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Add the full source of BambuStudio

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lane.wei 2022-07-15 23:37:19 +08:00 • committed by Lane.Wei
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src/libslic3r/Geometry/ConvexHull.cpp Normal file
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#include "libslic3r.h"
#include "ConvexHull.hpp"
#include "BoundingBox.hpp"
#include <boost/multiprecision/integer.hpp>
namespace Slic3r { namespace Geometry {
// This implementation is based on Andrew's monotone chain 2D convex hull algorithm
Polygon convex_hull(Points pts)
{
std::sort(pts.begin(), pts.end(), [](const Point& a, const Point& b) { return a.x() < b.x() || (a.x() == b.x() && a.y() < b.y()); });
pts.erase(std::unique(pts.begin(), pts.end(), [](const Point& a, const Point& b) { return a.x() == b.x() && a.y() == b.y(); }), pts.end());
Polygon hull;
int n = (int)pts.size();
if (n >= 3) {
int k = 0;
hull.points.resize(2 * n);
// Build lower hull
for (int i = 0; i < n; ++ i) {
while (k >= 2 && pts[i].ccw(hull[k-2], hull[k-1]) <= 0)
-- k;
hull[k ++] = pts[i];
}
// Build upper hull
for (int i = n-2, t = k+1; i >= 0; i--) {
while (k >= t && pts[i].ccw(hull[k-2], hull[k-1]) <= 0)
-- k;
hull[k ++] = pts[i];
}
hull.points.resize(k);
assert(hull.points.front() == hull.points.back());
hull.points.pop_back();
}
return hull;
}
Pointf3s convex_hull(Pointf3s points)
{
assert(points.size() >= 3);
// sort input points
std::sort(points.begin(), points.end(), [](const Vec3d &a, const Vec3d &b){ return a.x() < b.x() || (a.x() == b.x() && a.y() < b.y()); });
int n = points.size(), k = 0;
Pointf3s hull;
if (n >= 3)
{
hull.resize(2 * n);
// Build lower hull
for (int i = 0; i < n; ++i)
{
Point p = Point::new_scale(points[i](0), points[i](1));
while (k >= 2)
{
Point k1 = Point::new_scale(hull[k - 1](0), hull[k - 1](1));
Point k2 = Point::new_scale(hull[k - 2](0), hull[k - 2](1));
if (p.ccw(k2, k1) <= 0)
--k;
else
break;
}
hull[k++] = points[i];
}
// Build upper hull
for (int i = n - 2, t = k + 1; i >= 0; --i)
{
Point p = Point::new_scale(points[i](0), points[i](1));
while (k >= t)
{
Point k1 = Point::new_scale(hull[k - 1](0), hull[k - 1](1));
Point k2 = Point::new_scale(hull[k - 2](0), hull[k - 2](1));
if (p.ccw(k2, k1) <= 0)
--k;
else
break;
}
hull[k++] = points[i];
}
hull.resize(k);
assert(hull.front() == hull.back());
hull.pop_back();
}
return hull;
}
Polygon convex_hull(const Polygons &polygons)
{
Points pp;
for (Polygons::const_iterator p = polygons.begin(); p != polygons.end(); ++p) {
pp.insert(pp.end(), p->points.begin(), p->points.end());
}
return convex_hull(std::move(pp));
}
namespace rotcalip {
using int256_t = boost::multiprecision::int256_t;
using int128_t = boost::multiprecision::int128_t;
template<class Scalar = int64_t>
inline Scalar magnsq(const Point &p)
{
return Scalar(p.x()) * p.x() + Scalar(p.y()) * p.y();
}
template<class Scalar = int64_t>
inline Scalar dot(const Point &a, const Point &b)
{
return Scalar(a.x()) * b.x() + Scalar(a.y()) * b.y();
}
template<class Scalar = int64_t>
inline Scalar dotperp(const Point &a, const Point &b)
{
return Scalar(a.x()) * b.y() - Scalar(a.y()) * b.x();
}
using boost::multiprecision::abs;
// Compares the angle enclosed by vectors dir and dirA (alpha) with the angle
// enclosed by -dir and dirB (beta). Returns -1 if alpha is less than beta, 0
// if they are equal and 1 if alpha is greater than beta. Note that dir is
// reversed for beta, because it represents the opposite side of a caliper.
