[wpimath] Move math functionality into new wpimath library (#2629)

The wpimath library is a new library designed to separate the reusable math functionality
from the common utility library (wpiutil) and the hardware-dependent library (wpilibc/j).

Package names / include file names were NOT changed to minimize breakage.  In a future year
it would be good to revamp these for a more uniform user experience and to reduce the risk
of accidental naming conflicts.

While theoretically all of this functionality could be placed into wpiutil, several pieces
of this library (e.g. DARE) are very time-consuming to compile, so it's nice to avoid this
expense for users who only want cscore or ntcore.  It also allows for easy future separation
of build tasks vs number of workers on memory-constrained machines.

This moves the following functionality from wpiutil into wpimath:
- Eigen
- ejml
- Drake
- DARE
- wpiutil.math package (Matrix etc)
- units

And the following functionality from wpilibc/j into wpimath:
- Geometry
- Kinematics
- Spline
- Trajectory
- LinearFilter
- MedianFilter
- Feed-forward controllers

wpimath/src/main/native/include/frc/geometry/Rotation2d.h

@@ -0,0 +1,193 @@
+/*----------------------------------------------------------------------------*/
+/* Copyright (c) 2019-2020 FIRST. All Rights Reserved.                        */
+/* Open Source Software - may be modified and shared by FRC teams. The code   */
+/* must be accompanied by the FIRST BSD license file in the root directory of */
+/* the project.                                                               */
+/*----------------------------------------------------------------------------*/
+
+#pragma once
+
+#include <units/angle.h>
+
+namespace wpi {
+class json;
+}  // namespace wpi
+
+namespace frc {
+
+/**
+ * A rotation in a 2d coordinate frame represented a point on the unit circle
+ * (cosine and sine).
+ */
+class Rotation2d {
+ public:
+  /**
+   * Constructs a Rotation2d with a default angle of 0 degrees.
+   */
+  constexpr Rotation2d() = default;
+
+  /**
+   * Constructs a Rotation2d with the given radian value.
+   *
+   * @param value The value of the angle in radians.
+   */
+  Rotation2d(units::radian_t value);  // NOLINT(runtime/explicit)
+
+  /**
+   * Constructs a Rotation2d with the given degree value.
+   *
+   * @param value The value of the angle in degrees.
+   */
+  Rotation2d(units::degree_t value);  // NOLINT(runtime/explicit)
+
+  /**
+   * 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.
+   */
+  Rotation2d(double x, double y);
+
+  /**
+   * Adds two rotations together, with the result being bounded between -pi and
+   * pi.
+   *
+   * For example, Rotation2d.FromDegrees(30) + Rotation2d.FromDegrees(60) =
+   * Rotation2d{-pi/2}
+   *
+   * @param other The rotation to add.
+   *
+   * @return The sum of the two rotations.
+   */
+  Rotation2d operator+(const Rotation2d& other) const;
+
+  /**
+   * Adds a rotation to the current rotation.
+   *
+   * This is similar to the + operator except that it mutates the current
+   * object.
+   *
+   * @param other The rotation to add.
+   *
+   * @return The reference to the new mutated object.
+   */
+  Rotation2d& operator+=(const Rotation2d& other);
+
+  /**
+   * Subtracts the new rotation from the current rotation and returns the new
+   * rotation.
+   *
+   * For example, Rotation2d.FromDegrees(10) - Rotation2d.FromDegrees(100) =
+   * Rotation2d{-pi/2}
+   *
+   * @param other The rotation to subtract.
+   *
+   * @return The difference between the two rotations.
+   */
+  Rotation2d operator-(const Rotation2d& other) const;
+
+  /**
+   * Subtracts the new rotation from the current rotation.
+   *
+   * This is similar to the - operator except that it mutates the current
+   * object.
+   *
+   * @param other The rotation to subtract.
+   *
+   * @return The reference to the new mutated object.
+   */
+  Rotation2d& operator-=(const Rotation2d& 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.
+   */
+  Rotation2d operator-() const;
+
+  /**
+   * Multiplies the current rotation by a scalar.
+   * @param scalar The scalar.
+   *
+   * @return The new scaled Rotation2d.
+   */
+  Rotation2d operator*(double scalar) const;
+
+  /**
+   * Checks equality between this Rotation2d and another object.
+   *
+   * @param other The other object.
+   * @return Whether the two objects are equal.
+   */
+  bool operator==(const Rotation2d& other) const;
+
+  /**
+   * Checks inequality between this Rotation2d and another object.
+   *
+   * @param other The other object.
+   * @return Whether the two objects are not equal.
+   */
+  bool operator!=(const Rotation2d& other) const;
+
+  /**
+   * Adds the new rotation to the current rotation using a rotation matrix.
+   *
+   * [cos_new]   [other.cos, -other.sin][cos]
+   * [sin_new] = [other.sin,  other.cos][sin]
+   *
+   * value_new = std::atan2(cos_new, sin_new)
+   *
+   * @param other The rotation to rotate by.
+   *
+   * @return The new rotated Rotation2d.
+   */
+  Rotation2d RotateBy(const Rotation2d& other) const;
+
+  /**
+   * Returns the radian value of the rotation.
+   *
+   * @return The radian value of the rotation.
+   */
+  units::radian_t Radians() const { return m_value; }
+
+  /**
+   * Returns the degree value of the rotation.
+   *
+   * @return The degree value of the rotation.
+   */
+  units::degree_t Degrees() const { return m_value; }
+
+  /**
+   * Returns the cosine of the rotation.
+   *
+   * @return The cosine of the rotation.
+   */
+  double Cos() const { return m_cos; }
+
+  /**
+   * Returns the sine of the rotation.
+   *
+   * @return The sine of the rotation.
+   */
+  double Sin() const { return m_sin; }
+
+  /**
+   * Returns the tangent of the rotation.
+   *
+   * @return The tangent of the rotation.
+   */
+  double Tan() const { return m_sin / m_cos; }
+
+ private:
+  units::radian_t m_value = 0_rad;
+  double m_cos = 1;
+  double m_sin = 0;
+};
+
+void to_json(wpi::json& json, const Rotation2d& rotation);
+
+void from_json(const wpi::json& json, Rotation2d& rotation);
+
+}  // namespace frc