transforms.hpp

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#pragma once
 
#include <pcl/common/transforms.h>
 
#if defined(__SSE2__)
#include <xmmintrin.h>
#endif
 
#if defined(__AVX__)
#include <immintrin.h>
#endif
 
#include <algorithm>
#include <cmath>
#include <cstddef>
#include <vector>
 
 
namespace pcl
{
 
namespace detail
{
 
/** A helper struct to apply an SO3 or SE3 transform to a 3D point.
  * Supports single and double precision transform matrices. */
template<typename Scalar>
struct Transformer
{
  const Eigen::Matrix<Scalar, 4, 4>& tf;
 
  /** Construct a transformer object.
    * The transform matrix is captured by const reference. Make sure that it does not go out of scope before this
    * object does. */
  Transformer (const Eigen::Matrix<Scalar, 4, 4>& transform) : tf (transform) { };
 
  /** Apply SO3 transform (top-left corner of the transform matrix).
    * \param[in] src input 3D point (pointer to 3 floats)
    * \param[out] tgt output 3D point (pointer to 4 floats), can be the same as input. The fourth element is set to 0. */
  void so3 (const float* src, float* tgt) const
  {
    const Scalar p[3] = { src[0], src[1], src[2] };  // need this when src == tgt
    tgt[0] = static_cast<float> (tf (0, 0) * p[0] + tf (0, 1) * p[1] + tf (0, 2) * p[2]);
    tgt[1] = static_cast<float> (tf (1, 0) * p[0] + tf (1, 1) * p[1] + tf (1, 2) * p[2]);
    tgt[2] = static_cast<float> (tf (2, 0) * p[0] + tf (2, 1) * p[1] + tf (2, 2) * p[2]);
    tgt[3] = 0;
  }
 
  /** Apply SE3 transform.
    * \param[in] src input 3D point (pointer to 3 floats)
    * \param[out] tgt output 3D point (pointer to 4 floats), can be the same as input. The fourth element is set to 1. */
  void se3 (const float* src, float* tgt) const
  {
    const Scalar p[3] = { src[0], src[1], src[2] };  // need this when src == tgt
    tgt[0] = static_cast<float> (tf (0, 0) * p[0] + tf (0, 1) * p[1] + tf (0, 2) * p[2] + tf (0, 3));
    tgt[1] = static_cast<float> (tf (1, 0) * p[0] + tf (1, 1) * p[1] + tf (1, 2) * p[2] + tf (1, 3));
    tgt[2] = static_cast<float> (tf (2, 0) * p[0] + tf (2, 1) * p[1] + tf (2, 2) * p[2] + tf (2, 3));
    tgt[3] = 1;
  }
};
 
#if defined(__SSE2__)
 
/** Optimized version for single-precision transforms using SSE2 intrinsics. */
template<>
struct Transformer<float>
{
  /// Columns of the transform matrix stored in XMM registers.
  __m128 c[4];
 
  Transformer(const Eigen::Matrix4f& tf)
  {
    for (std::size_t i = 0; i < 4; ++i)
      c[i] = _mm_load_ps (tf.col (i).data ());
  }
 
  void so3 (const float* src, float* tgt) const
  {
    __m128 p0 = _mm_mul_ps (_mm_load_ps1 (&src[0]), c[0]);
    __m128 p1 = _mm_mul_ps (_mm_load_ps1 (&src[1]), c[1]);
    __m128 p2 = _mm_mul_ps (_mm_load_ps1 (&src[2]), c[2]);
    _mm_store_ps (tgt, _mm_add_ps(p0, _mm_add_ps(p1, p2)));
  }
 
  void se3 (const float* src, float* tgt) const
  {
    __m128 p0 = _mm_mul_ps (_mm_load_ps1 (&src[0]), c[0]);
    __m128 p1 = _mm_mul_ps (_mm_load_ps1 (&src[1]), c[1]);
    __m128 p2 = _mm_mul_ps (_mm_load_ps1 (&src[2]), c[2]);
    _mm_store_ps (tgt, _mm_add_ps(p0, _mm_add_ps(p1, _mm_add_ps(p2, c[3]))));
  }
};
 
#if !defined(__AVX__)
 
/** Optimized version for double-precision transform using SSE2 intrinsics. */
template<>
struct Transformer<double>
{
  /// Columns of the transform matrix stored in XMM registers.
  __m128d c[4][2];
 
