i < NDOF; ++i) {
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mFree[i] = (mask >> i) & 1;
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}
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}
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Type type() const override { return Type::RigidBody; }
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std::string dofName(int idx) const override { return RigidBodyDOFNames[idx]; }
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void fillDerivatives(const DerivativeContext& ctx, Eigen::Ref<Eigen::MatrixXd> out) const override;
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uint8_t mask() const
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{
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uint8_t m = 0;
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for (int i = 0; i < NDOF; ++i) {
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m |= (uint8_t(mFree[i]) << i);
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}
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return m;
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}
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};
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// Legendre DOFs
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// Describing radial misplacement
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class LegendreDOFSet final : public DOFSet
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{
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public:
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explicit LegendreDOFSet(int order) : DOFSet((order + 1) * (order + 2) / 2), mOrder(order) {}
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Type type() const override { return Type::Legendre; }
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int order() const { return mOrder; }
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std::string dofName(int idx) const override
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{
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int i = 0;
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while ((i + 1) * (i + 2) / 2 <= idx) {
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++i;
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}
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int j = idx - (i * (i + 1) / 2);
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return std::format("L({},{})", i, j);
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}
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void fillDerivatives(const DerivativeContext& ctx, Eigen::Ref<Eigen::MatrixXd> out) const override;
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private:
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int mOrder;
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};
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// In-extensional deformation DOFs for cylindrical half-shells
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// Fourier modes n=2..N: 4 params each (a_n, b_n, c_n, d_n)
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// Plus 2 non-periodic modes (alpha, beta) for the half-cylinder open edges
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// Total: 4*(N-1) + 2
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class InextensionalDOFSet final : public DOFSet
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{
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public:
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explicit InextensionalDOFSet(int maxOrder) : DOFSet((4 * (maxOrder - 1)) + 2), mMaxOrder(maxOrder)
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{
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if (maxOrder < 2) {
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// the rest is eq. to rigid body
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throw std::invalid_argument("InextensionalDOFSet requires maxOrder >= 2");
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}
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}
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Type type() const override { return Type::Inextensional; }
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int maxOrder() const { return mMaxOrder; }
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// number of periodic DOFs (before alpha, beta)
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int nPeriodic() const { return 4 * (mMaxOrder - 1); }
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// flat index layout: [a_2, b_2, c_2, d_2, a_3, b_3, c_3, d_3, ..., alpha, beta]
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// index of first DOF for mode n
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static int modeOffset(int n) { return 4 * (n - 2); }
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// indices of the non-periodic modes
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int alphaIdx() const { return nPeriodic(); }
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int betaIdx() const { return nPeriodic() + 1; }
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std::string dofName(int idx) const override
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{
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if (idx == alphaIdx()) {
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return "alpha";
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}
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if (idx == betaIdx()) {
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return "beta";
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}
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int n = (idx / 4) + 2;
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int sub = idx % 4;
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static constexpr const char* subNames[] = {"a", "b", "c", "d"};
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return std::format("{}_{}", subNames[sub], n);
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}
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void fillDerivatives(const DerivativeContext& ctx, Eigen::Ref<Eigen::MatrixXd> out) const override;
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private:
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int mMaxOrder;
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};
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#endif

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