auxiliary.h
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#ifndef PCL_RECOGNITION_RANSAC_BASED_AUX_H_
#define PCL_RECOGNITION_RANSAC_BASED_AUX_H_
#include <cmath>
#include <cstdlib>
#include <pcl/common/eigen.h>
#include <pcl/point_types.h>
#define AUX_PI_FLOAT 3.14159265358979323846f
#define AUX_HALF_PI 1.57079632679489661923f
#define AUX_DEG_TO_RADIANS (3.14159265358979323846f/180.0f)
namespace pcl
{
namespace recognition
{
namespace aux
{
template<typename T> bool
compareOrderedPairs (const std::pair<T,T>& a, const std::pair<T,T>& b)
{
if ( a.first == b.first )
return static_cast<bool> (a.second < b.second);
return static_cast<bool> (a.first < b.first);
}
template<typename T> T
sqr (T a)
{
return (a*a);
}
template<typename T> T
clamp (T value, T min, T max)
{
if ( value < min )
return min;
else if ( value > max )
return max;
return value;
}
/** \brief Expands the destination bounding box 'dst' such that it contains 'src'. */
template<typename T> void
expandBoundingBox (T dst[6], const T src[6])
{
if ( src[0] < dst[0] ) dst[0] = src[0];
if ( src[2] < dst[2] ) dst[2] = src[2];
if ( src[4] < dst[4] ) dst[4] = src[4];
if ( src[1] > dst[1] ) dst[1] = src[1];
if ( src[3] > dst[3] ) dst[3] = src[3];
if ( src[5] > dst[5] ) dst[5] = src[5];
}
/** \brief Expands the bounding box 'bbox' such that it contains the point 'p'. */
template<typename T> void
expandBoundingBoxToContainPoint (T bbox[6], const T p[3])
{
if ( p[0] < bbox[0] ) bbox[0] = p[0];
else if ( p[0] > bbox[1] ) bbox[1] = p[0];
if ( p[1] < bbox[2] ) bbox[2] = p[1];
else if ( p[1] > bbox[3] ) bbox[3] = p[1];
if ( p[2] < bbox[4] ) bbox[4] = p[2];
else if ( p[2] > bbox[5] ) bbox[5] = p[2];
}
/** \brief v[0] = v[1] = v[2] = value */
template <typename T> void
set3 (T v[3], T value)
{
v[0] = v[1] = v[2] = value;
}
/** \brief dst = src */
template <typename T> void
copy3 (const T src[3], T dst[3])
{
dst[0] = src[0];
dst[1] = src[1];
dst[2] = src[2];
}
/** \brief dst = src */
template <typename T> void
copy3 (const T src[3], pcl::PointXYZ& dst)
{
dst.x = src[0];
dst.y = src[1];
dst.z = src[2];
}
/** \brief a = -a */
template <typename T> void
flip3 (T a[3])
{
a[0] = -a[0];
a[1] = -a[1];
a[2] = -a[2];
}
/** \brief a = b */
template <typename T> bool
equal3 (const T a[3], const T b[3])
{
return (a[0] == b[0] && a[1] == b[1] && a[2] == b[2]);
}
/** \brief a += b */
template <typename T> void
add3 (T a[3], const T b[3])
{
a[0] += b[0];
a[1] += b[1];
a[2] += b[2];
}
/** \brief c = a + b */
template <typename T> void
sum3 (const T a[3], const T b[3], T c[3])
{
c[0] = a[0] + b[0];
c[1] = a[1] + b[1];
c[2] = a[2] + b[2];
}
/** \brief c = a - b */
template <typename T> void
diff3 (const T a[3], const T b[3], T c[3])
