Rotation2d.hpp

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// Copyright (c) FIRST and other WPILib contributors.
// Open Source Software; you can modify and/or share it under the terms of
// the WPILib BSD license file in the root directory of this project.
 
#pragma once
 
#include <type_traits>
#include <utility>
 
#include <Eigen/Core>
#include <gcem.hpp>
 
#include "wpi/math/linalg/ct_matrix.hpp"
#include "wpi/math/util/MathShared.hpp"
#include "wpi/units/angle.hpp"
#include "wpi/util/StackTrace.hpp"
#include "wpi/util/SymbolExports.hpp"
#include "wpi/util/json_fwd.hpp"
 
namespace wpi::math {
 
/**
 * A rotation in a 2D coordinate frame represented by a point on the unit circle
 * (cosine and sine).
 */
class WPILIB_DLLEXPORT Rotation2d {
 public:
  /**
   * Constructs a Rotation2d with a default angle of 0 degrees.
   */
  constexpr Rotation2d() = default;
 
  /**
   * Constructs a Rotation2d with the given angle.
   *
   * @param value The value of the angle.
   */
  constexpr Rotation2d(wpi::units::angle_unit auto value)  // NOLINT
      : m_cos{gcem::cos(value.template convert<wpi::units::radian>().value())},
        m_sin{gcem::sin(value.template convert<wpi::units::radian>().value())} {
  }
 
  /**
   * Constructs a Rotation2d with the given x and y (cosine and sine)
   * components. The x and y don't have to be normalized.
   *
   * @param x The x component or cosine of the rotation.
   * @param y The y component or sine of the rotation.
   */
  constexpr Rotation2d(double x, double y) {
    double magnitude = gcem::hypot(x, y);
    if (magnitude > 1e-6) {
      m_cos = x / magnitude;
      m_sin = y / magnitude;
    } else {
      m_cos = 1.0;
      m_sin = 0.0;
      if (!std::is_constant_evaluated()) {
        wpi::math::MathSharedStore::ReportError(
            "x and y components of Rotation2d are zero\n{}",
            wpi::util::GetStackTrace(1));
      }
    }
  }
 
  /**
   * Constructs a Rotation2d from a rotation matrix.
   *
   * @param rotationMatrix The rotation matrix.
   * @throws std::domain_error if the rotation matrix isn't special orthogonal.
   */
  constexpr explicit Rotation2d(const Eigen::Matrix2d& rotationMatrix) {
    auto impl =
        []<typename Matrix2d>(const Matrix2d& R) -> std::pair<double, double> {
      // Require that the rotation matrix is special orthogonal. This is true if
      // the matrix is orthogonal (RRᵀ = I) and normalized (determinant is 1).
      if ((R * R.transpose() - Matrix2d::Identity()).norm() > 1e-9) {
        throw std::domain_error("Rotation matrix isn't orthogonal");
      }
      // HACK: Uses ct_matrix instead of <Eigen/LU> for determinant because
      //       including <Eigen/LU> doubles compilation times on MSVC, even if
      //       this constructor is unused. MSVC's frontend inefficiently parses
      //       large headers; GCC and Clang are largely unaffected.
      if (gcem::abs(ct_matrix{R}.determinant() - 1.0) > 1e-9) {
        throw std::domain_error(
            "Rotation matrix is orthogonal but not special orthogonal");
      }
 
      // R = [cosθ  −sinθ]
      //     [sinθ   cosθ]
      return {R(0, 0), R(1, 0)};
    };
 
    if (std::is_constant_evaluated()) {
      auto cossin = impl(ct_matrix2d{rotationMatrix});
      m_cos = std::get<0>(cossin);
      m_sin = std::get<1>(cossin);
    } else {
      auto cossin = impl(rotationMatrix);
      m_cos = std::get<0>(cossin);
      m_sin = std::get<1>(cossin);
    }
  }
 
  /**
   * Adds two rotations together, with the result being bounded between -π and
   * π.
   *
   * For example, <code>Rotation2d{30_deg} + Rotation2d{60_deg}</code> equals
   * <code>Rotation2d{wpi::units::radian_t{std::numbers::pi/2.0}}</code>
   *
   * @param other The rotation to add.
   *
   * @return The sum of the two rotations.
   */
  constexpr Rotation2d operator+(const Rotation2d& other) const {
    return RotateBy(other);
  }
 
