[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/trajectory/TrapezoidProfile.inc

@@ -0,0 +1,165 @@
+/*----------------------------------------------------------------------------*/
+/* 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 <algorithm>
+
+#include "units/math.h"
+
+namespace frc {
+template <class Distance>
+TrapezoidProfile<Distance>::TrapezoidProfile(Constraints constraints,
+                                             State goal, State initial)
+    : m_direction{ShouldFlipAcceleration(initial, goal) ? -1 : 1},
+      m_constraints(constraints),
+      m_initial(Direct(initial)),
+      m_goal(Direct(goal)) {
+  if (m_initial.velocity > m_constraints.maxVelocity) {
+    m_initial.velocity = m_constraints.maxVelocity;
+  }
+
+  // Deal with a possibly truncated motion profile (with nonzero initial or
+  // final velocity) by calculating the parameters as if the profile began and
+  // ended at zero velocity
+  units::second_t cutoffBegin =
+      m_initial.velocity / m_constraints.maxAcceleration;
+  Distance_t cutoffDistBegin =
+      cutoffBegin * cutoffBegin * m_constraints.maxAcceleration / 2.0;
+
+  units::second_t cutoffEnd = m_goal.velocity / m_constraints.maxAcceleration;
+  Distance_t cutoffDistEnd =
+      cutoffEnd * cutoffEnd * m_constraints.maxAcceleration / 2.0;
+
+  // Now we can calculate the parameters as if it was a full trapezoid instead
+  // of a truncated one
+
+  Distance_t fullTrapezoidDist =
+      cutoffDistBegin + (m_goal.position - m_initial.position) + cutoffDistEnd;
+  units::second_t accelerationTime =
+      m_constraints.maxVelocity / m_constraints.maxAcceleration;
+
+  Distance_t fullSpeedDist =
+      fullTrapezoidDist -
+      accelerationTime * accelerationTime * m_constraints.maxAcceleration;
+
+  // Handle the case where the profile never reaches full speed
+  if (fullSpeedDist < Distance_t(0)) {
+    accelerationTime =
+        units::math::sqrt(fullTrapezoidDist / m_constraints.maxAcceleration);
+    fullSpeedDist = Distance_t(0);
+  }
+
+  m_endAccel = accelerationTime - cutoffBegin;
+  m_endFullSpeed = m_endAccel + fullSpeedDist / m_constraints.maxVelocity;
+  m_endDeccel = m_endFullSpeed + accelerationTime - cutoffEnd;
+}
+
+template <class Distance>
+typename TrapezoidProfile<Distance>::State
+TrapezoidProfile<Distance>::Calculate(units::second_t t) const {
+  State result = m_initial;
+
+  if (t < m_endAccel) {
+    result.velocity += t * m_constraints.maxAcceleration;
+    result.position +=
+        (m_initial.velocity + t * m_constraints.maxAcceleration / 2.0) * t;
+  } else if (t < m_endFullSpeed) {
+    result.velocity = m_constraints.maxVelocity;
+    result.position += (m_initial.velocity +
+                        m_endAccel * m_constraints.maxAcceleration / 2.0) *
+                           m_endAccel +
+                       m_constraints.maxVelocity * (t - m_endAccel);
+  } else if (t <= m_endDeccel) {
+    result.velocity =
+        m_goal.velocity + (m_endDeccel - t) * m_constraints.maxAcceleration;
+    units::second_t timeLeft = m_endDeccel - t;
+    result.position =
+        m_goal.position -
+        (m_goal.velocity + timeLeft * m_constraints.maxAcceleration / 2.0) *
+            timeLeft;
+  } else {
+    result = m_goal;
+  }
+
+  return Direct(result);
+}
+
+template <class Distance>
+units::second_t TrapezoidProfile<Distance>::TimeLeftUntil(
+    Distance_t target) const {
+  Distance_t position = m_initial.position * m_direction;
+  Velocity_t velocity = m_initial.velocity * m_direction;
+
+  units::second_t endAccel = m_endAccel * m_direction;
+  units::second_t endFullSpeed = m_endFullSpeed * m_direction - endAccel;
+
+  if (target < position) {
+    endAccel *= -1.0;
+    endFullSpeed *= -1.0;
+    velocity *= -1.0;
+  }
+
+  endAccel = units::math::max(endAccel, 0_s);
+  endFullSpeed = units::math::max(endFullSpeed, 0_s);
+  units::second_t endDeccel = m_endDeccel - endAccel - endFullSpeed;
+  endDeccel = units::math::max(endDeccel, 0_s);
+
+  const Acceleration_t acceleration = m_constraints.maxAcceleration;
+  const Acceleration_t decceleration = -m_constraints.maxAcceleration;
+
+  Distance_t distToTarget = units::math::abs(target - position);
+
+  if (distToTarget < Distance_t(1e-6)) {
+    return 0_s;
+  }
+
+  Distance_t accelDist =
+      velocity * endAccel + 0.5 * acceleration * endAccel * endAccel;
+
+  Velocity_t deccelVelocity;
+  if (endAccel > 0_s) {
+    deccelVelocity = units::math::sqrt(
+        units::math::abs(velocity * velocity + 2 * acceleration * accelDist));
+  } else {
+    deccelVelocity = velocity;
+  }
+
+  Distance_t deccelDist =
+      deccelVelocity * endDeccel + 0.5 * decceleration * endDeccel * endDeccel;
+
+  deccelDist = units::math::max(deccelDist, Distance_t(0));
+
+  Distance_t fullSpeedDist = m_constraints.maxVelocity * endFullSpeed;
+
+  if (accelDist > distToTarget) {
+    accelDist = distToTarget;
+    fullSpeedDist = Distance_t(0);
+    deccelDist = Distance_t(0);
+  } else if (accelDist + fullSpeedDist > distToTarget) {
+    fullSpeedDist = distToTarget - accelDist;
+    deccelDist = Distance_t(0);
+  } else {
+    deccelDist = distToTarget - fullSpeedDist - accelDist;
+  }
+
+  units::second_t accelTime =
+      (-velocity + units::math::sqrt(units::math::abs(
+                       velocity * velocity + 2 * acceleration * accelDist))) /
+      acceleration;
+
+  units::second_t deccelTime =
+      (-deccelVelocity +
+       units::math::sqrt(units::math::abs(deccelVelocity * deccelVelocity +
+                                          2 * decceleration * deccelDist))) /
+      decceleration;
+
+  units::second_t fullSpeedTime = fullSpeedDist / m_constraints.maxVelocity;
+
+  return accelTime + fullSpeedTime + deccelTime;
+}
+}  // namespace frc