float SupportPolygon::getSquaredDistLine(Eigen::Vector2f& p, Eigen::Vector2f& pt1, Eigen::Vector2f& pt2)
{
//nearestPointOnLine
Eigen::Vector2f lp = p - pt1;
Eigen::Vector2f dir = (pt2 - pt1);
dir.normalize();
float lambda = dir.dot(lp);
Eigen::Vector2f ptOnLine = pt1 + lambda * dir;
//distPointLine
return (ptOnLine - p).squaredNorm();
}
template <typename PointT> void
pcl16::approximatePolygon2D (const typename pcl16::PointCloud<PointT>::VectorType &polygon,
typename pcl16::PointCloud<PointT>::VectorType &approx_polygon,
float threshold, bool refine, bool closed)
{
approx_polygon.clear ();
if (polygon.size () < 3)
return;
std::vector<std::pair<unsigned, unsigned> > intervals;
std::pair<unsigned,unsigned> interval (0, 0);
if (closed)
{
float max_distance = .0f;
for (unsigned idx = 1; idx < polygon.size (); ++idx)
{
float distance = (polygon [0].x - polygon [idx].x) * (polygon [0].x - polygon [idx].x) +
(polygon [0].y - polygon [idx].y) * (polygon [0].y - polygon [idx].y);
if (distance > max_distance)
{
max_distance = distance;
interval.second = idx;
}
}
for (unsigned idx = 1; idx < polygon.size (); ++idx)
{
float distance = (polygon [interval.second].x - polygon [idx].x) * (polygon [interval.second].x - polygon [idx].x) +
(polygon [interval.second].y - polygon [idx].y) * (polygon [interval.second].y - polygon [idx].y);
if (distance > max_distance)
{
max_distance = distance;
interval.first = idx;
}
}
if (max_distance < threshold * threshold)
return;
intervals.push_back (interval);
std::swap (interval.first, interval.second);
intervals.push_back (interval);
}
else
{
interval.first = 0;
interval.second = static_cast<unsigned int> (polygon.size ()) - 1;
intervals.push_back (interval);
}
std::vector<unsigned> result;
// recursively refine
while (!intervals.empty ())
{
std::pair<unsigned, unsigned>& currentInterval = intervals.back ();
float line_x = polygon [currentInterval.first].y - polygon [currentInterval.second].y;
float line_y = polygon [currentInterval.second].x - polygon [currentInterval.first].x;
float line_d = polygon [currentInterval.first].x * polygon [currentInterval.second].y - polygon [currentInterval.first].y * polygon [currentInterval.second].x;
float linelen = 1.0f / sqrt (line_x * line_x + line_y * line_y);
line_x *= linelen;
line_y *= linelen;
line_d *= linelen;
float max_distance = 0.0;
unsigned first_index = currentInterval.first + 1;
unsigned max_index = 0;
// => 0-crossing
if (currentInterval.first > currentInterval.second)
{
for (unsigned idx = first_index; idx < polygon.size(); idx++)
{
float distance = fabsf (line_x * polygon[idx].x + line_y * polygon[idx].y + line_d);
if (distance > max_distance)
{
max_distance = distance;
max_index = idx;
}
}
first_index = 0;
}
for (unsigned int idx = first_index; idx < currentInterval.second; idx++)
{
float distance = fabsf (line_x * polygon[idx].x + line_y * polygon[idx].y + line_d);
if (distance > max_distance)
{
max_distance = distance;
max_index = idx;
}
}
if (max_distance > threshold)
{
std::pair<unsigned, unsigned> interval (max_index, currentInterval.second);
currentInterval.second = max_index;
intervals.push_back (interval);
}
else
{
result.push_back (currentInterval.second);
intervals.pop_back ();
}
}
approx_polygon.reserve (result.size ());
if (refine)
{
std::vector<Eigen::Vector3f> lines (result.size ());
std::reverse (result.begin (), result.end ());
for (unsigned rIdx = 0; rIdx < result.size (); ++rIdx)
{
unsigned nIdx = rIdx + 1;
