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Reworked algorithm for Voronoi Offset curve extraction.

Browse Source 
Now the algorithm is very different from the OpenVoronoi implementation
and hopefully it is now correct (save numerical issues, which will be
a big PITA).
This commit is contained in:
Vojtech Bubnik 2020-06-11 16:09:51 +02:00
parent 9566a05d8f
commit 1c95ceaeaa
7 changed files with 908 additions and 583 deletions
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1
src/libslic3r/CMakeLists.txt
View File

@ -190,6 +190,7 @@ add_library(libslic3r STATIC
MTUtils.hpp
VoronoiOffset.cpp
VoronoiOffset.hpp
VoronoiVisualUtils.hpp
Zipper.hpp
Zipper.cpp
MinAreaBoundingBox.hpp

2
src/libslic3r/Line.cpp
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@ -135,4 +135,4 @@ BoundingBox get_extents(const Lines &lines)
return bbox;
}
}
} // namespace Slic3r

4
src/libslic3r/Line.hpp
View File

@ -103,7 +103,7 @@ public:
Vec3d b;
};
extern BoundingBox get_extents(const Lines &lines);
BoundingBox get_extents(const Lines &lines);
} // namespace Slic3r
@ -125,4 +125,4 @@ namespace boost { namespace polygon {
} }
// end Boost
#endif
#endif // slic3r_Line_hpp_

643
src/libslic3r/VoronoiOffset.cpp
View File

@ -1,11 +1,15 @@
// Polygon offsetting code inspired by OpenVoronoi by Anders Wallin
// https://github.com/aewallin/openvoronoi
// This offsetter uses results of boost::polygon Voronoi.
// Polygon offsetting using Voronoi diagram prodiced by boost::polygon.
#include "VoronoiOffset.hpp"
#include <cmath>
// #define VORONOI_DEBUG_OUT
#ifdef VORONOI_DEBUG_OUT
#include <libslic3r/VoronoiVisualUtils.hpp>
#endif
namespace Slic3r {
using VD = Geometry::VoronoiDiagram;
@ -48,6 +52,93 @@ namespace detail {
}
}
struct Intersections
{
int count;
Vec2d pts[2];
};
// Return maximum two points, that are at distance "d" from both points
Intersections point_point_equal_distance_points(const Point &pt1, const Point &pt2, const double d)
{
// input points
const auto cx = double(pt1.x());
const auto cy = double(pt1.y());
const auto qx = double(pt2.x());
const auto qy = double(pt2.y());
// Calculating determinant.
auto x0 = 2. * qy;
auto cx2 = cx * cx;
auto cy2 = cy * cy;
auto x5 = 2 * cx * qx;
auto x6 = cy * x0;
auto qx2 = qx * qx;
auto qy2 = qy * qy;
auto x9 = qx2 + qy2;
auto x10 = cx2 + cy2 - x5 - x6 + x9;
auto x11 = - cx2 - cy2;
auto discr = x10 * (4. * d + x11 + x5 + x6 - qx2 - qy2);
if (discr < 0.)
// No intersection point found, the two circles are too far away.
return Intersections { 0, { Vec2d(), Vec2d() } };
// Some intersections are found.
int npoints = (discr > 0) ? 2 : 1;
auto x1 = 2. * cy - x0;
auto x2 = cx - qx;
auto x12 = 0.5 * x2 * sqrt(discr) / x10;
auto x13 = 0.5 * (cy + qy);
auto x14 = - x12 + x13;
auto x15 = x11 + x9;
auto x16 = 0.5 / x2;
auto x17 = x12 + x13;
return Intersections { npoints, { Vec2d(- x16 * (x1 * x14 + x15), x14),
Vec2d(- x16 * (x1 * x17 + x15), x17) } };
}
// Return maximum two points, that are at distance "d" from both the line and point.
Intersections line_point_equal_distance_points(const Line &line, const Point &pt, const double d)
{
assert(line.a != pt && line.b != pt);
// Calculating two points of distance "d" to a ray and a point.
// Point.
auto x0 = double(pt.x());
auto y0 = double(pt.y());
// Ray equation. Vector (a, b) is perpendicular to line.
auto a = double(line.a.y() - line.b.y());
auto b = double(line.b.x() - line.a.x());
// pt shall not lie on line.
assert(std::abs((x0 - line.a.x()) * a + (y0 - line.a.y()) * b) < SCALED_EPSILON);
// Orient line so that the vector (a, b) points towards pt.
if (a * (x0 - line.a.x()) + b * (y0 - line.a.y()) < 0.)
std::swap(x0, y0);
double c = - a * double(line.a.x()) - b * double(line.a.y());
// Calculate the two points.
double a2 = a * a;
double b2 = b * b;
double a2b2 = a2 + b2;
double d2 = d * d;
double s = a2*d2 - a2*sqr(x0) - 2*a*b*x0*y0 - 2*a*c*x0 + 2*a*d*x0 + b2*d2 - b2*sqr(y0) - 2*b*c*y0 + 2*b*d*y0 - sqr(c) + 2*c*d - d2;
if (s < 0.)
// Distance of pt from line is bigger than 2 * d.
return Intersections { 0 };
double u;
int cnt;
if (s == 0.) {
// Distance of pt from line is 2 * d.
cnt = 1;
u = 0.;
} else {
// Distance of pt from line is smaller than 2 * d.
cnt = 2;
u = a*sqrt(s)/a2b2;
}
double v = (-a2*y0 + a*b*x0 + b*c - b*d)/a2b2;
return Intersections { cnt, { Vec2d((b * ( u + v) - c + d) / a, - u - v),
Vec2d((b * (- u + v) - c + d) / a, u - v) } };
}
Vec2d voronoi_edge_offset_point(
const VD &vd,
const Lines &lines,
@ -131,174 +222,384 @@ namespace detail {
}
};
Polygons voronoi_offset(const VD &vd, const Lines &lines, double offset_distance, double discretization_error)
static Vec2d foot_pt(const Line &iline, const Point &ipt)
{
// Distance of a VD vertex to the closest site (input polygon edge or vertex).
std::vector<double> vertex_dist(vd.num_vertices(), std::numeric_limits<double>::max());
Vec2d pt = iline.a.cast<double>();
Vec2d dir = (iline.b - iline.a).cast<double>();
Vec2d v = ipt.cast<double>() - pt;
double l2 = dir.squaredNorm();
double t = (l2 == 0.) ? 0. : v.dot(dir) / l2;
return pt + dir * t;
}
// Minium distance of a VD edge to the closest site (input polygon edge or vertex).