  Transformer(const Eigen::Matrix4d& tf)
  {
    for (std::size_t i = 0; i < 4; ++i)
    {
      c[i][0] = _mm_load_pd (tf.col (i).data () + 0);
      c[i][1] = _mm_load_pd (tf.col (i).data () + 2);
    }
  }
 
  void so3 (const float* src, float* tgt) const
  {
    __m128d xx = _mm_cvtps_pd (_mm_load_ps1 (&src[0]));
    __m128d p0 = _mm_mul_pd (xx, c[0][0]);
    __m128d p1 = _mm_mul_pd (xx, c[0][1]);
 
    for (std::size_t i = 1; i < 3; ++i)
    {
      __m128d vv = _mm_cvtps_pd (_mm_load_ps1 (&src[i]));
      p0 = _mm_add_pd (_mm_mul_pd (vv, c[i][0]), p0);
      p1 = _mm_add_pd (_mm_mul_pd (vv, c[i][1]), p1);
    }
 
    _mm_store_ps (tgt, _mm_movelh_ps (_mm_cvtpd_ps (p0), _mm_cvtpd_ps (p1)));
  }
 
  void se3 (const float* src, float* tgt) const
  {
    __m128d p0 = c[3][0];
    __m128d p1 = c[3][1];
 
    for (std::size_t i = 0; i < 3; ++i)
    {
      __m128d vv = _mm_cvtps_pd (_mm_load_ps1 (&src[i]));
      p0 = _mm_add_pd (_mm_mul_pd (vv, c[i][0]), p0);
      p1 = _mm_add_pd (_mm_mul_pd (vv, c[i][1]), p1);
    }
 
    _mm_store_ps (tgt, _mm_movelh_ps (_mm_cvtpd_ps (p0), _mm_cvtpd_ps (p1)));
  }
};
 
#else
 
/** Optimized version for double-precision transform using AVX intrinsics. */
template<>
struct Transformer<double>
{
  __m256d c[4];
 
  Transformer(const Eigen::Matrix4d& tf)
  {
    for (std::size_t i = 0; i < 4; ++i)
      c[i] = _mm256_load_pd (tf.col (i).data ());
  }
 
  void so3 (const float* src, float* tgt) const
  {
    __m256d p0 = _mm256_mul_pd (_mm256_cvtps_pd (_mm_load_ps1 (&src[0])), c[0]);
    __m256d p1 = _mm256_mul_pd (_mm256_cvtps_pd (_mm_load_ps1 (&src[1])), c[1]);
    __m256d p2 = _mm256_mul_pd (_mm256_cvtps_pd (_mm_load_ps1 (&src[2])), c[2]);
    _mm_store_ps (tgt, _mm256_cvtpd_ps (_mm256_add_pd(p0, _mm256_add_pd(p1, p2))));
  }
 
  void se3 (const float* src, float* tgt) const
  {
    __m256d p0 = _mm256_mul_pd (_mm256_cvtps_pd (_mm_load_ps1 (&src[0])), c[0]);
    __m256d p1 = _mm256_mul_pd (_mm256_cvtps_pd (_mm_load_ps1 (&src[1])), c[1]);
    __m256d p2 = _mm256_mul_pd (_mm256_cvtps_pd (_mm_load_ps1 (&src[2])), c[2]);
    _mm_store_ps (tgt, _mm256_cvtpd_ps (_mm256_add_pd(p0, _mm256_add_pd(p1, _mm256_add_pd(p2, c[3])))));
  }
};
 
#endif // !defined(__AVX__)
#endif // defined(__SSE2__)
 
} // namespace detail
 
 
template <typename PointT, typename Scalar> void
transformPointCloud (const pcl::PointCloud<PointT> &cloud_in,
                     pcl::PointCloud<PointT> &cloud_out,
                     const Eigen::Matrix<Scalar, 4, 4> &transform,
                     bool copy_all_fields)
{
  if (&cloud_in != &cloud_out)
  {
    cloud_out.header   = cloud_in.header;
    cloud_out.is_dense = cloud_in.is_dense;
    cloud_out.width    = cloud_in.width;
    cloud_out.height   = cloud_in.height;
    cloud_out.reserve (cloud_in.size ());
    if (copy_all_fields)
      cloud_out.assign (cloud_in.begin (), cloud_in.end ());
    else
      cloud_out.resize (cloud_in.size ());
    cloud_out.sensor_orientation_ = cloud_in.sensor_orientation_;
    cloud_out.sensor_origin_      = cloud_in.sensor_origin_;
  }
 
  pcl::detail::Transformer<Scalar> tf (transform);
  if (cloud_in.is_dense)
  {
    // If the dataset is dense, simply transform it!
    for (std::size_t i = 0; i < cloud_out.size (); ++i)
      tf.se3 (cloud_in[i].data, cloud_out[i].data);
  }
  else
  {
    // Dataset might contain NaNs and Infs, so check for them first,
    // otherwise we get errors during the multiplication (?)
    for (std::size_t i = 0; i < cloud_out.size (); ++i)
    {
      if (!std::isfinite (cloud_in[i].x) ||
          !std::isfinite (cloud_in[i].y) ||
          !std::isfinite (cloud_in[i].z))
        continue;
      tf.se3 (cloud_in[i].data, cloud_out[i].data);
    }
  }
}
 