if (nIdx == result.size ())
nIdx = 0;
Eigen::Vector2f centroid = Eigen::Vector2f::Zero ();
Eigen::Matrix2f covariance = Eigen::Matrix2f::Zero ();
unsigned pIdx = result[rIdx];
unsigned num_points = 0;
if (pIdx > result[nIdx])
{
num_points = static_cast<unsigned> (polygon.size ()) - pIdx;
for (; pIdx < polygon.size (); ++pIdx)
{
covariance.coeffRef (0) += polygon [pIdx].x * polygon [pIdx].x;
covariance.coeffRef (1) += polygon [pIdx].x * polygon [pIdx].y;
covariance.coeffRef (3) += polygon [pIdx].y * polygon [pIdx].y;
centroid [0] += polygon [pIdx].x;
centroid [1] += polygon [pIdx].y;
}
pIdx = 0;
}
num_points += result[nIdx] - pIdx;
for (; pIdx < result[nIdx]; ++pIdx)
{
covariance.coeffRef (0) += polygon [pIdx].x * polygon [pIdx].x;
covariance.coeffRef (1) += polygon [pIdx].x * polygon [pIdx].y;
covariance.coeffRef (3) += polygon [pIdx].y * polygon [pIdx].y;
centroid [0] += polygon [pIdx].x;
centroid [1] += polygon [pIdx].y;
}
covariance.coeffRef (2) = covariance.coeff (1);
float norm = 1.0f / float (num_points);
centroid *= norm;
covariance *= norm;
covariance.coeffRef (0) -= centroid [0] * centroid [0];
covariance.coeffRef (1) -= centroid [0] * centroid [1];
covariance.coeffRef (3) -= centroid [1] * centroid [1];
float eval;
Eigen::Vector2f normal;
eigen22 (covariance, eval, normal);
// select the one which is more "parallel" to the original line
Eigen::Vector2f direction;
direction [0] = polygon[result[nIdx]].x - polygon[result[rIdx]].x;
direction [1] = polygon[result[nIdx]].y - polygon[result[rIdx]].y;
direction.normalize ();
if (fabs (direction.dot (normal)) > float(M_SQRT1_2))
{
std::swap (normal [0], normal [1]);
normal [0] = -normal [0];
}
// needs to be on the left side of the edge
if (direction [0] * normal [1] < direction [1] * normal [0])
normal *= -1.0;
lines [rIdx].head<2> () = normal;
lines [rIdx] [2] = -normal.dot (centroid);
}
float threshold2 = threshold * threshold;
for (unsigned rIdx = 0; rIdx < lines.size (); ++rIdx)
{
unsigned nIdx = rIdx + 1;
if (nIdx == result.size ())
nIdx = 0;
Eigen::Vector3f vertex = lines [rIdx].cross (lines [nIdx]);
vertex /= vertex [2];
vertex [2] = 0.0;
PointT point;
// test whether we need another edge since the intersection point is too far away from the original vertex
Eigen::Vector3f pq = polygon [result[nIdx]].getVector3fMap () - vertex;
pq [2] = 0.0;
float distance = pq.squaredNorm ();
if (distance > threshold2)
{
// test whether the old point is inside the new polygon or outside
if ((pq [0] * lines [rIdx] [0] + pq [1] * lines [rIdx] [1] < 0.0) &&
(pq [0] * lines [nIdx] [0] + pq [1] * lines [nIdx] [1] < 0.0) )
{
float distance1 = lines [rIdx] [0] * polygon[result[nIdx]].x + lines [rIdx] [1] * polygon[result[nIdx]].y + lines [rIdx] [2];
float distance2 = lines [nIdx] [0] * polygon[result[nIdx]].x + lines [nIdx] [1] * polygon[result[nIdx]].y + lines [nIdx] [2];
point.x = polygon[result[nIdx]].x - distance1 * lines [rIdx] [0];
point.y = polygon[result[nIdx]].y - distance1 * lines [rIdx] [1];
approx_polygon.push_back (point);
vertex [0] = polygon[result[nIdx]].x - distance2 * lines [nIdx] [0];
vertex [1] = polygon[result[nIdx]].y - distance2 * lines [nIdx] [1];
}
}
point.getVector3fMap () = vertex;
approx_polygon.push_back (point);
}
}
else
{
// we have a new polygon in results, but inverted (clockwise <-> counter-clockwise)
for (std::vector<unsigned>::reverse_iterator it = result.rbegin (); it != result.rend (); ++it)
approx_polygon.push_back (polygon [*it]);
}
}