// For a parabolic segment the distance may be smaller than the distance of the two end points.
std::vector<double> edge_dist(vd.num_edges(), std::numeric_limits<double>::max());
// Calculate minimum distance of input polygons to voronoi vertices and voronoi edges.
for (const VD::edge_type &edge : vd.edges()) {
const VD::vertex_type *v0 = edge.vertex0();
const VD::vertex_type *v1 = edge.vertex1();
const VD::cell_type *cell = edge.cell();
const VD::cell_type *cell2 = edge.twin()->cell();
const Line &line0 = lines[cell->source_index()];
const Line &line1 = lines[cell2->source_index()];
double d0, d1, dmin;
if (v0 == nullptr || v1 == nullptr) {
assert(edge.is_infinite());
if (cell->contains_point() && cell2->contains_point()) {
const Point &pt0 = (cell->source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_START_POINT) ? line0.a : line0.b;
const Point &pt1 = (cell2->source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_START_POINT) ? line1.a : line1.b;
d0 = d1 = std::numeric_limits<double>::max();
if (v0 == nullptr && v1 == nullptr) {
dmin = (pt1.cast<double>() - pt0.cast<double>()).norm();
} else {
Vec2d pt((pt0 + pt1).cast<double>() * 0.5);
Vec2d dir(double(pt0.y() - pt1.y()), double(pt1.x() - pt0.x()));
Vec2d pt0d(pt0.x(), pt0.y());
if (v0) {
Vec2d a(v0->x(), v0->y());
d0 = (a - pt0d).norm();
dmin = ((a - pt).dot(dir) < 0.) ? (a - pt0d).norm() : d0;
vertex_dist[v0 - &vd.vertices().front()] = d0;
} else {
Vec2d a(v1->x(), v1->y());
d1 = (a - pt0d).norm();
dmin = ((a - pt).dot(dir) < 0.) ? (a - pt0d).norm() : d1;
vertex_dist[v1 - &vd.vertices().front()] = d1;
}
}
} else {
// Infinite edges could not be created by two segment sites.
assert(cell->contains_point() != cell2->contains_point());
// Linear edge goes through the endpoint of a segment.
assert(edge.is_linear());
assert(edge.is_secondary());
Polygons voronoi_offset(
const Geometry::VoronoiDiagram &vd,
const Lines &lines,
double offset_distance,
double discretization_error)
{
#ifndef NDEBUG
if (cell->contains_segment()) {
const Point &pt1 = (cell2->source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_START_POINT) ? line1.a : line1.b;
assert((pt1.x() == line0.a.x() && pt1.y() == line0.a.y()) ||
(pt1.x() == line0.b.x() && pt1.y() == line0.b.y()));
// Verify that twin halfedges are stored next to the other in vd.
for (size_t i = 0; i < vd.num_edges(); i += 2) {
const VD::edge_type &e = vd.edges()[i];
const VD::edge_type &e2 = vd.edges()[i + 1];
assert(e.twin() == &e2);
assert(e2.twin() == &e);
assert(e.is_secondary() == e2.is_secondary());
if (e.is_secondary()) {
assert(e.cell()->contains_point() != e2.cell()->contains_point());
const VD::edge_type &ex = (e.cell()->contains_point() ? e : e2);
// Verify that the Point defining the cell left of ex is an end point of a segment
// defining the cell right of ex.
const Line &line0 = lines[ex.cell()->source_index()];
const Line &line1 = lines[ex.twin()->cell()->source_index()];
const Point &pt = (ex.cell()->source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_START_POINT) ? line0.a : line0.b;
assert(pt == line1.a || pt == line1.b);
}
}
#endif // NDEBUG
// Mark edges with outward vertex pointing outside the polygons, thus there is a chance
// that such an edge will have an intersection with our desired offset curve.
bool outside = offset_distance > 0.;
std::vector<char> edge_candidate(vd.num_edges(), 2); // unknown state
const VD::edge_type *front_edge = &vd.edges().front();
for (const VD::edge_type &edge : vd.edges())
if (edge.vertex1() == nullptr) {
// Infinite Voronoi edge separating two Point sites.
// Infinite edge is always outside and it has at least one valid vertex.
assert(edge.vertex0() != nullptr);
edge_candidate[&edge - front_edge] = outside;
// Opposite edge of an infinite edge is certainly not active.
edge_candidate[edge.twin() - front_edge] = 0;
} else if (edge.vertex1() != nullptr) {
// Finite edge.
const VD::cell_type *cell = edge.cell();
const Line *line = cell->contains_segment() ? &lines[cell->source_index()] : nullptr;
if (line == nullptr) {
cell = edge.twin()->cell();
line = cell->contains_segment() ? &lines[cell->source_index()] : nullptr;
}
if (line) {
const VD::vertex_type *v1 = edge.vertex1();
assert(v1);
Vec2d l0(line->a.cast<double>());
Vec2d lv((line->b - line->a).cast<double>());
double side = cross2(lv, Vec2d(v1->x(), v1->y()) - l0);
edge_candidate[&edge - front_edge] = outside ? (side < 0.) : (side > 0.);
}
}
for (const VD::edge_type &edge : vd.edges())
if (edge_candidate[&edge - front_edge] == 2) {
assert(edge.cell()->contains_point() && edge.twin()->cell()->contains_point());
// Edge separating two point sources, not yet classified as inside / outside.
const VD::edge_type *e = &edge;
char state;
do {
state = edge_candidate[e - front_edge];
if (state != 2)
break;
e = e->next();
} while (e != &edge);
e = &edge;
do {
char &s = edge_candidate[e - front_edge];
if (s == 2) {
assert(e->cell()->contains_point() && e->twin()->cell()->contains_point());
assert(edge_candidate[e->twin() - front_edge] == 2);
s = state;
edge_candidate[e->twin() - front_edge] = state;
}
e = e->next();
} while (e != &edge);
}
if (! outside)
offset_distance = - offset_distance;
#ifdef VORONOI_DEBUG_OUT
BoundingBox bbox;
{
bbox.merge(get_extents(lines));
bbox.min -= (0.01 * bbox.size().cast<double>()).cast<coord_t>();
bbox.max += (0.01 * bbox.size().cast<double>()).cast<coord_t>();
}
{
Lines helper_lines;
for (const VD::edge_type &edge : vd.edges())
if (edge_candidate[&edge - front_edge]) {
const VD::vertex_type *v0 = edge.vertex0();
const VD::vertex_type *v1 = edge.vertex1();
assert(v0 != nullptr);
Vec2d pt1(v0->x(), v0->y());
Vec2d pt2;
if (v1 == nullptr) {
// Unconstrained edge. Calculate a trimmed position.
assert(edge.is_linear());
const VD::cell_type *cell = edge.cell();
const VD::cell_type *cell2 = edge.twin()->cell();
const Line &line0 = lines[cell->source_index()];
const Line &line1 = lines[cell2->source_index()];
if (cell->contains_point() && cell2->contains_point()) {
const Point &pt0 = (cell->source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_START_POINT) ? line0.a : line0.b;
const Point &pt1 = (cell2->source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_START_POINT) ? line1.a : line1.b;
// Direction vector of this unconstrained Voronoi edge.
Vec2d dir(double(pt0.y() - pt1.y()), double(pt1.x() - pt0.x()));
pt2 = Vec2d(v0->x(), v0->y()) + dir.normalized() * scale_(10.);
} else {
// Infinite edges could not be created by two segment sites.
assert(cell->contains_point() != cell2->contains_point());
// Linear edge goes through the endpoint of a segment.
assert(edge.is_secondary());
const Point &ipt = cell->contains_segment() ?
((cell2->source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_START_POINT) ? line1.a : line1.b) :
((cell->source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_START_POINT) ? line0.a : line0.b);
// Infinite edge starts at an input contour, therefore there is always an intersection with an offset curve.
const Line &line = cell->contains_segment() ? line0 : line1;
assert(line.a == ipt || line.b == ipt);
// dir is perpendicular to line.