{
c[0] = a[0] - b[0];
c[1] = a[1] - b[1];
c[2] = a[2] - b[2];
}
template <typename T> void
cross3 (const T v1[3], const T v2[3], T out[3])
{
out[0] = v1[1]*v2[2] - v1[2]*v2[1];
out[1] = v1[2]*v2[0] - v1[0]*v2[2];
out[2] = v1[0]*v2[1] - v1[1]*v2[0];
}
/** \brief Returns the length of v. */
template <typename T> T
length3 (const T v[3])
{
return (std::sqrt (v[0]*v[0] + v[1]*v[1] + v[2]*v[2]));
}
/** \brief Returns the Euclidean distance between a and b. */
template <typename T> T
distance3 (const T a[3], const T b[3])
{
T l[3] = {a[0]-b[0], a[1]-b[1], a[2]-b[2]};
return (length3 (l));
}
/** \brief Returns the squared Euclidean distance between a and b. */
template <typename T> T
sqrDistance3 (const T a[3], const T b[3])
{
return (aux::sqr (a[0]-b[0]) + aux::sqr (a[1]-b[1]) + aux::sqr (a[2]-b[2]));
}
/** \brief Returns the dot product a*b */
template <typename T> T
dot3 (const T a[3], const T b[3])
{
return (a[0]*b[0] + a[1]*b[1] + a[2]*b[2]);
}
/** \brief Returns the dot product (x, y, z)*(u, v, w) = x*u + y*v + z*w */
template <typename T> T
dot3 (T x, T y, T z, T u, T v, T w)
{
return (x*u + y*v + z*w);
}
/** \brief v = scalar*v. */
template <typename T> void
mult3 (T* v, T scalar)
{
v[0] *= scalar;
v[1] *= scalar;
v[2] *= scalar;
}
/** \brief out = scalar*v. */
template <typename T> void
mult3 (const T* v, T scalar, T* out)
{
out[0] = v[0]*scalar;
out[1] = v[1]*scalar;
out[2] = v[2]*scalar;
}
/** \brief Normalize v */
template <typename T> void
normalize3 (T v[3])
{
T inv_len = (static_cast<T> (1.0))/aux::length3 (v);
v[0] *= inv_len;
v[1] *= inv_len;
v[2] *= inv_len;
}
/** \brief Returns the square length of v. */
template <typename T> T
sqrLength3 (const T v[3])
{
return (v[0]*v[0] + v[1]*v[1] + v[2]*v[2]);
}
/** Projects 'x' on the plane through 0 and with normal 'planeNormal' and saves the result in 'out'. */
template <typename T> void
projectOnPlane3 (const T x[3], const T planeNormal[3], T out[3])
{
T dot = aux::dot3 (planeNormal, x);
// Project 'x' on the plane normal
T nproj[3] = {-dot*planeNormal[0], -dot*planeNormal[1], -dot*planeNormal[2]};
aux::sum3 (x, nproj, out);
}
/** \brief Sets 'm' to the 3x3 identity matrix. */
template <typename T> void
identity3x3 (T m[9])
{
m[0] = m[4] = m[8] = 1.0;
m[1] = m[2] = m[3] = m[5] = m[6] = m[7] = 0.0;
}
/** \brief out = mat*v. 'm' is an 1D array of 9 elements treated as a 3x3 matrix (row major order). */
template <typename T> void
mult3x3(const T m[9], const T v[3], T out[3])
{
out[0] = v[0]*m[0] + v[1]*m[1] + v[2]*m[2];
out[1] = v[0]*m[3] + v[1]*m[4] + v[2]*m[5];
out[2] = v[0]*m[6] + v[1]*m[7] + v[2]*m[8];
}
/** Let x, y, z be the columns of the matrix a = [x|y|z]. The method computes out = a*m.