int cmp_angles(const Point &dir, const Point &dirA, const Point &dirB) {
int128_t dotA = dot(dir, dirA);
int128_t dotB = dot(-dir, dirB);
int256_t dcosa = int256_t(magnsq(dirB)) * int256_t(abs(dotA)) * dotA;
int256_t dcosb = int256_t(magnsq(dirA)) * int256_t(abs(dotB)) * dotB;
int256_t diff = dcosa - dcosb;
return diff > 0? -1 : (diff < 0 ? 1 : 0);
}
// A helper class to navigate on a polygon. Given a vertex index, one can
// get the edge belonging to that vertex, the coordinates of the vertex, the
// next and previous edges. Stuff that is needed in the rotating calipers algo.
class Idx
{
size_t m_idx;
const Polygon *m_poly;
public:
explicit Idx(const Polygon &p): m_idx{0}, m_poly{&p} {}
explicit Idx(size_t idx, const Polygon &p): m_idx{idx}, m_poly{&p} {}
size_t idx() const { return m_idx; }
void set_idx(size_t i) { m_idx = i; }
size_t next() const { return (m_idx + 1) % m_poly->size(); }
size_t inc() { return m_idx = (m_idx + 1) % m_poly->size(); }
Point prev_dir() const {
return pt() - (*m_poly)[(m_idx + m_poly->size() - 1) % m_poly->size()];
}
const Point &pt() const { return (*m_poly)[m_idx]; }
const Point dir() const { return (*m_poly)[next()] - pt(); }
const Point next_dir() const
{
return (*m_poly)[(m_idx + 2) % m_poly->size()] - (*m_poly)[next()];
}
const Polygon &poly() const { return *m_poly; }
};
enum class AntipodalVisitMode { Full, EdgesOnly };
// Visit all antipodal pairs starting from the initial ia, ib pair which
// has to be a valid antipodal pair (not checked). fn is called for every
// antipodal pair encountered including the initial one.
// The callback Fn has a signiture of bool(size_t i, size_t j, const Point &dir)
// where i,j are the vertex indices of the antipodal pair and dir is the
// direction of the calipers touching the i vertex.
template<AntipodalVisitMode mode = AntipodalVisitMode::Full, class Fn>
void visit_antipodals (Idx& ia, Idx &ib, Fn &&fn)
{
// Set current caliper direction to be the lower edge angle from X axis
int cmp = cmp_angles(ia.prev_dir(), ia.dir(), ib.dir());
Idx *current = cmp <= 0 ? &ia : &ib, *other = cmp <= 0 ? &ib : &ia;
Idx *initial = current;
bool visitor_continue = true;
size_t start = initial->idx();
bool finished = false;
while (visitor_continue && !finished) {
Point current_dir_a = current == &ia ? current->dir() : -current->dir();
visitor_continue = fn(ia.idx(), ib.idx(), current_dir_a);
// Parallel edges encountered. An additional pair of antipodals
// can be yielded.
if constexpr (mode == AntipodalVisitMode::Full)
if (cmp == 0 && visitor_continue) {
visitor_continue = fn(current == &ia ? ia.idx() : ia.next(),
current == &ib ? ib.idx() : ib.next(),
current_dir_a);
}
cmp = cmp_angles(current->dir(), current->next_dir(), other->dir());
current->inc();
if (cmp > 0) {
std::swap(current, other);
}
if (initial->idx() == start) finished = true;
}
}
} // namespace rotcalip
bool convex_polygons_intersect(const Polygon &A, const Polygon &B)
{
using namespace rotcalip;
// Establish starting antipodals as extremes in XY plane. Use the
// easily obtainable bounding boxes to check if A and B is disjoint
// and return false if the are.