Vec2d dir(line.a.y() - line.b.y(), line.b.x() - line.a.x());
assert(dir.norm() > 0.);
if (((line.a == ipt) == cell->contains_point()) == (v0 == nullptr))
dir = - dir;
pt2 = ipt.cast<double>() + dir.normalized() * scale_(10.);
}
} else {
pt2 = Vec2d(v1->x(), v1->y());
// Clip the line by the bounding box, so that the coloring of the line will be visible.
Geometry::liang_barsky_line_clipping(pt1, pt2, BoundingBoxf(bbox.min.cast<double>(), bbox.max.cast<double>()));
}
helper_lines.emplace_back(Line(Point(pt1.cast<coord_t>()), Point(((pt1 + pt2) * 0.5).cast<coord_t>())));
}
dump_voronoi_to_svg(debug_out_path("voronoi-offset-candidates1.svg").c_str(), vd, Points(), lines, Polygons(), helper_lines);
}
#endif // VORONOI_DEBUG_OUT
std::vector<Vec2d> edge_offset_point(vd.num_edges(), Vec2d());
const double offset_distance2 = offset_distance * offset_distance;
for (const VD::edge_type &edge : vd.edges()) {
assert(edge_candidate[&edge - front_edge] != 2);
size_t edge_idx = &edge - front_edge;
if (edge_candidate[edge_idx] == 1) {
// Edge candidate, intersection points were not calculated yet.
const VD::vertex_type *v0 = edge.vertex0();
const VD::vertex_type *v1 = edge.vertex1();
assert(v0 != nullptr);
const VD::cell_type *cell = edge.cell();
const VD::cell_type *cell2 = edge.twin()->cell();
const Line &line0 = lines[cell->source_index()];
const Line &line1 = lines[cell2->source_index()];
size_t edge_idx2 = edge.twin() - front_edge;
if (v1 == nullptr) {
assert(edge.is_infinite());
assert(edge_candidate[edge_idx2] == 0);
if (cell->contains_point() && cell2->contains_point()) {
const Point &pt0 = (cell->source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_START_POINT) ? line0.a : line0.b;
assert((pt0.x() == line1.a.x() && pt0.y() == line1.a.y()) ||
(pt0.x() == line1.b.x() && pt0.y() == line1.b.y()));
}
const Point &pt = cell->contains_segment() ?
((cell2->source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_START_POINT) ? line1.a : line1.b) :
((cell->source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_START_POINT) ? line0.a : line0.b);
#endif /* NDEBUG */
if (v0) {
assert((Point(v0->x(), v0->y()) - pt).cast<double>().norm() < SCALED_EPSILON);
d0 = dmin = 0.;
vertex_dist[v0 - &vd.vertices().front()] = d0;
const Point &pt1 = (cell2->source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_START_POINT) ? line1.a : line1.b;
double dmin2 = (Vec2d(v0->x(), v0->y()) - pt0.cast<double>()).squaredNorm();
if (dmin2 <= offset_distance2) {
// There shall be an intersection of this unconstrained edge with the offset curve.
// Direction vector of this unconstrained Voronoi edge.
Vec2d dir(double(pt0.y() - pt1.y()), double(pt1.x() - pt0.x()));
Vec2d pt(v0->x(), v0->y());
double t = detail::first_circle_segment_intersection_parameter(Vec2d(pt0.x(), pt0.y()), offset_distance, pt, dir);
edge_offset_point[edge_idx] = pt + t * dir;
edge_candidate[edge_idx] = 3;
} else
edge_candidate[edge_idx] = 0;
} else {
assert((Point(v1->x(), v1->y()) - pt).cast<double>().norm() < SCALED_EPSILON);
d1 = dmin = 0.;
vertex_dist[v1 - &vd.vertices().front()] = d1;
// Infinite edges could not be created by two segment sites.
assert(cell->contains_point() != cell2->contains_point());
// Linear edge goes through the endpoint of a segment.
assert(edge.is_linear());
assert(edge.is_secondary());
const Point &ipt = cell->contains_segment() ?
((cell2->source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_START_POINT) ? line1.a : line1.b) :
((cell->source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_START_POINT) ? line0.a : line0.b);
#ifndef NDEBUG
if (cell->contains_segment()) {
const Point &pt1 = (cell2->source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_START_POINT) ? line1.a : line1.b;
assert((pt1.x() == line0.a.x() && pt1.y() == line0.a.y()) ||
(pt1.x() == line0.b.x() && pt1.y() == line0.b.y()));
} else {
const Point &pt0 = (cell->source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_START_POINT) ? line0.a : line0.b;
assert((pt0.x() == line1.a.x() && pt0.y() == line1.a.y()) ||
(pt0.x() == line1.b.x() && pt0.y() == line1.b.y()));
}
assert((Vec2d(v0->x(), v0->y()) - ipt.cast<double>()).norm() < SCALED_EPSILON);
#endif /* NDEBUG */
// Infinite edge starts at an input contour, therefore there is always an intersection with an offset curve.
const Line &line = cell->contains_segment() ? line0 : line1;
assert(line.a == ipt || line.b == ipt);
Vec2d pt = ipt.cast<double>();
Vec2d dir(line.a.y() - line.b.y(), line.b.x() - line.a.x());
assert(dir.norm() > 0.);
double t = offset_distance / dir.norm();
if (((line.a == ipt) == cell->contains_point()) == (v0 == nullptr))
t = - t;
edge_offset_point[edge_idx] = pt + t * dir;
edge_candidate[edge_idx] = 3;
}
}
} else {
// Finite edge has valid points at both sides.
if (cell->contains_segment() && cell2->contains_segment()) {
// This edge is a bisector of two line segments. Project v0, v1 onto one of the line segments.
Vec2d pt(line0.a.cast<double>());
Vec2d dir(line0.b.cast<double>() - pt);
Vec2d vec0 = Vec2d(v0->x(), v0->y()) - pt;
Vec2d vec1 = Vec2d(v1->x(), v1->y()) - pt;
double l2 = dir.squaredNorm();
assert(l2 > 0.);
d0 = (dir * (vec0.dot(dir) / l2) - vec0).norm();
d1 = (dir * (vec1.dot(dir) / l2) - vec1).norm();
dmin = std::min(d0, d1);
} else {
assert(cell->contains_point() || cell2->contains_point());
const Point &pt0 = cell->contains_point() ?
// The other edge of an unconstrained edge starting with null vertex shall never be intersected.
edge_candidate[edge_idx2] = 0;
} else if (edge.is_secondary()) {
assert(cell->contains_point() != cell2->contains_point());
const Line &line0 = lines[edge.cell()->source_index()];
const Line &line1 = lines[edge.twin()->cell()->source_index()];
const Point &pt = cell->contains_point() ?
((cell->source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_START_POINT) ? line0.a : line0.b) :
((cell2->source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_START_POINT) ? line1.a : line1.b);
// Project p0 to line segment <v0, v1>.
Vec2d p0(v0->x(), v0->y());
Vec2d p1(v1->x(), v1->y());
Vec2d px(pt0.x(), pt0.y());
Vec2d v = p1 - p0;
d0 = (p0 - px).norm();
d1 = (p1 - px).norm();
double t = v.dot(px - p0);
double l2 = v.squaredNorm();
if (t > 0. && t < l2) {
// Foot point on the line segment.