* Note that 'out' is a 1D array of 9 elements and the resulting matrix is stored in row
* major order, i.e., the first matrix row is (out[0] out[1] out[2]), the second
* (out[3] out[4] out[5]) and the third (out[6] out[7] out[8]). */
template <typename T> void
mult3x3 (const T x[3], const T y[3], const T z[3], const T m[3][3], T out[9])
{
out[0] = x[0]*m[0][0] + y[0]*m[1][0] + z[0]*m[2][0];
out[1] = x[0]*m[0][1] + y[0]*m[1][1] + z[0]*m[2][1];
out[2] = x[0]*m[0][2] + y[0]*m[1][2] + z[0]*m[2][2];
out[3] = x[1]*m[0][0] + y[1]*m[1][0] + z[1]*m[2][0];
out[4] = x[1]*m[0][1] + y[1]*m[1][1] + z[1]*m[2][1];
out[5] = x[1]*m[0][2] + y[1]*m[1][2] + z[1]*m[2][2];
out[6] = x[2]*m[0][0] + y[2]*m[1][0] + z[2]*m[2][0];
out[7] = x[2]*m[0][1] + y[2]*m[1][1] + z[2]*m[2][1];
out[8] = x[2]*m[0][2] + y[2]*m[1][2] + z[2]*m[2][2];
}
/** \brief The first 9 elements of 't' are treated as a 3x3 matrix (row major order) and the last 3 as a translation.
* First, 'p' is multiplied by that matrix and then translated. The result is saved in 'out'. */
template<class T> void
transform(const T t[12], const T p[3], T out[3])
{
out[0] = t[0]*p[0] + t[1]*p[1] + t[2]*p[2] + t[9];
out[1] = t[3]*p[0] + t[4]*p[1] + t[5]*p[2] + t[10];
out[2] = t[6]*p[0] + t[7]*p[1] + t[8]*p[2] + t[11];
}
/** \brief The first 9 elements of 't' are treated as a 3x3 matrix (row major order) and the last 3 as a translation.
* First, (x, y, z) is multiplied by that matrix and then translated. The result is saved in 'out'. */
template<class T> void
transform(const T t[12], T x, T y, T z, T out[3])
{
out[0] = t[0]*x + t[1]*y + t[2]*z + t[9];
out[1] = t[3]*x + t[4]*y + t[5]*z + t[10];
out[2] = t[6]*x + t[7]*y + t[8]*z + t[11];
}
/** \brief Compute out = (upper left 3x3 of mat)*p + last column of mat. */
template<class T> void
transform(const Eigen::Matrix<T,4,4>& mat, const pcl::PointXYZ& p, pcl::PointXYZ& out)
{
out.x = mat(0,0)*p.x + mat(0,1)*p.y + mat(0,2)*p.z + mat(0,3);
out.y = mat(1,0)*p.x + mat(1,1)*p.y + mat(1,2)*p.z + mat(1,3);
out.z = mat(2,0)*p.x + mat(2,1)*p.y + mat(2,2)*p.z + mat(2,3);
}
/** \brief The first 9 elements of 't' are treated as a 3x3 matrix (row major order) and the last 3 as a translation.
* First, 'p' is multiplied by that matrix and then translated. The result is saved in 'out'. */
template<class T> void
transform(const T t[12], const pcl::PointXYZ& p, T out[3])
{
out[0] = t[0]*p.x + t[1]*p.y + t[2]*p.z + t[9];
out[1] = t[3]*p.x + t[4]*p.y + t[5]*p.z + t[10];
out[2] = t[6]*p.x + t[7]*p.y + t[8]*p.z + t[11];
}
/** \brief Returns true if the points 'p1' and 'p2' are co-planar and false otherwise. The method assumes that 'n1'
* is a normal at 'p1' and 'n2' is a normal at 'p2'. 'max_angle' is the threshold used for the test. The bigger
* the value the larger the deviation between the normals can be which still leads to a positive test result. The
* angle has to be in radians. */
template<typename T> bool
pointsAreCoplanar (const T p1[3], const T n1[3], const T p2[3], const T n2[3], T max_angle)
{
