[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/spline/SplineHelper.h

@@ -0,0 +1,109 @@
+/*----------------------------------------------------------------------------*/
+/* 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 <array>
+#include <utility>
+#include <vector>
+
+#include "frc/spline/CubicHermiteSpline.h"
+#include "frc/spline/QuinticHermiteSpline.h"
+
+namespace frc {
+/**
+ * Helper class that is used to generate cubic and quintic splines from user
+ * provided waypoints.
+ */
+class SplineHelper {
+ public:
+  /**
+   * Returns 2 cubic control vectors from a set of exterior waypoints and
+   * interior translations.
+   *
+   * @param start             The starting pose.
+   * @param interiorWaypoints The interior waypoints.
+   * @param end               The ending pose.
+   * @return 2 cubic control vectors.
+   */
+  static std::array<Spline<3>::ControlVector, 2>
+  CubicControlVectorsFromWaypoints(
+      const Pose2d& start, const std::vector<Translation2d>& interiorWaypoints,
+      const Pose2d& end);
+
+  /**
+   * Returns quintic control vectors from a set of waypoints.
+   *
+   * @param waypoints The waypoints
+   * @return List of control vectors
+   */
+  static std::vector<Spline<5>::ControlVector>
+  QuinticControlVectorsFromWaypoints(const std::vector<Pose2d>& waypoints);
+
+  /**
+   * Returns a set of cubic splines corresponding to the provided control
+   * vectors. The user is free to set the direction of the start and end
+   * point. The directions for the middle waypoints are determined
+   * automatically to ensure continuous curvature throughout the path.
+   *
+   * The derivation for the algorithm used can be found here:
+   * <https://www.uio.no/studier/emner/matnat/ifi/nedlagte-emner/INF-MAT4350/h08/undervisningsmateriale/chap7alecture.pdf>
+   *
+   * @param start The starting control vector.
+   * @param waypoints The middle waypoints. This can be left blank if you
+   * only wish to create a path with two waypoints.
+   * @param end The ending control vector.
+   *
+   * @return A vector of cubic hermite splines that interpolate through the
+   * provided waypoints.
+   */
+  static std::vector<CubicHermiteSpline> CubicSplinesFromControlVectors(
+      const Spline<3>::ControlVector& start,
+      std::vector<Translation2d> waypoints,
+      const Spline<3>::ControlVector& end);
+
+  /**
+   * Returns a set of quintic splines corresponding to the provided control
+   * vectors. The user is free to set the direction of all waypoints. Continuous
+   * curvature is guaranteed throughout the path.
+   *
+   * @param controlVectors The control vectors.
+   * @return A vector of quintic hermite splines that interpolate through the
+   * provided waypoints.
+   */
+  static std::vector<QuinticHermiteSpline> QuinticSplinesFromControlVectors(
+      const std::vector<Spline<5>::ControlVector>& controlVectors);
+
+ private:
+  static Spline<3>::ControlVector CubicControlVector(double scalar,
+                                                     const Pose2d& point) {
+    return {{point.X().to<double>(), scalar * point.Rotation().Cos()},
+            {point.Y().to<double>(), scalar * point.Rotation().Sin()}};
+  }
+
+  static Spline<5>::ControlVector QuinticControlVector(double scalar,
+                                                       const Pose2d& point) {
+    return {{point.X().to<double>(), scalar * point.Rotation().Cos(), 0.0},
+            {point.Y().to<double>(), scalar * point.Rotation().Sin(), 0.0}};
+  }
+
+  /**
+   * Thomas algorithm for solving tridiagonal systems Af = d.
+   *
+   * @param a the values of A above the diagonal
+   * @param b the values of A on the diagonal
+   * @param c the values of A below the diagonal
+   * @param d the vector on the rhs
+   * @param solutionVector the unknown (solution) vector, modified in-place
+   */
+  static void ThomasAlgorithm(const std::vector<double>& a,
+                              const std::vector<double>& b,
+                              const std::vector<double>& c,
+                              const std::vector<double>& d,
+                              std::vector<double>* solutionVector);
+};
+}  // namespace frc