Vec2d foot = p0 + (t / l2) * v;
dmin = (foot - px).norm();
} else
dmin = std::min(d0, d1);
}
vertex_dist[v0 - &vd.vertices().front()] = d0;
vertex_dist[v1 - &vd.vertices().front()] = d1;
const Line &line = cell->contains_segment() ? line0 : line1;
assert(pt == line.a || pt == line.b);
assert((pt.cast<double>() - Vec2d(v0->x(), v0->y())).norm() < SCALED_EPSILON);
Vec2d dir(v1->x() - v0->x(), v1->y() - v0->y());
double l2 = dir.squaredNorm();
if (offset_distance2 <= l2) {
edge_offset_point[edge_idx] = pt.cast<double>() + (offset_distance / sqrt(l2)) * dir;
edge_candidate[edge_idx] = 3;
} else {
edge_candidate[edge_idx] = 0;
}
edge_candidate[edge_idx2] = 0;
} else {
// Finite edge has valid points at both sides.
bool done = false;
if (cell->contains_segment() && cell2->contains_segment()) {
// This edge is a bisector of two line segments. Project v0, v1 onto one of the line segments.
Vec2d pt(line0.a.cast<double>());
Vec2d dir(line0.b.cast<double>() - pt);
Vec2d vec0 = Vec2d(v0->x(), v0->y()) - pt;
Vec2d vec1 = Vec2d(v1->x(), v1->y()) - pt;
double l2 = dir.squaredNorm();
assert(l2 > 0.);
double dmin = (dir * (vec0.dot(dir) / l2) - vec0).squaredNorm();
double dmax = (dir * (vec1.dot(dir) / l2) - vec1).squaredNorm();
bool flip = dmin > dmax;
if (flip)
std::swap(dmin, dmax);
if (offset_distance2 >= dmin && offset_distance2 <= dmax) {
// Intersect. Maximum one intersection will be found.
// This edge is a bisector of two line segments. Distance to the input polygon increases/decreases monotonically.
dmin = sqrt(dmin);
dmax = sqrt(dmax);
assert(offset_distance > dmin - EPSILON && offset_distance < dmax + EPSILON);
double ddif = dmax - dmin;
if (ddif == 0.) {
// line, line2 are exactly parallel. This is a singular case, the offset curve should miss it.
} else {
if (flip) {
std::swap(edge_idx, edge_idx2);
std::swap(v0, v1);
}
double t = clamp(0., 1., (offset_distance - dmin) / ddif);
edge_offset_point[edge_idx] = Vec2d(lerp(v0->x(), v1->x(), t), lerp(v0->y(), v1->y(), t));
edge_candidate[edge_idx] = 3;
edge_candidate[edge_idx2] = 0;
done = true;
}
}
} else {
assert(cell->contains_point() || cell2->contains_point());
bool point_vs_segment = cell->contains_point() != cell2->contains_point();
const Point &pt0 = cell->contains_point() ?
((cell->source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_START_POINT) ? line0.a : line0.b) :
((cell2->source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_START_POINT) ? line1.a : line1.b);
// Project p0 to line segment <v0, v1>.
Vec2d p0(v0->x(), v0->y());
Vec2d p1(v1->x(), v1->y());
Vec2d px(pt0.x(), pt0.y());
double d0 = (p0 - px).squaredNorm();
double d1 = (p1 - px).squaredNorm();
double dmin = std::min(d0, d1);
double dmax = std::max(d0, d1);
bool has_intersection = false;
if (offset_distance2 <= dmax) {
if (offset_distance2 >= dmin) {
has_intersection = true;
} else {
double dmin_new;
if (point_vs_segment) {
Vec2d ft = foot_pt(cell->contains_segment() ? line0 : line1, pt0);
dmin_new = (ft - px).squaredNorm() * 0.25;
} else {
// point vs. point
const Point &pt1 = (cell2->source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_START_POINT) ? line1.a : line1.b;
dmin_new = (pt1.cast<double>() - px).squaredNorm() * 0.25;
}
assert(dmin_new < dmax + SCALED_EPSILON);
assert(dmin_new < dmin + SCALED_EPSILON);
dmin = dmin_new;
has_intersection = offset_distance2 >= dmin;
}
}
if (has_intersection) {
detail::Intersections intersections;
if (point_vs_segment) {
assert(cell->contains_point() || cell2->contains_point());
intersections = detail::line_point_equal_distance_points(cell->contains_segment() ? line0 : line1, pt0, offset_distance);
} else {
const Point &pt1 = (cell2->source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_START_POINT) ? line1.a : line1.b;
intersections = detail::point_point_equal_distance_points(pt0, pt1, offset_distance);
}
if (intersections.count == 2) {
// Now decide which points fall on this Voronoi edge.
// Tangential points (single intersection) are ignored.
Vec2d v = p1 - p0;
double l2 = v.squaredNorm();
double t0 = v.dot(intersections.pts[0] - p0);
double t1 = v.dot(intersections.pts[1] - p0);
if (t0 > t1) {
std::swap(t0, t1);
std::swap(intersections.pts[0], intersections.pts[1]);
}
// Remove points outside of the line range.
if (t0 < 0. || t0 > l2) {
if (t1 < 0. || t1 > l2)
intersections.count = 0;
else {
-- intersections.count;
t0 = t1;
intersections.pts[0] = intersections.pts[1];
}
} else if (t1 < 0. || t1 > l2)
-- intersections.count;
if (intersections.count == 2) {
edge_candidate[edge_idx] = edge_candidate[edge_idx2] = 3;
edge_offset_point[edge_idx] = intersections.pts[0];
edge_offset_point[edge_idx2] = intersections.pts[1];
done = true;
} else if (intersections.count == 1) {
if (d1 > d0) {
std::swap(edge_idx, edge_idx2);
edge_candidate[edge_idx] = 3;
edge_candidate[edge_idx2] = 0;
edge_offset_point[edge_idx] = intersections.pts[0];
}
done = true;
}
}
if (! done)
edge_candidate[edge_idx] = edge_candidate[edge_idx2] = 0;
}
}
}
}
edge_dist[&edge - &vd.edges().front()] = dmin;
}
}
// Mark cells intersected by the offset curve.
std::vector<unsigned char> seed_cells(vd.num_cells(), false);
for (const VD::cell_type &cell : vd.cells()) {
const VD::edge_type *first_edge = cell.incident_edge();
const VD::edge_type *edge = first_edge;
do {
double dmin = edge_dist[edge - &vd.edges().front()];
double dmax = std::numeric_limits<double>::max();
const VD::vertex_type *v0 = edge->vertex0();
const VD::vertex_type *v1 = edge->vertex1();
if (v0 != nullptr)
dmax = vertex_dist[v0 - &vd.vertices().front()];
if (v1 != nullptr)
dmax = std::max(dmax, vertex_dist[v1 - &vd.vertices().front()]);
if (offset_distance >= dmin && offset_distance <= dmax) {
// This cell is being intersected by the offset curve.