// Compute the angle between 'n1' and 'n2' and compare it with 'max_angle'
if ( std::acos (aux::clamp (aux::dot3 (n1, n2), -1.0f, 1.0f)) > max_angle )
return (false);
T cl[3] = {p2[0] - p1[0], p2[1] - p1[1], p2[2] - p1[2]};
aux::normalize3 (cl);
// Compute the angle between 'cl' and 'n1'
T tmp_angle = std::acos (aux::clamp (aux::dot3 (n1, cl), -1.0f, 1.0f));
// 'tmp_angle' should not deviate too much from 90 degrees
if ( std::fabs (tmp_angle - AUX_HALF_PI) > max_angle )
return (false);
// All tests passed => the points are coplanar
return (true);
}
template<typename Scalar> void
array12ToMatrix4x4 (const Scalar src[12], Eigen::Matrix<Scalar, 4, 4>& dst)
{
dst(0,0) = src[0]; dst(0,1) = src[1]; dst(0,2) = src[2]; dst(0,3) = src[9];
dst(1,0) = src[3]; dst(1,1) = src[4]; dst(1,2) = src[5]; dst(1,3) = src[10];
dst(2,0) = src[6]; dst(2,1) = src[7]; dst(2,2) = src[8]; dst(2,3) = src[11];
dst(3,0) = dst(3,1) = dst(3,2) = 0.0; dst(3,3) = 1.0;
}
template<typename Scalar> void
matrix4x4ToArray12 (const Eigen::Matrix<Scalar, 4, 4>& src, Scalar dst[12])
{
dst[0] = src(0,0); dst[1] = src(0,1); dst[2] = src(0,2); dst[9] = src(0,3);
dst[3] = src(1,0); dst[4] = src(1,1); dst[5] = src(1,2); dst[10] = src(1,3);
dst[6] = src(2,0); dst[7] = src(2,1); dst[8] = src(2,2); dst[11] = src(2,3);
}
/** \brief The method copies the input array 'src' to the eigen matrix 'dst' in row major order.
* dst[0] = src(0,0); dst[1] = src(0,1); dst[2] = src(0,2);
* dst[3] = src(1,0); dst[4] = src(1,1); dst[5] = src(1,2);
* dst[6] = src(2,0); dst[7] = src(2,1); dst[8] = src(2,2);
* */
template <typename T> void
eigenMatrix3x3ToArray9RowMajor (const Eigen::Matrix<T,3,3>& src, T dst[9])
{
dst[0] = src(0,0); dst[1] = src(0,1); dst[2] = src(0,2);
dst[3] = src(1,0); dst[4] = src(1,1); dst[5] = src(1,2);
dst[6] = src(2,0); dst[7] = src(2,1); dst[8] = src(2,2);
}
/** \brief The method copies the input array 'src' to the eigen matrix 'dst' in row major order.
* dst(0,0) = src[0]; dst(0,1) = src[1]; dst(0,2) = src[2];
* dst(1,0) = src[3]; dst(1,1) = src[4]; dst(1,2) = src[5];
* dst(2,0) = src[6]; dst(2,1) = src[7]; dst(2,2) = src[8];
* */
template <typename T> void
toEigenMatrix3x3RowMajor (const T src[9], Eigen::Matrix<T,3,3>& dst)
{
dst(0,0) = src[0]; dst(0,1) = src[1]; dst(0,2) = src[2];
dst(1,0) = src[3]; dst(1,1) = src[4]; dst(1,2) = src[5];
dst(2,0) = src[6]; dst(2,1) = src[7]; dst(2,2) = src[8];
}
/** brief Computes a rotation matrix from the provided input vector 'axis_angle'. The direction of 'axis_angle' is the rotation axis
* and its magnitude is the angle of rotation about that axis. 'rotation_matrix' is the output rotation matrix saved in row major order. */
template <typename T> void
axisAngleToRotationMatrix (const T axis_angle[3], T rotation_matrix[9])
{
// Get the angle of rotation
T angle = aux::length3 (axis_angle);
if ( angle == 0.0 )
{
// Undefined rotation -> set to identity
aux::identity3x3 (rotation_matrix);
return;
}
// Normalize the input
T normalized_axis_angle[3];
aux::mult3 (axis_angle, static_cast<T> (1.0)/angle, normalized_axis_angle);
