Add geometry classes (#1766)

These classes introduce ways to represent poses and provide easy ways to transform, rotate, and translate poses across 2d space. This classes will be especially useful for a planned odometry and kinematics suite.

Furthermore, these classes can also be used to simply represent waypoints on a field, do superstructure motion planning, etc.

wpilibc/src/main/native/cpp/geometry/Pose2d.cpp

@@ -0,0 +1,61 @@
+/*----------------------------------------------------------------------------*/
+/* Copyright (c) 2019 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.                                                               */
+/*----------------------------------------------------------------------------*/
+
+#include "frc/geometry/Pose2d.h"
+
+#include <cmath>
+
+using namespace frc;
+
+Pose2d::Pose2d(Translation2d translation, Rotation2d rotation)
+    : m_translation(translation), m_rotation(rotation) {}
+
+Pose2d::Pose2d(double x, double y, Rotation2d rotation)
+    : m_translation(x, y), m_rotation(rotation) {}
+
+Pose2d Pose2d::operator+(const Transform2d& other) const {
+  return TransformBy(other);
+}
+
+Pose2d& Pose2d::operator+=(const Transform2d& other) {
+  m_translation += other.Translation().RotateBy(m_rotation);
+  m_rotation += other.Rotation();
+  return *this;
+}
+
+Pose2d Pose2d::TransformBy(const Transform2d& other) const {
+  return {m_translation + (other.Translation().RotateBy(m_rotation)),
+          m_rotation + other.Rotation()};
+}
+
+Pose2d Pose2d::RelativeTo(const Pose2d& other) const {
+  const Transform2d transform{other, *this};
+  return {transform.Translation(), transform.Rotation()};
+}
+
+Pose2d Pose2d::Exp(const Twist2d& twist) const {
+  const auto dx = twist.dx;
+  const auto dy = twist.dy;
+  const auto dtheta = twist.dtheta;
+
+  const auto sinTheta = std::sin(dtheta);
+  const auto cosTheta = std::cos(dtheta);
+
+  double s, c;
+  if (std::abs(dtheta) < 1E-9) {
+    s = 1.0 - 1.0 / 6.0 * dtheta * dtheta;
+    c = 0.5 * dtheta;
+  } else {
+    s = sinTheta / dtheta;
+    c = (1 - cosTheta) / dtheta;
+  }
+
+  const Transform2d transform{Translation2d{dx * s - dy * c, dx * c + dy * s},
+                              Rotation2d{cosTheta, sinTheta}};
+
+  return *this + transform;
+}

wpilibc/src/main/native/cpp/geometry/Rotation2d.cpp

@@ -0,0 +1,60 @@
+/*----------------------------------------------------------------------------*/
+/* Copyright (c) 2019 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.                                                               */
+/*----------------------------------------------------------------------------*/
+
+#include "frc/geometry/Rotation2d.h"
+
+#include <cmath>
+
+using namespace frc;
+
+Rotation2d::Rotation2d(double value)
+    : m_value(value), m_cos(std::cos(value)), m_sin(std::sin(value)) {}
+
+Rotation2d::Rotation2d(double x, double y) {
+  const auto magnitude = std::hypot(x, y);
+  if (magnitude > 1e-6) {
+    m_sin = y / magnitude;
+    m_cos = x / magnitude;
+  } else {
+    m_sin = 0.0;
+    m_cos = 1.0;
+  }
+  m_value = std::atan2(m_sin, m_cos);
+}
+
+Rotation2d Rotation2d::FromDegrees(double degrees) {
+  return Rotation2d(Deg2Rad(degrees));
+}
+
+Rotation2d Rotation2d::operator+(const Rotation2d& other) const {
+  return RotateBy(other);
+}
+
+Rotation2d& Rotation2d::operator+=(const Rotation2d& other) {
+  double cos = Cos() * other.Cos() - Sin() * other.Sin();
+  double sin = Cos() * other.Sin() + Sin() * other.Cos();
+  m_cos = cos;
+  m_sin = sin;
+  m_value = std::atan2(m_sin, m_cos);
+  return *this;
+}
+
+Rotation2d Rotation2d::operator-(const Rotation2d& other) const {
+  return *this + -other;
+}
+
+Rotation2d& Rotation2d::operator-=(const Rotation2d& other) {
+  *this += -other;
+  return *this;
+}
+
+Rotation2d Rotation2d::operator-() const { return Rotation2d(-m_value); }
+
+Rotation2d Rotation2d::RotateBy(const Rotation2d& other) const {
+  return {Cos() * other.Cos() - Sin() * other.Sin(),
+          Cos() * other.Sin() + Sin() * other.Cos()};
+}

wpilibc/src/main/native/cpp/geometry/Transform2d.cpp

@@ -0,0 +1,25 @@
+/*----------------------------------------------------------------------------*/
+/* Copyright (c) 2019 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.                                                               */
+/*----------------------------------------------------------------------------*/
+
+#include "frc/geometry/Transform2d.h"
+
+#include "frc/geometry/Pose2d.h"
+
+using namespace frc;
+
+Transform2d::Transform2d(Pose2d initial, Pose2d final) {
+  // We are rotating the difference between the translations
+  // using a clockwise rotation matrix. This transforms the global
+  // delta into a local delta (relative to the initial pose).
+  m_translation = (final.Translation() - initial.Translation())
+                      .RotateBy(-initial.Rotation());
+
+  m_rotation = final.Rotation() - initial.Rotation();
+}
+
+Transform2d::Transform2d(Translation2d translation, Rotation2d rotation)
+    : m_translation(translation), m_rotation(rotation) {}

wpilibc/src/main/native/cpp/geometry/Translation2d.cpp

@@ -0,0 +1,65 @@
+/*----------------------------------------------------------------------------*/
+/* Copyright (c) 2019 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.                                                               */
+/*----------------------------------------------------------------------------*/
+
+#include "frc/geometry/Translation2d.h"
+
+#include <cmath>
+
+using namespace frc;
+
+Translation2d::Translation2d(double x, double y) : m_x(x), m_y(y) {}
+
+double Translation2d::Distance(const Translation2d& other) const {
+  return std::hypot(other.m_x - m_x, other.m_y - m_y);
+}
+
+double Translation2d::Norm() const { return std::hypot(m_x, m_y); }
+
+Translation2d Translation2d::RotateBy(const Rotation2d& other) const {
+  return {m_x * other.Cos() - m_y * other.Sin(),
+          m_x * other.Sin() + m_y * other.Cos()};
+}
+
+Translation2d Translation2d::operator+(const Translation2d& other) const {
+  return {X() + other.X(), Y() + other.Y()};
+}
+
+Translation2d& Translation2d::operator+=(const Translation2d& other) {
+  m_x += other.m_x;
+  m_y += other.m_y;
+  return *this;
+}
+
+Translation2d Translation2d::operator-(const Translation2d& other) const {
+  return *this + -other;
+}
+
+Translation2d& Translation2d::operator-=(const Translation2d& other) {
+  *this += -other;
+  return *this;
+}
+
+Translation2d Translation2d::operator-() const { return {-m_x, -m_y}; }
+
+Translation2d Translation2d::operator*(double scalar) const {
+  return {scalar * m_x, scalar * m_y};
+}
+
+Translation2d& Translation2d::operator*=(double scalar) {
+  m_x *= scalar;
+  m_y *= scalar;
+  return *this;
+}
+
+Translation2d Translation2d::operator/(double scalar) const {
+  return *this * (1.0 / scalar);
+}
+
+Translation2d& Translation2d::operator/=(double scalar) {
+  *this *= (1.0 / scalar);
+  return *this;
+}