seed_cells[&cell - &vd.cells().front()] = true;
break;
}
edge = edge->next();
} while (edge != first_edge);
}
auto edge_dir = [&vd, &vertex_dist, &edge_dist, offset_distance](const VD::edge_type *edge) {
const VD::vertex_type *v0 = edge->vertex0();
const VD::vertex_type *v1 = edge->vertex1();
double d0 = v0 ? vertex_dist[v0 - &vd.vertices().front()] : std::numeric_limits<double>::max();
double d1 = v1 ? vertex_dist[v1 - &vd.vertices().front()] : std::numeric_limits<double>::max();
if (d0 < offset_distance && offset_distance < d1)
return true;
else if (d1 < offset_distance && offset_distance < d0)
return false;
else {
assert(false);
return false;
}
};
#ifdef VORONOI_DEBUG_OUT
{
Lines helper_lines;
for (const VD::edge_type &edge : vd.edges())
if (edge_candidate[&edge - front_edge] == 3)
helper_lines.emplace_back(Line(Point(edge.vertex0()->x(), edge.vertex0()->y()), Point(edge_offset_point[&edge - front_edge].cast<coord_t>())));
dump_voronoi_to_svg(debug_out_path("voronoi-offset-candidates2.svg").c_str(), vd, Points(), lines, Polygons(), helper_lines);
}
#endif // VORONOI_DEBUG_OUT
/// \brief starting at e, find the next edge on the face that brackets t
///
/// we can be in one of two modes.
/// if direction==false then we are looking for an edge where src_t < t < trg_t
/// if direction==true we are looning for an edge where trg_t < t < src_t
auto next_offset_edge =
[&vd, &vertex_dist, &edge_dist, offset_distance]
(const VD::edge_type *start_edge, bool direction) -> const VD::edge_type* {
const VD::edge_type *edge = start_edge;
do {
const VD::vertex_type *v0 = edge->vertex0();
const VD::vertex_type *v1 = edge->vertex1();
double d0 = v0 ? vertex_dist[v0 - &vd.vertices().front()] : std::numeric_limits<double>::max();
double d1 = v1 ? vertex_dist[v1 - &vd.vertices().front()] : std::numeric_limits<double>::max();
if (direction ? (d1 < offset_distance && offset_distance < d0) : (d0 < offset_distance && offset_distance < d1))
return edge;
edge = edge->next();
} while (edge != start_edge);
auto next_offset_edge = [&edge_candidate, front_edge](const VD::edge_type *start_edge) -> const VD::edge_type* {
for (const VD::edge_type *edge = start_edge->next(); edge != start_edge; edge = edge->next())
if (edge_candidate[edge->twin() - front_edge] == 3)
return edge->twin();
assert(false);
return nullptr;
};
@ -316,28 +617,20 @@ Polygons voronoi_offset(const VD &vd, const Lines &lines, double offset_distance
Polygons out;
double angle_step = 2. * acos((offset_distance - discretization_error) / offset_distance);
double sin_threshold = sin(angle_step) + EPSILON;
for (size_t seed_cell_idx = 0; seed_cell_idx < vd.num_cells(); ++ seed_cell_idx)
if (seed_cells[seed_cell_idx]) {
seed_cells[seed_cell_idx] = false;
// Initial direction should not matter, an offset curve shall intersect a cell at least at two points
// (if it is not just touching the cell at a single vertex), and such two intersection points shall have
// opposite direction.
bool direction = false;
// the first edge on the start-face
const VD::cell_type &cell = vd.cells()[seed_cell_idx];
const VD::edge_type *start_edge = next_offset_edge(cell.incident_edge(), direction);
assert(start_edge->cell() == &cell);
for (size_t seed_edge_idx = 0; seed_edge_idx < vd.num_edges(); ++ seed_edge_idx)
if (edge_candidate[seed_edge_idx] == 3) {
const VD::edge_type *start_edge = &vd.edges()[seed_edge_idx];
const VD::edge_type *edge = start_edge;
Polygon poly;
do {
direction = edge_dir(edge);
// find the next edge
const VD::edge_type *next_edge = next_offset_edge(edge->next(), direction);
const VD::edge_type *next_edge = next_offset_edge(edge);
//std::cout << "offset-output: "; print_edge(edge); std::cout << " to "; print_edge(next_edge); std::cout << "\n";
// Interpolate a circular segment or insert a linear segment between edge and next_edge.
const VD::cell_type *cell = edge->cell();
Vec2d p1 = detail::voronoi_edge_offset_point(vd, lines, vertex_dist, edge_dist, *edge, offset_distance);
Vec2d p2 = detail::voronoi_edge_offset_point(vd, lines, vertex_dist, edge_dist, *next_edge, offset_distance);
edge_candidate[next_edge - front_edge] = 0;
Vec2d p1 = edge_offset_point[edge - front_edge];
Vec2d p2 = edge_offset_point[next_edge - front_edge];
#ifndef NDEBUG
{
double err = dist_to_site(*cell, p1) - offset_distance;
@ -380,9 +673,7 @@ Polygons voronoi_offset(const VD &vd, const Lines &lines, double offset_distance
}
}
poly.points.emplace_back(Point(coord_t(p2.x()), coord_t(p2.y())));
// although we may revisit current_face (if it is non-convex), it seems safe to mark it "done" here.
seed_cells[cell - &vd.cells().front()] = false;
edge = next_edge->twin();
edge = next_edge;
} while (edge != start_edge);
out.emplace_back(std::move(poly));
}

13
src/libslic3r/VoronoiOffset.hpp
View File

@ -1,3 +1,5 @@
// Polygon offsetting using Voronoi diagram prodiced by boost::polygon.
#ifndef slic3r_VoronoiOffset_hpp_
#define slic3r_VoronoiOffset_hpp_
@ -7,7 +9,16 @@
namespace Slic3r {
Polygons voronoi_offset(const Geometry::VoronoiDiagram &vd, const Lines &lines, double offset_distance, double discretization_error);
// Offset a polygon or a set of polygons possibly with holes by traversing a Voronoi diagram.
// The input polygons are stored in lines and lines are referenced by vd.
// Outer curve will be extracted for a positive offset_distance,
// inner curve will be extracted for a negative offset_distance.
// Circular arches will be discretized to achieve discretization_error.
Polygons voronoi_offset(
const Geometry::VoronoiDiagram &vd,
const Lines &lines,
double offset_distance,
double discretization_error);
} // namespace Slic3r

407
src/libslic3r/VoronoiVisualUtils.hpp Normal file
View File

@ -0,0 +1,407 @@
#include <stack>
#include <libslic3r/Geometry.hpp>
#include <libslic3r/Line.hpp>
#include <libslic3r/Polygon.hpp>
#include <libslic3r/SVG.hpp>
namespace boost { namespace polygon {
// The following code for the visualization of the boost Voronoi diagram is based on:
//
// Boost.Polygon library voronoi_graphic_utils.hpp header file
// Copyright Andrii Sydorchuk 2010-2012.
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)
template <typename CT>
class voronoi_visual_utils {
public:
// Discretize parabolic Voronoi edge.
// Parabolic Voronoi edges are always formed by one point and one segment
// from the initial input set.
//
// Args:
// point: input point.
// segment: input segment.
// max_dist: maximum discretization distance.
// discretization: point discretization of the given Voronoi edge.
//
// Template arguments:
// InCT: coordinate type of the input geometries (usually integer).
// Point: point type, should model point concept.