 
template <typename PointT, typename Scalar> void
transformPointCloud (const pcl::PointCloud<PointT> &cloud_in,
                     const Indices &indices,
                     pcl::PointCloud<PointT> &cloud_out,
                     const Eigen::Matrix<Scalar, 4, 4> &transform,
                     bool copy_all_fields)
{
  std::size_t npts = indices.size ();
  // In order to transform the data, we need to remove NaNs
  cloud_out.is_dense = cloud_in.is_dense;
  cloud_out.header   = cloud_in.header;
  cloud_out.width    = static_cast<int> (npts);
  cloud_out.height   = 1;
  cloud_out.resize (npts);
  cloud_out.sensor_orientation_ = cloud_in.sensor_orientation_;
  cloud_out.sensor_origin_      = cloud_in.sensor_origin_;
 
  pcl::detail::Transformer<Scalar> tf (transform);
  if (cloud_in.is_dense)
  {
    // If the dataset is dense, simply transform it!
    for (std::size_t i = 0; i < npts; ++i)
    {
      // Copy fields first, then transform xyz data
      if (copy_all_fields)
        cloud_out[i] = cloud_in[indices[i]];
      tf.se3 (cloud_in[indices[i]].data, cloud_out[i].data);
    }
  }
  else
  {
    // Dataset might contain NaNs and Infs, so check for them first,
    // otherwise we get errors during the multiplication (?)
    for (std::size_t i = 0; i < npts; ++i)
    {
      if (copy_all_fields)
        cloud_out[i] = cloud_in[indices[i]];
      if (!std::isfinite (cloud_in[indices[i]].x) ||
          !std::isfinite (cloud_in[indices[i]].y) ||
          !std::isfinite (cloud_in[indices[i]].z))
        continue;
      tf.se3 (cloud_in[indices[i]].data, cloud_out[i].data);
    }
  }
}
 
 
template <typename PointT, typename Scalar> void
transformPointCloudWithNormals (const pcl::PointCloud<PointT> &cloud_in,
                                pcl::PointCloud<PointT> &cloud_out,
                                const Eigen::Matrix<Scalar, 4, 4> &transform,
                                bool copy_all_fields)
{
  if (&cloud_in != &cloud_out)
  {
    // Note: could be replaced by cloud_out = cloud_in
    cloud_out.header   = cloud_in.header;
    cloud_out.width    = cloud_in.width;
    cloud_out.height   = cloud_in.height;
    cloud_out.is_dense = cloud_in.is_dense;
    cloud_out.reserve (cloud_out.size ());
    if (copy_all_fields)
      cloud_out.assign (cloud_in.begin (), cloud_in.end ());
    else
      cloud_out.resize (cloud_in.size ());
    cloud_out.sensor_orientation_ = cloud_in.sensor_orientation_;
    cloud_out.sensor_origin_      = cloud_in.sensor_origin_;
  }
 
  pcl::detail::Transformer<Scalar> tf (transform);
  // If the data is dense, we don't need to check for NaN
  if (cloud_in.is_dense)
  {
    for (std::size_t i = 0; i < cloud_out.size (); ++i)
    {
      tf.se3 (cloud_in[i].data, cloud_out[i].data);
      tf.so3 (cloud_in[i].data_n, cloud_out[i].data_n);
    }
  }
  // Dataset might contain NaNs and Infs, so check for them first.
  else
  {
    for (std::size_t i = 0; i < cloud_out.size (); ++i)
    {
      if (!std::isfinite (cloud_in[i].x) ||
          !std::isfinite (cloud_in[i].y) ||
          !std::isfinite (cloud_in[i].z))
        continue;
      tf.se3 (cloud_in[i].data, cloud_out[i].data);
      tf.so3 (cloud_in[i].data_n, cloud_out[i].data_n);
    }
  }
}
 
 
template <typename PointT, typename Scalar> void
transformPointCloudWithNormals (const pcl::PointCloud<PointT> &cloud_in,
                                const Indices &indices,
                                pcl::PointCloud<PointT> &cloud_out,
                                const Eigen::Matrix<Scalar, 4, 4> &transform,
                                bool copy_all_fields)
{
  std::size_t npts = indices.size ();
  // In order to transform the data, we need to remove NaNs
  cloud_out.is_dense = cloud_in.is_dense;
  cloud_out.header   = cloud_in.header;
  cloud_out.width    = static_cast<int> (npts);
  cloud_out.height   = 1;
  cloud_out.resize (npts);
  cloud_out.sensor_orientation_ = cloud_in.sensor_orientation_;
  cloud_out.sensor_origin_      = cloud_in.sensor_origin_;
 
