test_so2.cpp

// Copyright (C) 2021-2022 Petter Nilsson. MIT License.

#include <gtest/gtest.h>

#include "smooth/so2.hpp"
#include "smooth/so3.hpp"

TEST(SO2, Angle)
{
  for (auto i = 0; i != 5; ++i) {
    const auto g1 = smooth::SO2d::Random();
    const auto g2 = smooth::SO2d::Random();
    {
      smooth::SO2d g_prod(g1.angle() + g2.angle());

      ASSERT_TRUE(g_prod.isApprox(g1 * g2));
      ASSERT_LE(g1.angle(), M_PI);
      ASSERT_GE(g1.angle(), -M_PI);
    }
    {
      smooth::SO2d g_prod(g1.angle_cw() + g2.angle_cw());

      ASSERT_TRUE(g_prod.isApprox(g1 * g2));
      ASSERT_LE(g1.angle_cw(), 0);
      ASSERT_GE(g1.angle_cw(), -2. * M_PI);
    }
    {
      smooth::SO2d g_prod(g1.angle_ccw() + g2.angle_ccw());

      ASSERT_TRUE(g_prod.isApprox(g1 * g2));
      ASSERT_LE(g1.angle_ccw(), 2. * M_PI);
      ASSERT_GE(g1.angle_ccw(), 0);
    }
  }
}

TEST(SO2, Complex)
{
  for (auto i = 0; i != 5; ++i) {
    const auto g1 = smooth::SO2d::Random();
    const auto g2 = smooth::SO2d::Random();

    smooth::SO2d g_prod(g1.u1() * g2.u1());

    ASSERT_TRUE(g_prod.isApprox(g1 * g2));
  }
}

TEST(SO2, Action)
{
  for (auto i = 0; i != 5; ++i) {
    const auto g1 = smooth::SO2d::Random();
    auto ex_rot   = g1 * Eigen::Vector2d::UnitX();
    auto ey_rot   = g1 * Eigen::Vector2d::UnitY();

    ASSERT_TRUE(ex_rot.isApprox(g1.matrix().col(0)));
    ASSERT_TRUE(ey_rot.isApprox(g1.matrix().col(1)));
  }
}

TEST(SO2, LiftProject)
{
  for (auto i = 0u; i != 5; ++i) {
    const smooth::SO2d g = smooth::SO2d::Random();
    const auto so3       = g.lift_so3();
    const auto so2       = so3.project_so2();

    ASSERT_TRUE(so2.isApprox(g, 1e-6));
  }
}