#pragma once
#ifndef TCG_POLYLINE_OPS_HPP
#define TCG_POLYLINE_OPS_HPP
// tcg includes
#include "../polyline_ops.h"
#include "../iterator_ops.h"
#include "../sequence_ops.h"
#include "../point_ops.h"
// STD includes
#include <assert.h>
namespace tcg {
namespace polyline_ops {
using tcg::point_ops::operator/;
//***********************************************************************************
// Standard Deviation Evaluator
//***********************************************************************************
template <typename RanIt>
StandardDeviationEvaluator<RanIt>::StandardDeviationEvaluator(
const RanIt &begin, const RanIt &end)
: m_begin(begin), m_end(end) {
// Let m_sum[i] and m_sum2[i] be respectively the sums of vertex coordinates
//(relative to begin is sufficient) from 0 to i, and the sums of their
// squares;
// m_sumsMix contain sums of xy terms.
diff_type i, n = m_end - m_begin;
diff_type n2 = n * 2;
m_sums_x.resize(n);
m_sums_y.resize(n);
m_sums2_x.resize(n);
m_sums2_y.resize(n);
m_sums_xy.resize(n);
m_sums_x[0] = m_sums_y[0] = m_sums2_x[0] = m_sums2_y[0] = m_sums_xy[0] = 0.0;
// Build sums following the path
point_type posToBegin;
i = 0;
iterator_type a = m_begin;
for (a = m_begin, ++a; a != m_end; ++a, ++i) {
posToBegin = point_type(a->x - m_begin->x, a->y - m_begin->y);
m_sums_x[i + 1] = m_sums_x[i] + posToBegin.x;
m_sums_y[i + 1] = m_sums_y[i] + posToBegin.y;
m_sums2_x[i + 1] = m_sums2_x[i] + sq(posToBegin.x);
m_sums2_y[i + 1] = m_sums2_y[i] + sq(posToBegin.y);
m_sums_xy[i + 1] = m_sums_xy[i] + posToBegin.x * posToBegin.y;
}
}
//------------------------------------------------------------------------------------
template <typename RanIt>
typename StandardDeviationEvaluator<RanIt>::penalty_type
StandardDeviationEvaluator<RanIt>::penalty(const iterator_type &a,
const iterator_type &b) {
diff_type aIdx = a - m_begin, bIdx = b - m_begin;
point_type v(b->x - a->x, b->y - a->y),
a_(a->x - m_begin->x, a->y - m_begin->y);
double n = b - a; // Needs to be of higher precision than diff_type
double sumX = m_sums_x[bIdx] - m_sums_x[aIdx];
double sumY = m_sums_y[bIdx] - m_sums_y[aIdx];
double sum2X = m_sums2_x[bIdx] - m_sums2_x[aIdx];
double sum2Y = m_sums2_y[bIdx] - m_sums2_y[aIdx];
double sumMix = m_sums_xy[bIdx] - m_sums_xy[aIdx];
if (bIdx < aIdx) {
int count = m_end - m_begin, count_1 = count - 1;
n += count;
sumX += m_sums_x[count_1];
sumY += m_sums_y[count_1];
sum2X += m_sums2_x[count_1];
sum2Y += m_sums2_y[count_1];
sumMix += m_sums_xy[count_1];
}
double A = sum2Y - 2.0 * sumY * a_.y + n * sq(a_.y);
double B = sum2X - 2.0 * sumX * a_.x + n * sq(a_.x);
double C = sumMix - sumX * a_.y - sumY * a_.x + n * a_.x * a_.y;
return sqrt((v.x * v.x * A + v.y * v.y * B - 2 * v.x * v.y * C) / n);
}
//***********************************************************************************
// Quadratics approximation Evaluator
//***********************************************************************************
template <typename Point>
class _QuadraticsEdgeEvaluator {
public:
typedef Point point_type;
typedef typename tcg::point_traits<point_type>::value_type value_type;
