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feat: VectorHelpers - Add generic eta method #5598

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Add generic eta
Jun 16, 2026
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14 changes: 14 additions & 0 deletions Core/include/Acts/Utilities/VectorHelpers.hpp
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Expand Up @@ -143,6 +143,20 @@
}
}

/// Calculate the pseudo rapdity from anything implementing a method
/// like `theta()` returning anything convertible to `double`.
/// @tparam T anything that has a theta method
/// @param v Any type that implements a theta method
/// @return The pseudo rapidity value
template <typename T>
double eta(const T& v) noexcept

@benjaminhuth benjaminhuth Jun 17, 2026

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Hmm why not double eta(double theta), wouldn't that be even more generic?

@junggjo9 junggjo9 Jun 17, 2026

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I was taking the phi implementation as my template here. Yeah, that would be another option

@andiwand andiwand Jun 17, 2026

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in the best case we could have both. we have many implementations for eta -> theta and the other way flying around which could be centralized. but a scalar transformation is out of scope for vector helpers I believe

@junggjo9 junggjo9 Jun 17, 2026

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Do we already have a central eta implementation?

@benjaminhuth benjaminhuth Jun 17, 2026 •
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Hmm yeah make sense that its not for vector helpers. But I think code like eta(myFancyType) which internally calls myFancyType.theta() is just less transparent as eta(myFancyType.theta())...

So I don't like the phi function either I think :D

@andiwand andiwand Jun 17, 2026

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ah we actually have a helper

acts/Core/include/Acts/Utilities/AngleHelpers.hpp

Lines 35 to 89 in 0dda19a

/// Conversion limits for `double` eta/theta calculations.
///
/// Defines safe min/max theta and eta values for `double` precision.
template <>
struct EtaThetaConversionTraits<double> {
/// Minimum theta value for double precision
static constexpr double minTheta = 1e-12;
/// Maximum theta value for double precision
static constexpr double maxTheta = std::numbers::pi - minTheta;
/// Maximum eta value for double precision
static constexpr double maxEta = 700.0;
/// Minimum eta value for double precision
static constexpr double minEta = -maxEta;
};
/// Calculate the pseudorapidity from the polar angle theta.
///
/// This function aims to be FPE safe and returns infinity for theta values
/// outside the floating point precision range.
///
/// @param theta is the polar angle in radian towards the z-axis.
///
/// @return the pseudorapidity towards the z-axis.
template <typename Scalar>
Scalar etaFromTheta(Scalar theta) {
if (theta <= EtaThetaConversionTraits<Scalar>::minTheta) {
return std::numeric_limits<Scalar>::infinity();
}
if (theta >= EtaThetaConversionTraits<Scalar>::maxTheta) {
return -std::numeric_limits<Scalar>::infinity();
}
return -std::log(std::tan(theta / 2));
}
/// Calculate the polar angle theta from the pseudorapidity.
///
/// This function aims to be FPE safe and returns 0/pi for eta values outside
/// the floating point precision range.
///
/// @param eta is the pseudorapidity towards the z-axis.
///
/// @return the polar angle in radian towards the z-axis.
template <typename Scalar>
Scalar thetaFromEta(Scalar eta) {
if (eta <= EtaThetaConversionTraits<Scalar>::minEta) {
return std::numbers::pi_v<Scalar>;
}
if (eta >= EtaThetaConversionTraits<Scalar>::maxEta) {
return 0;
}
return 2 * std::atan(std::exp(-eta));
}

requires requires {

Check warning on line 153 in Core/include/Acts/Utilities/VectorHelpers.hpp

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Extract this requires expression into a named concept. 


See more on https://sonarcloud.io/project/issues?id=acts-project_acts&issues=AZ7SaitsGTnYtFigQtFH&open=AZ7SaitsGTnYtFigQtFH&pullRequest=5598
{ v.theta() } -> std::floating_point;
}
{
return -std::log(std::tan(0.5 * v.theta()));
}

/// @brief Fast evaluation of trigonomic functions.
///
/// @param direction for this evaluatoin
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