// The eigen objects
Eigen::Matrix<T,3,1> mat_axis(normalized_axis_angle);
Eigen::AngleAxis<T> eigen_angle_axis (angle, mat_axis);
// Save the output
aux::eigenMatrix3x3ToArray9RowMajor (eigen_angle_axis.toRotationMatrix (), rotation_matrix);
}
/** brief Extracts the angle-axis representation from 'rotation_matrix', i.e., computes a rotation 'axis' and an 'angle'
* of rotation about that axis from the provided input. The output 'angle' is in the range [0, pi] and 'axis' is normalized. */
template <typename T> void
rotationMatrixToAxisAngle (const T rotation_matrix[9], T axis[3], T& angle)
{
// The eigen objects
Eigen::AngleAxis<T> angle_axis;
Eigen::Matrix<T,3,3> rot_mat;
// Copy the input matrix to the eigen matrix in row major order
aux::toEigenMatrix3x3RowMajor (rotation_matrix, rot_mat);
// Do the computation
angle_axis.fromRotationMatrix (rot_mat);
// Save the result
axis[0] = angle_axis.axis () (0,0);
axis[1] = angle_axis.axis () (1,0);
axis[2] = angle_axis.axis () (2,0);
angle = angle_axis.angle ();
// Make sure that 'angle' is in the range [0, pi]
if ( angle > AUX_PI_FLOAT )
{
angle = 2.0f*AUX_PI_FLOAT - angle;
aux::flip3 (axis);
}
}
} // namespace aux
} // namespace recognition
} // namespace pcl
#endif // AUX_H_
pcl::recognition::aux::expandBoundingBox
void expandBoundingBox(T dst[6], const T src[6])
Expands the destination bounding box &#39;dst&#39; such that it contains &#39;src&#39;.
Definition: auxiliary.h:84
pcl::recognition::aux::sqrDistance3
T sqrDistance3(const T a[3], const T b[3])
Returns the squared Euclidean distance between a and b.
Definition: auxiliary.h:202
pcl::recognition::aux::pointsAreCoplanar
bool pointsAreCoplanar(const T p1[3], const T n1[3], const T p2[3], const T n2[3], T max_angle)
Returns true if the points &#39;p1&#39; and &#39;p2&#39; are co-planar and false otherwise.
Definition: auxiliary.h:347
pcl::recognition::aux::mult3
void mult3(T *v, T scalar)
v = scalar*v.
Definition: auxiliary.h:223
pcl::recognition::aux::compareOrderedPairs
bool compareOrderedPairs(const std::pair< T, T > &a, const std::pair< T, T > &b)
Definition: auxiliary.h:57
pcl
Definition: convolution.h:45
pcl::recognition::aux::mult3x3
void mult3x3(const T m[9], const T v[3], T out[3])
out = mat*v.
Definition: auxiliary.h:276
pcl::recognition::aux::toEigenMatrix3x3RowMajor
void toEigenMatrix3x3RowMajor(const T src[9], Eigen::Matrix< T, 3, 3 > &dst)
The method copies the input array &#39;src&#39; to the eigen matrix &#39;dst&#39; in row major order.
Definition: auxiliary.h:403
pcl::recognition::aux::sqr
T sqr(T a)
Definition: auxiliary.h:66
pcl::recognition::aux::projectOnPlane3
void projectOnPlane3(const T x[3], const T planeNormal[3], T out[3])
Projects &#39;x&#39; on the plane through 0 and with normal &#39;planeNormal&#39; and saves the result in &#39;out&#39;...
Definition: auxiliary.h:258
pcl::recognition::aux::expandBoundingBoxToContainPoint
void expandBoundingBoxToContainPoint(T bbox[6], const T p[3])
Expands the bounding box &#39;bbox&#39; such that it contains the point &#39;p&#39;.