typedef typename std::vector<Point>::iterator cp_iterator;
typedef typename tcg::step_iterator<cp_iterator> quad_iterator;
typedef double penalty_type;
private:
quad_iterator m_begin, m_end;
penalty_type m_tol;
public:
_QuadraticsEdgeEvaluator(const quad_iterator &begin, const quad_iterator &end,
penalty_type tol);
quad_iterator furthestFrom(const quad_iterator &a);
penalty_type penalty(const quad_iterator &a, const quad_iterator &b);
};
//---------------------------------------------------------------------------
template <typename Point>
_QuadraticsEdgeEvaluator<Point>::_QuadraticsEdgeEvaluator(
const quad_iterator &begin, const quad_iterator &end, penalty_type tol)
: m_begin(begin), m_end(end), m_tol(tol) {}
//---------------------------------------------------------------------------
template <typename Point>
typename _QuadraticsEdgeEvaluator<Point>::quad_iterator
_QuadraticsEdgeEvaluator<Point>::furthestFrom(const quad_iterator &at) {
const point_type &A = *at;
const point_type &A1 = *(at.it() + 1);
// Build at (opposite) side
int atSide_ = -tcg::numeric_ops::sign(cross(A - A1, *(at + 1) - A1));
bool atSideNotZero = (atSide_ != 0);
quad_iterator bt,
last = this->m_end - 1; // Don't do the last (it's a dummy quad)
for (bt = at + 1; bt != last; ++bt) // Always allow 1 step
{
// Trying to reach (bt + 1) from at
const point_type &C = *(bt + 1);
const point_type &C1 = *(bt.it() + 1);
// Ensure that bt is not a corner
if (std::abs(tcg::point_ops::cross(*(bt.it() - 1) - *bt, *(bt.it() + 1) - *bt)) >
1e-3)
break;
// Ensure there is no sign inversion
int btSide =
tcg::numeric_ops::sign(tcg::point_ops::cross(*bt - C1, C - C1));
if (atSideNotZero && btSide != 0 && btSide == atSide_) break;
// Build the approximating new quad if any
value_type s, t;
tcg::point_ops::intersectionSegCoords(A, A1, C, C1, s, t, 1e-4);
if (s == tcg::numeric_ops::NaN<value_type>()) {
// A-A1 and C1-C are parallel. There are 2 cases:
if ((A1 - A) * (C - C1) >= 0)
// Either we're still on a straight line
continue;
else
// Or, we just can't build the new quad
break;
}
point_type B(A + s * (A1 - A));
point_type A_B(A - B);
point_type AC_2B(A_B + C - B);
// Now, for each quadratic between at and bt, build the 'distance' from our
// new
// approximating quad (ABC)
quad_iterator qt, end = bt + 1;
for (qt = at; qt != end; ++qt) {
const point_type &Q_A(*qt);
const point_type &Q_B(*(qt.it() + 1));
const point_type &Q_C(*(qt + 1));
// Check the distance of Q_B from the ABC tangent whose direction
// is the same as Q'_B - ie, Q_A -> Q_C.
point_type dir(Q_C - Q_A);
value_type dirNorm = tcg::point_ops::norm(dir);
if (dirNorm < 1e-4) break;
dir = dir / dirNorm;
value_type den = tcg::point_ops::cross(AC_2B, dir);
if (den < 1e-4 && den > -1e-4) break;
value_type t = tcg::point_ops::cross(A_B, dir) / den;
if (t < 0.0 || t > 1.0) break;
value_type t1 = 1.0 - t;
point_type P(sq(t1) * A + 2.0 * t * t1 * B + sq(t) * C);
point_type Q(0.25 * Q_A + 0.5 * Q_B + 0.25 * Q_C);
if (tcg::point_ops::lineDist(Q, P, dir) > m_tol) break;
value_type pos = ((P - Q_A) * dir);
if (pos < 0.0 || pos > dirNorm) break;
/*if(pos < -m_tol || pos > dirNorm + m_tol) //Should this be relaxed
too?