// Segment: segment type, should model segment concept.
//
// Important:
// discretization should contain both edge endpoints initially.
template <class InCT1, class InCT2,
template<class> class Point,
template<class> class Segment>
static
typename enable_if<
typename gtl_and<
typename gtl_if<
typename is_point_concept<
typename geometry_concept< Point<InCT1> >::type
>::type
>::type,
typename gtl_if<
typename is_segment_concept<
typename geometry_concept< Segment<InCT2> >::type
>::type
>::type
>::type,
void
>::type discretize(
const Point<InCT1>& point,
const Segment<InCT2>& segment,
const CT max_dist,
std::vector< Point<CT> >* discretization) {
// Apply the linear transformation to move start point of the segment to
// the point with coordinates (0, 0) and the direction of the segment to
// coincide the positive direction of the x-axis.
CT segm_vec_x = cast(x(high(segment))) - cast(x(low(segment)));
CT segm_vec_y = cast(y(high(segment))) - cast(y(low(segment)));
CT sqr_segment_length = segm_vec_x * segm_vec_x + segm_vec_y * segm_vec_y;
// Compute x-coordinates of the endpoints of the edge
// in the transformed space.
CT projection_start = sqr_segment_length *
get_point_projection((*discretization)[0], segment);
CT projection_end = sqr_segment_length *
get_point_projection((*discretization)[1], segment);
// Compute parabola parameters in the transformed space.
// Parabola has next representation:
// f(x) = ((x-rot_x)^2 + rot_y^2) / (2.0*rot_y).
CT point_vec_x = cast(x(point)) - cast(x(low(segment)));
CT point_vec_y = cast(y(point)) - cast(y(low(segment)));
CT rot_x = segm_vec_x * point_vec_x + segm_vec_y * point_vec_y;
CT rot_y = segm_vec_x * point_vec_y - segm_vec_y * point_vec_x;
// Save the last point.
Point<CT> last_point = (*discretization)[1];
discretization->pop_back();
// Use stack to avoid recursion.
std::stack<CT> point_stack;
point_stack.push(projection_end);
CT cur_x = projection_start;
CT cur_y = parabola_y(cur_x, rot_x, rot_y);
// Adjust max_dist parameter in the transformed space.
const CT max_dist_transformed = max_dist * max_dist * sqr_segment_length;
while (!point_stack.empty()) {
CT new_x = point_stack.top();
CT new_y = parabola_y(new_x, rot_x, rot_y);
// Compute coordinates of the point of the parabola that is
// furthest from the current line segment.
CT mid_x = (new_y - cur_y) / (new_x - cur_x) * rot_y + rot_x;
CT mid_y = parabola_y(mid_x, rot_x, rot_y);
// Compute maximum distance between the given parabolic arc
// and line segment that discretize it.
CT dist = (new_y - cur_y) * (mid_x - cur_x) -
(new_x - cur_x) * (mid_y - cur_y);
dist = dist * dist / ((new_y - cur_y) * (new_y - cur_y) +
(new_x - cur_x) * (new_x - cur_x));
if (dist <= max_dist_transformed) {
// Distance between parabola and line segment is less than max_dist.
point_stack.pop();
CT inter_x = (segm_vec_x * new_x - segm_vec_y * new_y) /
sqr_segment_length + cast(x(low(segment)));
CT inter_y = (segm_vec_x * new_y + segm_vec_y * new_x) /
sqr_segment_length + cast(y(low(segment)));
discretization->push_back(Point<CT>(inter_x, inter_y));
cur_x = new_x;
cur_y = new_y;
} else {
point_stack.push(mid_x);
}
}
// Update last point.
discretization->back() = last_point;
}
private:
// Compute y(x) = ((x - a) * (x - a) + b * b) / (2 * b).
static CT parabola_y(CT x, CT a, CT b) {
return ((x - a) * (x - a) + b * b) / (b + b);
}
// Get normalized length of the distance between:
// 1) point projection onto the segment
// 2) start point of the segment
// Return this length divided by the segment length. This is made to avoid
// sqrt computation during transformation from the initial space to the
// transformed one and vice versa. The assumption is made that projection of
// the point lies between the start-point and endpoint of the segment.
template <class InCT,
template<class> class Point,
template<class> class Segment>
static
typename enable_if<
typename gtl_and<
typename gtl_if<
typename is_point_concept<
typename geometry_concept< Point<int> >::type
>::type
>::type,
typename gtl_if<
typename is_segment_concept<
typename geometry_concept< Segment<long> >::type
>::type
>::type
>::type,
CT
>::type get_point_projection(
const Point<CT>& point, const Segment<InCT>& segment) {
CT segment_vec_x = cast(x(high(segment))) - cast(x(low(segment)));
CT segment_vec_y = cast(y(high(segment))) - cast(y(low(segment)));
CT point_vec_x = x(point) - cast(x(low(segment)));
CT point_vec_y = y(point) - cast(y(low(segment)));
CT sqr_segment_length =
segment_vec_x * segment_vec_x + segment_vec_y * segment_vec_y;
CT vec_dot = segment_vec_x * point_vec_x + segment_vec_y * point_vec_y;
return vec_dot / sqr_segment_length;
}
template <typename InCT>
static CT cast(const InCT& value) {
return static_cast<CT>(value);
}
};
} } // namespace boost::polygon
namespace Slic3r
{
// The following code for the visualization of the boost Voronoi diagram is based on:
//
// Boost.Polygon library voronoi_visualizer.cpp file
// Copyright Andrii Sydorchuk 2010-2012.
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)
namespace Voronoi { namespace Internal {
using VD = Geometry::VoronoiDiagram;
typedef double coordinate_type;
typedef boost::polygon::point_data<coordinate_type> point_type;
typedef boost::polygon::segment_data<coordinate_type> segment_type;
typedef boost::polygon::rectangle_data<coordinate_type> rect_type;
typedef VD::cell_type cell_type;
typedef VD::cell_type::source_index_type source_index_type;
typedef VD::cell_type::source_category_type source_category_type;
typedef VD::edge_type edge_type;
typedef VD::cell_container_type cell_container_type;
typedef VD::cell_container_type vertex_container_type;
typedef VD::edge_container_type edge_container_type;
typedef VD::const_cell_iterator const_cell_iterator;
typedef VD::const_vertex_iterator const_vertex_iterator;
typedef VD::const_edge_iterator const_edge_iterator;
static const std::size_t EXTERNAL_COLOR = 1;
inline void color_exterior(const VD::edge_type* edge)
{
if (edge->color() == EXTERNAL_COLOR)
return;
edge->color(EXTERNAL_COLOR);
edge->twin()->color(EXTERNAL_COLOR);
const VD::vertex_type* v = edge->vertex1();
if (v == NULL || !edge->is_primary())
return;
v->color(EXTERNAL_COLOR);
const VD::edge_type* e = v->incident_edge();
do {
color_exterior(e);
e = e->rot_next();
} while (e != v->incident_edge());
}
inline point_type retrieve_point(const Points &points, const std::vector<segment_type> &segments, const cell_type& cell)
{
assert(cell.source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_START_POINT || cell.source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_END_POINT ||
cell.source_category() == boost::polygon::SOURCE_CATEGORY_SINGLE_POINT);
return cell.source_category() == boost::polygon::SOURCE_CATEGORY_SINGLE_POINT ?
