math.cpp

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#define _USE_MATH_DEFINES
#include <cmath>
 
#define BOOST_TEST_MODULE COAL_MATH
#include <boost/test/included/unit_test.hpp>
 
#include "coal/data_types.h"
#include "coal/math/transform.h"
 
#include "coal/internal/intersect.h"
#include "coal/internal/tools.h"
 
using namespace coal;
 
BOOST_AUTO_TEST_CASE(vec_test_eigen_vec64) {
  Vec3s v1(1.0, 2.0, 3.0);
  BOOST_CHECK(v1[0] == 1.0);
  BOOST_CHECK(v1[1] == 2.0);
  BOOST_CHECK(v1[2] == 3.0);
 
  Vec3s v2 = v1;
  Vec3s v3(3.3, 4.3, 5.3);
  v1 += v3;
  BOOST_CHECK(isEqual(v1, v2 + v3));
  v1 -= v3;
  BOOST_CHECK(isEqual(v1, v2));
  v1 -= v3;
  BOOST_CHECK(isEqual(v1, v2 - v3));
  v1 += v3;
 
  v1.array() *= v3.array();
  BOOST_CHECK(isEqual(v1, v2.cwiseProduct(v3)));
  v1.array() /= v3.array();
  BOOST_CHECK(isEqual(v1, v2));
  v1.array() /= v3.array();
  BOOST_CHECK(isEqual(v1, v2.cwiseQuotient(v3)));
  v1.array() *= v3.array();
 
  v1 *= 2.0;
  BOOST_CHECK(isEqual(v1, v2 * 2.0));
  v1 /= 2.0;
  BOOST_CHECK(isEqual(v1, v2));
  v1 /= 2.0;
  BOOST_CHECK(isEqual(v1, v2 / 2.0));
  v1 *= 2.0;
 
  v1.array() += 2.0;
  BOOST_CHECK(isEqual(v1, (v2.array() + 2.0).matrix()));
  v1.array() -= 2.0;
  BOOST_CHECK(isEqual(v1, v2));
  v1.array() -= 2.0;
  BOOST_CHECK(isEqual(v1, (v2.array() - 2.0).matrix()));
  v1.array() += 2.0;
 
  BOOST_CHECK(isEqual((-Vec3s(1.0, 2.0, 3.0)), Vec3s(-1.0, -2.0, -3.0)));
 
  v1 = Vec3s(1.0, 2.0, 3.0);
  v2 = Vec3s(3.0, 4.0, 5.0);
  BOOST_CHECK(isEqual((v1.cross(v2)), Vec3s(-2.0, 4.0, -2.0)));
  BOOST_CHECK(std::abs(v1.dot(v2) - 26) < 1e-5);
 
  v1 = Vec3s(3.0, 4.0, 5.0);
  BOOST_CHECK(std::abs(v1.squaredNorm() - 50) < 1e-5);
  BOOST_CHECK(std::abs(v1.norm() - sqrt(50)) < 1e-5);
  BOOST_CHECK(isEqual(v1.normalized(), v1 / v1.norm()));
 
  v1 = Vec3s(1.0, 2.0, 3.0);
  v2 = Vec3s(3.0, 4.0, 5.0);
  BOOST_CHECK(isEqual(v1.cross(v2), Vec3s(-2.0, 4.0, -2.0)));
  BOOST_CHECK(v1.dot(v2) == 26);
}
 
Vec3s rotate(Vec3s input, CoalScalar w, Vec3s vec) {
  return 2 * vec.dot(input) * vec + (w * w - vec.dot(vec)) * input +
         2 * w * vec.cross(input);
}
 
BOOST_AUTO_TEST_CASE(quaternion) {
  Quatf q1(Quatf::Identity()), q2, q3;
  q2 = fromAxisAngle(Vec3s(0, 0, 1), M_PI / 2);
  q3 = q2.inverse();
 
  Vec3s v(1, -1, 0);
 
  BOOST_CHECK(isEqual(v, q1 * v));
  BOOST_CHECK(isEqual(Vec3s(1, 1, 0), q2 * v));
  BOOST_CHECK(
      isEqual(rotate(v, q3.w(), Vec3s(q3.x(), q3.y(), q3.z())), q3 * v));
}
 
BOOST_AUTO_TEST_CASE(transform) {
  Quatf q = fromAxisAngle(Vec3s(0, 0, 1), M_PI / 2);
  Vec3s T(0, 1, 2);
  Transform3s tf(q, T);
 
  Vec3s v(1, -1, 0);
 
  BOOST_CHECK(isEqual(q * v + T, q * v + T));
 
  Vec3s rv(q * v);
  // typename Transform3s::transform_return_type<Vec3s>::type output =
  // tf * v;
  // std::cout << rv << std::endl;
  // std::cout << output.lhs() << std::endl;
  BOOST_CHECK(isEqual(rv + T, tf.transform(v)));
}
 
BOOST_AUTO_TEST_CASE(random_transform) {
  for (size_t i = 0; i < 100; ++i) {
    const Transform3s tf = Transform3s::Random();
    BOOST_CHECK((tf.inverseTimes(tf)).isIdentity());
  }
}