struct BB
{
size_t xmin = 0, xmax = 0, ymin = 0, ymax = 0;
const Polygon &P;
static bool cmpy(const Point &l, const Point &u)
{
return l.y() < u.y() || (l.y() == u.y() && l.x() < u.x());
}
BB(const Polygon &poly): P{poly}
{
for (size_t i = 0; i < P.size(); ++i) {
if (P[i] < P[xmin]) xmin = i;
if (P[xmax] < P[i]) xmax = i;
if (cmpy(P[i], P[ymin])) ymin = i;
if (cmpy(P[ymax], P[i])) ymax = i;
}
}
};
BB bA{A}, bB{B};
BoundingBox bbA{{A[bA.xmin].x(), A[bA.ymin].y()}, {A[bA.xmax].x(), A[bA.ymax].y()}};
BoundingBox bbB{{B[bB.xmin].x(), B[bB.ymin].y()}, {B[bB.xmax].x(), B[bB.ymax].y()}};
// if (!bbA.overlap(bbB))
// return false;
// Establish starting antipodals as extreme vertex pairs in X or Y direction
// which reside on different polygons. If no such pair is found, the two
// polygons are certainly not disjoint.
Idx imin{bA.xmin, A}, imax{bB.xmax, B};
if (B[bB.xmin] < imin.pt()) imin = Idx{bB.xmin, B};
if (imax.pt() < A[bA.xmax]) imax = Idx{bA.xmax, A};
if (&imin.poly() == &imax.poly()) {
imin = Idx{bA.ymin, A};
imax = Idx{bB.ymax, B};
if (B[bB.ymin] < imin.pt()) imin = Idx{bB.ymin, B};
if (imax.pt() < A[bA.ymax]) imax = Idx{bA.ymax, A};
}
if (&imin.poly() == &imax.poly())
return true;
bool found_divisor = false;
visit_antipodals<AntipodalVisitMode::EdgesOnly>(
imin, imax,
[&imin, &imax, &found_divisor](size_t ia, size_t ib, const Point &dir) {
// std::cout << "A" << ia << " B" << ib << " dir " <<
// dir.x() << " " << dir.y() << std::endl;
const Polygon &A = imin.poly(), &B = imax.poly();
Point ref_a = A[(ia + 2) % A.size()], ref_b = B[(ib + 2) % B.size()];
bool is_left_a = dotperp( dir, ref_a - A[ia]) > 0;
bool is_left_b = dotperp(-dir, ref_b - B[ib]) > 0;
// If both reference points are on the left (or right) of their
// respective support lines and the opposite support line is to
// the right (or left), the divisor line is found. We only test
// the reference point, as by definition, if that is on one side,
// all the other points must be on the same side of a support
// line. If the support lines are collinear, the polygons must be
// on the same side of their respective support lines.
auto d = dotperp(dir, B[ib] - A[ia]);
if (d == 0) {
// The caliper lines are collinear, not just parallel
found_divisor = (is_left_a && is_left_b) || (!is_left_a && !is_left_b);
} else if (d > 0) { // B is to the left of (A, A+1)
found_divisor = !is_left_a && !is_left_b;
} else { // B is to the right of (A, A+1)
found_divisor = is_left_a && is_left_b;
}
return !found_divisor;
});
// Intersects if the divisor was not found
return !found_divisor;
}
// Decompose source convex hull points into a top / bottom chains with monotonically increasing x,
// creating an implicit trapezoidal decomposition of the source convex polygon.