break;*/
if (qt == bt) continue;
// Check the distance of Q_C from the ABC tangent whose direction
// is the same as Q'_C.
dir = tcg::point_ops::direction(Q_B, Q_C);
den = tcg::point_ops::cross(AC_2B, dir);
if (den < 1e-4 && den > -1e-4) break;
t = tcg::point_ops::cross(A_B, dir) / den;
if (t < 0.0 || t > 1.0) break;
t1 = 1.0 - t;
P = sq(t1) * A + 2.0 * t * t1 * B + sq(t) * C;
if (tcg::point_ops::lineDist(Q_C, P, dir) > m_tol) break;
}
if (qt != end) break; // Constraints were violated
}
return std::min(bt, this->m_end - 1);
}
//---------------------------------------------------------------------------
template <typename Point>
typename _QuadraticsEdgeEvaluator<Point>::penalty_type
_QuadraticsEdgeEvaluator<Point>::penalty(const quad_iterator &at,
const quad_iterator &bt) {
if (bt == at + 1) return 0.0;
penalty_type penalty = 0.0;
const point_type &A(*at);
const point_type &A1(*(at.it() + 1));
const point_type &C(*bt);
const point_type &C1(*(bt.it() - 1));
// Build B
value_type s, t;
tcg::point_ops::intersectionSegCoords(A, A1, C, C1, s, t, 1e-4);
if (s == tcg::numeric_ops::NaN<value_type>()) return 0.0;
point_type B(A + s * (A1 - A));
// Iterate and build penalties
point_type A_B(A - B);
point_type AC_2B(A_B + C - B);
quad_iterator qt, bt_1 = bt - 1;
for (qt = at; qt != bt; ++qt) {
const point_type &Q_A(*qt);
const point_type &Q_B(*(qt.it() + 1));
const point_type &Q_C(*(qt + 1));
// point_type dir(tcg::point_ops::direction(Q_A, Q_C));
point_type dir(Q_C - Q_A);
dir = dir / tcg::point_ops::norm(dir);
value_type t =
tcg::point_ops::cross(A_B, dir) / tcg::point_ops::cross(AC_2B, dir);
assert(t >= 0.0 && t <= 1.0);
value_type t1 = 1.0 - t;
point_type P(sq(t1) * A + 2.0 * t * t1 * B + sq(t) * C);
point_type Q(0.25 * Q_A + 0.5 * Q_B + 0.25 * Q_C);
penalty += tcg::point_ops::lineDist(Q, P, dir);
if (qt == bt_1) continue;
dir = tcg::point_ops::direction(Q_B, Q_C);
t = tcg::point_ops::cross(A_B, dir) / tcg::point_ops::cross(AC_2B, dir);
assert(t >= 0.0 && t <= 1.0);
t1 = 1.0 - t;
P = sq(t1) * A + 2.0 * t * t1 * B + sq(t) * C;
penalty += tcg::point_ops::lineDist(Q_C, P, dir);
}
return penalty;
}
//***********************************************************************************
// Conversion to Quadratics functions
//***********************************************************************************
template <typename cps_reader>
class _QuadReader {
public:
typedef typename cps_reader::value_type point_type;
typedef typename tcg::point_traits<point_type>::value_type value_type;
typedef typename std::vector<point_type>::iterator cps_iterator;
typedef typename tcg::step_iterator<cps_iterator> quad_iterator;
private:
cps_reader &m_reader;
quad_iterator m_it;
public:
_QuadReader(cps_reader &reader) : m_reader(reader) {}
void openContainer(const quad_iterator &it) {
m_reader.openContainer(*it);
m_it = it;
}
void addElement(const quad_iterator &it) {
if (it == m_it + 1) {
m_reader.addElement(*(it.it() - 1));
m_reader.addElement(*it);
} else {
const point_type &A(*m_it);
const point_type &A1(*(m_it.it() + 1));
const point_type &C(*it);
const point_type &C1(*(it.it() - 1));
// Build B
value_type s, t;
tcg::point_ops::intersectionSegCoords(A, A1, C, C1, s, t, 1e-4);
point_type B((s == tcg::numeric_ops::NaN<value_type>())