Definition: auxiliary.h:97
pcl::recognition::aux::cross3
void cross3(const T v1[3], const T v2[3], T out[3])
Definition: auxiliary.h:178
pcl::recognition::aux::dot3
T dot3(const T a[3], const T b[3])
Returns the dot product a*b.
Definition: auxiliary.h:209
pcl::recognition::aux::flip3
void flip3(T a[3])
a = -a
Definition: auxiliary.h:136
point_types.h
Defines all the PCL implemented PointT point type structures.
pcl::PointXYZ
A point structure representing Euclidean xyz coordinates.
Definition: point_types.hpp:281
pcl::recognition::aux::clamp
T clamp(T value, T min, T max)
Definition: auxiliary.h:72
pcl::recognition::aux::sqrLength3
T sqrLength3(const T v[3])
Returns the square length of v.
Definition: auxiliary.h:251
pcl::recognition::aux::rotationMatrixToAxisAngle
void rotationMatrixToAxisAngle(const T rotation_matrix[9], T axis[3], T &angle)
brief Extracts the angle-axis representation from &#39;rotation_matrix&#39;, i.e., computes a rotation &#39;axis&#39;...
Definition: auxiliary.h:439
pcl::recognition::aux::distance3
T distance3(const T a[3], const T b[3])
Returns the Euclidean distance between a and b.
Definition: auxiliary.h:194
pcl::recognition::aux::identity3x3
void identity3x3(T m[9])
Sets &#39;m&#39; to the 3x3 identity matrix.
Definition: auxiliary.h:268
pcl::recognition::aux::sum3
void sum3(const T a[3], const T b[3], T c[3])
c = a + b
Definition: auxiliary.h:161
pcl::recognition::aux::axisAngleToRotationMatrix
void axisAngleToRotationMatrix(const T axis_angle[3], T rotation_matrix[9])
brief Computes a rotation matrix from the provided input vector &#39;axis_angle&#39;.
Definition: auxiliary.h:413
pcl::recognition::aux::set3
void set3(T v[3], T value)
v[0] = v[1] = v[2] = value
Definition: auxiliary.h:111
pcl::recognition::aux::normalize3
void normalize3(T v[3])
Normalize v.
Definition: auxiliary.h:241
pcl::recognition::aux::matrix4x4ToArray12
void matrix4x4ToArray12(const Eigen::Matrix< Scalar, 4, 4 > &src, Scalar dst[12])
Definition: auxiliary.h:377
pcl::recognition::aux::array12ToMatrix4x4
void array12ToMatrix4x4(const Scalar src[12], Eigen::Matrix< Scalar, 4, 4 > &dst)
Definition: auxiliary.h:368
pcl::recognition::aux::copy3
void copy3(const T src[3], T dst[3])
dst = src
Definition: auxiliary.h:118
pcl::recognition::aux::length3
T length3(const T v[3])
Returns the length of v.
Definition: auxiliary.h:187
pcl::recognition::aux::diff3
void diff3(const T a[3], const T b[3], T c[3])
c = a - b
Definition: auxiliary.h:170
pcl::recognition::aux::add3
void add3(T a[3], const T b[3])
a += b
Definition: auxiliary.h:152
pcl::recognition::aux::equal3
bool equal3(const T a[3], const T b[3])
a = b
Definition: auxiliary.h:145
pcl::recognition::aux::eigenMatrix3x3ToArray9RowMajor
void eigenMatrix3x3ToArray9RowMajor(const Eigen::Matrix< T, 3, 3 > &src, T dst[9])
The method copies the input array &#39;src&#39; to the eigen matrix &#39;dst&#39; in row major order.
Definition: auxiliary.h:390
pcl::recognition::aux::transform
void transform(const T t[12], const T p[3], T out[3])
The first 9 elements of &#39;t&#39; are treated as a 3x3 matrix (row major order) and the last 3 as a transla...
Definition: auxiliary.h:306