Voronoi::Internal::point_type(double(points[cell.source_index()].x()), double(points[cell.source_index()].y())) :
(cell.source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_START_POINT) ?
low(segments[cell.source_index()]) : high(segments[cell.source_index()]);
}
inline void clip_infinite_edge(const Points &points, const std::vector<segment_type> &segments, const edge_type& edge, coordinate_type bbox_max_size, std::vector<point_type>* clipped_edge)
{
const cell_type& cell1 = *edge.cell();
const cell_type& cell2 = *edge.twin()->cell();
point_type origin, direction;
// Infinite edges could not be created by two segment sites.
if (! cell1.contains_point() && ! cell2.contains_point()) {
printf("Error! clip_infinite_edge - infinite edge separates two segment cells\n");
return;
}
if (cell1.contains_point() && cell2.contains_point()) {
point_type p1 = retrieve_point(points, segments, cell1);
point_type p2 = retrieve_point(points, segments, cell2);
origin.x((p1.x() + p2.x()) * 0.5);
origin.y((p1.y() + p2.y()) * 0.5);
direction.x(p1.y() - p2.y());
direction.y(p2.x() - p1.x());
} else {
origin = cell1.contains_segment() ? retrieve_point(points, segments, cell2) : retrieve_point(points, segments, cell1);
segment_type segment = cell1.contains_segment() ? segments[cell1.source_index()] : segments[cell2.source_index()];
coordinate_type dx = high(segment).x() - low(segment).x();
coordinate_type dy = high(segment).y() - low(segment).y();
if ((low(segment) == origin) ^ cell1.contains_point()) {
direction.x(dy);
direction.y(-dx);
} else {
direction.x(-dy);
direction.y(dx);
}
}
coordinate_type koef = bbox_max_size / (std::max)(fabs(direction.x()), fabs(direction.y()));
if (edge.vertex0() == NULL) {
clipped_edge->push_back(point_type(
origin.x() - direction.x() * koef,
origin.y() - direction.y() * koef));
} else {
clipped_edge->push_back(
point_type(edge.vertex0()->x(), edge.vertex0()->y()));
}
if (edge.vertex1() == NULL) {
clipped_edge->push_back(point_type(
origin.x() + direction.x() * koef,
origin.y() + direction.y() * koef));
} else {
clipped_edge->push_back(
point_type(edge.vertex1()->x(), edge.vertex1()->y()));
}
}
inline void sample_curved_edge(const Points &points, const std::vector<segment_type> &segments, const edge_type& edge, std::vector<point_type> &sampled_edge, coordinate_type max_dist)
{
point_type point = edge.cell()->contains_point() ?
retrieve_point(points, segments, *edge.cell()) :
retrieve_point(points, segments, *edge.twin()->cell());
segment_type segment = edge.cell()->contains_point() ?
segments[edge.twin()->cell()->source_index()] :
segments[edge.cell()->source_index()];
::boost::polygon::voronoi_visual_utils<coordinate_type>::discretize(point, segment, max_dist, &sampled_edge);
}
} /* namespace Internal */ } // namespace Voronoi
BoundingBox get_extents(const Lines &lines);
static inline void dump_voronoi_to_svg(
const char *path,
const Geometry::VoronoiDiagram &vd,
const Points &points,
const Lines &lines,
const Polygons &offset_curves = Polygons(),
const Lines &helper_lines = Lines(),
const double scale = 0.7) // 0.2?
{
const std::string inputSegmentPointColor = "lightseagreen";
const coord_t inputSegmentPointRadius = coord_t(0.09 * scale / SCALING_FACTOR);
const std::string inputSegmentColor = "lightseagreen";
const coord_t inputSegmentLineWidth = coord_t(0.03 * scale / SCALING_FACTOR);
const std::string voronoiPointColor = "black";
const coord_t voronoiPointRadius = coord_t(0.06 * scale / SCALING_FACTOR);
const std::string voronoiLineColorPrimary = "black";
const std::string voronoiLineColorSecondary = "green";
const std::string voronoiArcColor = "red";
const coord_t voronoiLineWidth = coord_t(0.02 * scale / SCALING_FACTOR);
const std::string offsetCurveColor = "magenta";
const coord_t offsetCurveLineWidth = coord_t(0.09 * scale / SCALING_FACTOR);
const std::string helperLineColor = "orange";
const coord_t helperLineWidth = coord_t(0.09 * scale / SCALING_FACTOR);
const bool internalEdgesOnly = false;
const bool primaryEdgesOnly = false;
BoundingBox bbox;
bbox.merge(get_extents(points));
bbox.merge(get_extents(lines));
bbox.merge(get_extents(offset_curves));
bbox.min -= (0.01 * bbox.size().cast<double>()).cast<coord_t>();
bbox.max += (0.01 * bbox.size().cast<double>()).cast<coord_t>();
::Slic3r::SVG svg(path, bbox);
// bbox.scale(1.2);
// For clipping of half-lines to some reasonable value.
// The line will then be clipped by the SVG viewer anyway.
const double bbox_dim_max = double(std::max(bbox.size().x(), bbox.size().y()));
// For the discretization of the Voronoi parabolic segments.
const double discretization_step = 0.05 * bbox_dim_max;
// Make a copy of the input segments with the double type.
std::vector<Voronoi::Internal::segment_type> segments;
for (Lines::const_iterator it = lines.begin(); it != lines.end(); ++ it)
segments.push_back(Voronoi::Internal::segment_type(
Voronoi::Internal::point_type(double(it->a(0)), double(it->a(1))),
Voronoi::Internal::point_type(double(it->b(0)), double(it->b(1)))));
// Color exterior edges.
for (boost::polygon::voronoi_diagram<double>::const_edge_iterator it = vd.edges().begin(); it != vd.edges().end(); ++it)
if (!it->is_finite())
Voronoi::Internal::color_exterior(&(*it));
// Draw the end points of the input polygon.
for (Lines::const_iterator it = lines.begin(); it != lines.end(); ++it) {
svg.draw(it->a, inputSegmentPointColor, inputSegmentPointRadius);
svg.draw(it->b, inputSegmentPointColor, inputSegmentPointRadius);
}
// Draw the input polygon.
for (Lines::const_iterator it = lines.begin(); it != lines.end(); ++it)
svg.draw(Line(Point(coord_t(it->a(0)), coord_t(it->a(1))), Point(coord_t(it->b(0)), coord_t(it->b(1)))), inputSegmentColor, inputSegmentLineWidth);
#if 1
// Draw voronoi vertices.
for (boost::polygon::voronoi_diagram<double>::const_vertex_iterator it = vd.vertices().begin(); it != vd.vertices().end(); ++it)
if (! internalEdgesOnly || it->color() != Voronoi::Internal::EXTERNAL_COLOR)
svg.draw(Point(coord_t(it->x()), coord_t(it->y())), voronoiPointColor, voronoiPointRadius);
for (boost::polygon::voronoi_diagram<double>::const_edge_iterator it = vd.edges().begin(); it != vd.edges().end(); ++it) {
if (primaryEdgesOnly && !it->is_primary())
continue;
if (internalEdgesOnly && (it->color() == Voronoi::Internal::EXTERNAL_COLOR))
continue;
std::vector<Voronoi::Internal::point_type> samples;
std::string color = voronoiLineColorPrimary;
if (!it->is_finite()) {
Voronoi::Internal::clip_infinite_edge(points, segments, *it, bbox_dim_max, &samples);
if (! it->is_primary())
color = voronoiLineColorSecondary;
} else {
// Store both points of the segment into samples. sample_curved_edge will split the initial line
// until the discretization_step is reached.