? 0.5 * (A + C)
: A + s * (A1 - A));
m_reader.addElement(B);
m_reader.addElement(C);
}
m_it = it;
}
void closeContainer() { m_reader.closeContainer(); }
};
//---------------------------------------------------------------------------
template <typename iter_type, typename Reader, typename tripleToQuadsFunc>
void _naiveQuadraticConversion(const iter_type &begin, const iter_type &end,
Reader &reader,
tripleToQuadsFunc &tripleToQuadsF) {
typedef typename std::iterator_traits<iter_type>::value_type point_type;
point_type a, c;
iter_type it, jt;
iter_type last(end);
--last;
if (*begin != *last) {
reader.openContainer();
reader.addElement(*begin);
++(it = begin);
a = 0.5 * (*begin + *it);
reader.addElement(0.5 * (*begin + a));
reader.addElement(a);
// Work out each quadratic
for (++(jt = it); jt != end; it = jt, ++jt) {
c = 0.5 * (*it + *jt);
tripleToQuadsF(a, it, c, reader);
a = c;
}
reader.addElement(0.5 * (a + *it));
reader.addElement(*it);
} else {
++(it = begin);
point_type first = a = 0.5 * (*begin + *it);
reader.openContainer();
reader.addElement(a);
for (++(jt = it); jt != end; it = jt, ++jt) {
c = 0.5 * (*it + *jt);
tripleToQuadsF(a, it, c, reader);
a = c;
}
tripleToQuadsF(a, last, first, reader);
}
reader.closeContainer();
}
//---------------------------------------------------------------------------
template <typename iter_type, typename containers_reader, typename toQuadsFunc>
void toQuadratics(iter_type begin, iter_type end, containers_reader &output,
toQuadsFunc &toQuadsF, double reductionTol) {
typedef typename std::iterator_traits<iter_type>::difference_type diff_type;
typedef typename std::iterator_traits<iter_type>::value_type point_type;
typedef typename tcg::point_traits<point_type>::value_type value_type;
if (begin == end) return;
diff_type count = std::distance(begin, end);
if (count < 2) {
// Single point - add 2 points on top of it and quit.
output.openContainer(*begin);
output.addElement(*begin), output.addElement(*begin);
output.closeContainer();
return;
}
if (count == 2) {
// Segment case
iter_type it = begin;
++it;
output.openContainer(*begin);
output.addElement(0.5 * (*begin + *it)), output.addElement(*it);
output.closeContainer();
return;
}
// Build an intermediate vector of points containing the naive quadratic
// conversion.
std::vector<point_type> cps;
tcg::sequential_reader<std::vector<point_type>> cpsReader(&cps);
_naiveQuadraticConversion(begin, end, cpsReader, toQuadsF);
if (reductionTol <= 0) {
output.openContainer(*cps.begin());
// Directly output the naive conversion
typename std::vector<point_type>::iterator it, end = cps.end();
for (it = ++cps.begin(); it != end; ++it) output.addElement(*it);
output.closeContainer();
return;
}
// Resize the cps to cover a multiple of 2
cps.resize(cps.size() + 2 - (cps.size() % 2));
// Now, launch the quadratics reduction procedure
tcg::step_iterator<typename std::vector<point_type>::iterator> bt(cps.begin(),
2),
et(cps.end(), 2);
_QuadraticsEdgeEvaluator<point_type> eval(bt, et, reductionTol);
_QuadReader<containers_reader> quadReader(output);
bool ret = tcg::sequence_ops::minimalPath(bt, et, eval, quadReader);
assert(ret);
}
}
} // namespace tcg::polyline_ops
#endif // TCG_POLYLINE_OPS_HPP