// The source convex polygon has to be CCW oriented. O(n) time complexity.
std::pair<std::vector<Vec2d>, std::vector<Vec2d>> decompose_convex_polygon_top_bottom(const std::vector<Vec2d> &src)
{
std::pair<std::vector<Vec2d>, std::vector<Vec2d>> out;
std::vector<Vec2d> &bottom = out.first;
std::vector<Vec2d> &top = out.second;
// Find the minimum point.
auto left_bottom = std::min_element(src.begin(), src.end(), [](const auto &l, const auto &r) { return l.x() < r.x() || (l.x() == r.x() && l.y() < r.y()); });
auto right_top = std::max_element(src.begin(), src.end(), [](const auto &l, const auto &r) { return l.x() < r.x() || (l.x() == r.x() && l.y() < r.y()); });
if (left_bottom != src.end() && left_bottom != right_top) {
// Produce the bottom and bottom chains.
if (left_bottom < right_top) {
bottom.assign(left_bottom, right_top + 1);
size_t cnt = (src.end() - right_top) + (left_bottom + 1 - src.begin());
top.reserve(cnt);
top.assign(right_top, src.end());
top.insert(top.end(), src.begin(), left_bottom + 1);
} else {
size_t cnt = (src.end() - left_bottom) + (right_top + 1 - src.begin());
bottom.reserve(cnt);
bottom.assign(left_bottom, src.end());
bottom.insert(bottom.end(), src.begin(), right_top + 1);
top.assign(right_top, left_bottom + 1);
}
// Remove strictly vertical segments at the end.
if (bottom.size() > 1) {
auto it = bottom.end();
for (-- it; it != bottom.begin() && (it - 1)->x() == bottom.back().x(); -- it) ;
bottom.erase(it + 1, bottom.end());
}
if (top.size() > 1) {
auto it = top.end();
for (-- it; it != top.begin() && (it - 1)->x() == top.back().x(); -- it) ;
top.erase(it + 1, top.end());
}
std::reverse(top.begin(), top.end());
}
if (top.size() < 2 || bottom.size() < 2) {
// invalid
top.clear();
bottom.clear();
}
return out;
}
// Convex polygon check using a top / bottom chain decomposition with O(log n) time complexity.
bool inside_convex_polygon(const std::pair<std::vector<Vec2d>, std::vector<Vec2d>> &top_bottom_decomposition, const Vec2d &pt)
{
auto it_bottom = std::lower_bound(top_bottom_decomposition.first.begin(), top_bottom_decomposition.first.end(), pt, [](const auto &l, const auto &r){ return l.x() < r.x(); });
auto it_top = std::lower_bound(top_bottom_decomposition.second.begin(), top_bottom_decomposition.second.end(), pt, [](const auto &l, const auto &r){ return l.x() < r.x(); });
if (it_bottom == top_bottom_decomposition.first.end()) {
// Above max x.
assert(it_top == top_bottom_decomposition.second.end());
return false;
}
if (it_bottom == top_bottom_decomposition.first.begin()) {
// Below or at min x.
if (pt.x() < it_bottom->x()) {
// Below min x.
assert(pt.x() < it_top->x());
return false;
}
// At min x.
assert(pt.x() == it_bottom->x());
assert(pt.x() == it_top->x());
assert(it_bottom->y() <= pt.y() <= it_top->y());
return pt.y() >= it_bottom->y() && pt.y() <= it_top->y();
}
// Trapezoid or a triangle.
assert(it_bottom != top_bottom_decomposition.first .begin() && it_bottom != top_bottom_decomposition.first .end());
assert(it_top != top_bottom_decomposition.second.begin() && it_top != top_bottom_decomposition.second.end());
assert(pt.x() <= it_bottom->x());
assert(pt.x() <= it_top->x());
auto it_top_prev = it_top - 1;
auto it_bottom_prev = it_bottom - 1;
assert(pt.x() >= it_top_prev->x());
assert(pt.x() >= it_bottom_prev->x());
double det = cross2(*it_bottom - *it_bottom_prev, pt - *it_bottom_prev);
if (det < 0)
return false;
det = cross2(*it_top - *it_top_prev, pt - *it_top_prev);
return det <= 0;
}
} // namespace Geometry
} // namespace Slic3r