  pcl::detail::Transformer<Scalar> tf (transform);
  // If the data is dense, we don't need to check for NaN
  if (cloud_in.is_dense)
  {
    for (std::size_t i = 0; i < cloud_out.size (); ++i)
    {
      // Copy fields first, then transform
      if (copy_all_fields)
        cloud_out[i] = cloud_in[indices[i]];
      tf.se3 (cloud_in[indices[i]].data, cloud_out[i].data);
      tf.so3 (cloud_in[indices[i]].data_n, cloud_out[i].data_n);
    }
  }
  // Dataset might contain NaNs and Infs, so check for them first.
  else
  {
    for (std::size_t i = 0; i < cloud_out.size (); ++i)
    {
      // Copy fields first, then transform
      if (copy_all_fields)
        cloud_out[i] = cloud_in[indices[i]];
 
      if (!std::isfinite (cloud_in[indices[i]].x) ||
          !std::isfinite (cloud_in[indices[i]].y) ||
          !std::isfinite (cloud_in[indices[i]].z))
        continue;
 
      tf.se3 (cloud_in[indices[i]].data, cloud_out[i].data);
      tf.so3 (cloud_in[indices[i]].data_n, cloud_out[i].data_n);
    }
  }
}
 
 
template <typename PointT, typename Scalar> inline void
transformPointCloud (const pcl::PointCloud<PointT> &cloud_in,
                     pcl::PointCloud<PointT> &cloud_out,
                     const Eigen::Matrix<Scalar, 3, 1> &offset,
                     const Eigen::Quaternion<Scalar> &rotation,
                     bool copy_all_fields)
{
  Eigen::Translation<Scalar, 3> translation (offset);
  // Assemble an Eigen Transform
  Eigen::Transform<Scalar, 3, Eigen::Affine> t (translation * rotation);
  transformPointCloud (cloud_in, cloud_out, t, copy_all_fields);
}
 
 
template <typename PointT, typename Scalar> inline void
transformPointCloudWithNormals (const pcl::PointCloud<PointT> &cloud_in,
                                pcl::PointCloud<PointT> &cloud_out,
                                const Eigen::Matrix<Scalar, 3, 1> &offset,
                                const Eigen::Quaternion<Scalar> &rotation,
                                bool copy_all_fields)
{
  Eigen::Translation<Scalar, 3> translation (offset);
  // Assemble an Eigen Transform
  Eigen::Transform<Scalar, 3, Eigen::Affine> t (translation * rotation);
  transformPointCloudWithNormals (cloud_in, cloud_out, t, copy_all_fields);
}
 
 
template <typename PointT, typename Scalar> inline PointT
transformPoint (const PointT &point, const Eigen::Transform<Scalar, 3, Eigen::Affine> &transform)
{
  PointT ret = point;
  pcl::detail::Transformer<Scalar> tf (transform.matrix ());
  tf.se3 (point.data, ret.data);
  return (ret);
}
 
 
template <typename PointT, typename Scalar> inline PointT
transformPointWithNormal (const PointT &point, const Eigen::Transform<Scalar, 3, Eigen::Affine> &transform)
{
  PointT ret = point;
  pcl::detail::Transformer<Scalar> tf (transform.matrix ());
  tf.se3 (point.data, ret.data);
  tf.so3 (point.data_n, ret.data_n);
  return (ret);
}
 
 
template <typename PointT, typename Scalar> double
getPrincipalTransformation (const pcl::PointCloud<PointT> &cloud,
                            Eigen::Transform<Scalar, 3, Eigen::Affine> &transform)
{
  EIGEN_ALIGN16 Eigen::Matrix<Scalar, 3, 3> covariance_matrix;
  Eigen::Matrix<Scalar, 4, 1> centroid;
 
  pcl::computeMeanAndCovarianceMatrix (cloud, covariance_matrix, centroid);
 
  EIGEN_ALIGN16 Eigen::Matrix<Scalar, 3, 3> eigen_vects;
  Eigen::Matrix<Scalar, 3, 1> eigen_vals;
  pcl::eigen33 (covariance_matrix, eigen_vects, eigen_vals);
 
  double rel1 = eigen_vals.coeff (0) / eigen_vals.coeff (1);
  double rel2 = eigen_vals.coeff (1) / eigen_vals.coeff (2);
 
  transform.translation () = centroid.head (3);
  transform.linear () = eigen_vects;
 
  return (std::min (rel1, rel2));
}
 
} // namespace pcl