  /**
   * Returns this rotation relative to another rotation.
   *
   * For example, <code>Rotation2d{10_deg} - Rotation2d{100_deg}</code> equals
   * <code>Rotation2d{wpi::units::radian_t{-std::numbers::pi/2.0}}</code>
   *
   * @param other The rotation to subtract.
   *
   * @return The difference between the two rotations.
   */
  constexpr Rotation2d operator-(const Rotation2d& other) const {
    return *this + -other;
  }
 
  /**
   * Takes the inverse of the current rotation. This is simply the negative of
   * the current angular value.
   *
   * @return The inverse of the current rotation.
   */
  constexpr Rotation2d operator-() const { return Rotation2d{m_cos, -m_sin}; }
 
  /**
   * Multiplies the current rotation by a scalar.
   *
   * @param scalar The scalar.
   *
   * @return The new scaled Rotation2d.
   */
  constexpr Rotation2d operator*(double scalar) const {
    return Rotation2d{Radians() * scalar};
  }
 
  /**
   * Divides the current rotation by a scalar.
   *
   * @param scalar The scalar.
   *
   * @return The new scaled Rotation2d.
   */
  constexpr Rotation2d operator/(double scalar) const {
    return *this * (1.0 / scalar);
  }
 
  /**
   * Checks equality between this Rotation2d and another object.
   *
   * @param other The other object.
   * @return Whether the two objects are equal.
   */
  constexpr bool operator==(const Rotation2d& other) const {
    return gcem::hypot(Cos() - other.Cos(), Sin() - other.Sin()) < 1E-9;
  }
 
  /**
   * Adds the new rotation to the current rotation using a rotation matrix.
   *
   * <pre>
   * [cos_new]   [other.cos, -other.sin][cos]
   * [sin_new] = [other.sin,  other.cos][sin]
   * value_new = std::atan2(sin_new, cos_new)
   * </pre>
   *
   * @param other The rotation to rotate by.
   *
   * @return The new rotated Rotation2d.
   */
  constexpr Rotation2d RotateBy(const Rotation2d& other) const {
    return {Cos() * other.Cos() - Sin() * other.Sin(),
            Cos() * other.Sin() + Sin() * other.Cos()};
  }
 
  /**
   * Returns the current rotation relative to the given rotation.
   *
   * @param other The rotation describing the orientation of the new coordinate
   * frame that the current rotation will be converted into.
   *
   * @return The current rotation relative to the new orientation of the
   * coordinate frame.
   */
  constexpr Rotation2d RelativeTo(const Rotation2d& other) const {
    return RotateBy(-other);
  }
 
  /**
   * Returns matrix representation of this rotation.
   */
  constexpr Eigen::Matrix2d ToMatrix() const {
    // R = [cosθ  −sinθ]
    //     [sinθ   cosθ]
    return Eigen::Matrix2d{{m_cos, -m_sin}, {m_sin, m_cos}};
  }
 
  /**
   * Returns the radian value of the rotation constrained within [-π, π].
   *
   * @return The radian value of the rotation constrained within [-π, π].
   */
  constexpr wpi::units::radian_t Radians() const {
    return wpi::units::radian_t{gcem::atan2(m_sin, m_cos)};
  }
 
  /**
   * Returns the degree value of the rotation constrained within [-180, 180].
   *
   * @return The degree value of the rotation constrained within [-180, 180].
   */
  constexpr wpi::units::degree_t Degrees() const { return Radians(); }
 
  /**
   * Returns the cosine of the rotation.
   *
   * @return The cosine of the rotation.
   */
  constexpr double Cos() const { return m_cos; }
 
  /**
   * Returns the sine of the rotation.
   *
   * @return The sine of the rotation.
   */
  constexpr double Sin() const { return m_sin; }
 
  /**
   * Returns the tangent of the rotation.
   *
   * @return The tangent of the rotation.
   */
  constexpr double Tan() const { return Sin() / Cos(); }
 
 private:
  double m_cos = 1;
  double m_sin = 0;
};
 
WPILIB_DLLEXPORT
void to_json(wpi::util::json& json, const Rotation2d& rotation);
 
WPILIB_DLLEXPORT
void from_json(const wpi::util::json& json, Rotation2d& rotation);
 
}  // namespace wpi::math
 
#include "wpi/math/geometry/proto/Rotation2dProto.hpp"
#include "wpi/math/geometry/struct/Rotation2dStruct.hpp"