samples.push_back(Voronoi::Internal::point_type(it->vertex0()->x(), it->vertex0()->y()));
samples.push_back(Voronoi::Internal::point_type(it->vertex1()->x(), it->vertex1()->y()));
if (it->is_curved()) {
Voronoi::Internal::sample_curved_edge(points, segments, *it, samples, discretization_step);
color = voronoiArcColor;
} else if (! it->is_primary())
color = voronoiLineColorSecondary;
}
for (std::size_t i = 0; i + 1 < samples.size(); ++i)
svg.draw(Line(Point(coord_t(samples[i].x()), coord_t(samples[i].y())), Point(coord_t(samples[i+1].x()), coord_t(samples[i+1].y()))), color, voronoiLineWidth);
}
#endif
svg.draw_outline(offset_curves, offsetCurveColor, offsetCurveLineWidth);
svg.draw(helper_lines, helperLineColor, helperLineWidth);
svg.Close();
}
} // namespace Slic3r

421
tests/libslic3r/test_voronoi.cpp
View File

@ -1,16 +1,18 @@
#include <catch2/catch.hpp>
#include <test_utils.hpp>
#include <stack>
#include <libslic3r/Polygon.hpp>
#include <libslic3r/Polyline.hpp>
#include <libslic3r/EdgeGrid.hpp>
#include <libslic3r/Geometry.hpp>
#include <libslic3r/VoronoiOffset.hpp>
#define BOOST_VORONOI_USE_GMP 1
#include "boost/polygon/voronoi.hpp"
// #define VORONOI_DEBUG_OUT
#ifdef VORONOI_DEBUG_OUT
#include <libslic3r/VoronoiVisualUtils.hpp>
#endif
using boost::polygon::voronoi_builder;
using boost::polygon::voronoi_diagram;
@ -19,400 +21,6 @@ using namespace Slic3r;
using VD = Geometry::VoronoiDiagram;
// #define VORONOI_DEBUG_OUT
#ifdef VORONOI_DEBUG_OUT
#include <libslic3r/SVG.hpp>
#endif
#ifdef VORONOI_DEBUG_OUT
namespace boost { namespace polygon {
// The following code for the visualization of the boost Voronoi diagram is based on:
//
// Boost.Polygon library voronoi_graphic_utils.hpp header file
// Copyright Andrii Sydorchuk 2010-2012.
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)
template <typename CT>
class voronoi_visual_utils {
public:
// Discretize parabolic Voronoi edge.
// Parabolic Voronoi edges are always formed by one point and one segment
// from the initial input set.
//
// Args:
// point: input point.
// segment: input segment.
// max_dist: maximum discretization distance.
// discretization: point discretization of the given Voronoi edge.
//
// Template arguments:
// InCT: coordinate type of the input geometries (usually integer).
// Point: point type, should model point concept.
// Segment: segment type, should model segment concept.
//
// Important:
// discretization should contain both edge endpoints initially.
template <class InCT1, class InCT2,
template<class> class Point,
template<class> class Segment>
static
typename enable_if<
typename gtl_and<
typename gtl_if<
typename is_point_concept<
typename geometry_concept< Point<InCT1> >::type
>::type
>::type,
typename gtl_if<
typename is_segment_concept<
typename geometry_concept< Segment<InCT2> >::type
>::type
>::type
>::type,
void
>::type discretize(
const Point<InCT1>& point,
const Segment<InCT2>& segment,
const CT max_dist,
std::vector< Point<CT> >* discretization) {
// Apply the linear transformation to move start point of the segment to
// the point with coordinates (0, 0) and the direction of the segment to
// coincide the positive direction of the x-axis.
CT segm_vec_x = cast(x(high(segment))) - cast(x(low(segment)));
CT segm_vec_y = cast(y(high(segment))) - cast(y(low(segment)));
CT sqr_segment_length = segm_vec_x * segm_vec_x + segm_vec_y * segm_vec_y;
// Compute x-coordinates of the endpoints of the edge
// in the transformed space.
CT projection_start = sqr_segment_length *
get_point_projection((*discretization)[0], segment);
CT projection_end = sqr_segment_length *
get_point_projection((*discretization)[1], segment);
// Compute parabola parameters in the transformed space.
// Parabola has next representation:
// f(x) = ((x-rot_x)^2 + rot_y^2) / (2.0*rot_y).
CT point_vec_x = cast(x(point)) - cast(x(low(segment)));
CT point_vec_y = cast(y(point)) - cast(y(low(segment)));
CT rot_x = segm_vec_x * point_vec_x + segm_vec_y * point_vec_y;
CT rot_y = segm_vec_x * point_vec_y - segm_vec_y * point_vec_x;
// Save the last point.
Point<CT> last_point = (*discretization)[1];
discretization->pop_back();
// Use stack to avoid recursion.
std::stack<CT> point_stack;
point_stack.push(projection_end);
CT cur_x = projection_start;
CT cur_y = parabola_y(cur_x, rot_x, rot_y);
// Adjust max_dist parameter in the transformed space.
const CT max_dist_transformed = max_dist * max_dist * sqr_segment_length;
while (!point_stack.empty()) {
CT new_x = point_stack.top();
CT new_y = parabola_y(new_x, rot_x, rot_y);
// Compute coordinates of the point of the parabola that is
// furthest from the current line segment.
CT mid_x = (new_y - cur_y) / (new_x - cur_x) * rot_y + rot_x;
CT mid_y = parabola_y(mid_x, rot_x, rot_y);
// Compute maximum distance between the given parabolic arc
// and line segment that discretize it.
CT dist = (new_y - cur_y) * (mid_x - cur_x) -
(new_x - cur_x) * (mid_y - cur_y);
dist = dist * dist / ((new_y - cur_y) * (new_y - cur_y) +
(new_x - cur_x) * (new_x - cur_x));
if (dist <= max_dist_transformed) {
// Distance between parabola and line segment is less than max_dist.
point_stack.pop();
CT inter_x = (segm_vec_x * new_x - segm_vec_y * new_y) /
sqr_segment_length + cast(x(low(segment)));
CT inter_y = (segm_vec_x * new_y + segm_vec_y * new_x) /
sqr_segment_length + cast(y(low(segment)));
discretization->push_back(Point<CT>(inter_x, inter_y));
cur_x = new_x;
cur_y = new_y;
} else {
point_stack.push(mid_x);
}
}
// Update last point.
discretization->back() = last_point;
}
private:
// Compute y(x) = ((x - a) * (x - a) + b * b) / (2 * b).
static CT parabola_y(CT x, CT a, CT b) {
return ((x - a) * (x - a) + b * b) / (b + b);
}
// Get normalized length of the distance between:
// 1) point projection onto the segment
// 2) start point of the segment
// Return this length divided by the segment length. This is made to avoid
// sqrt computation during transformation from the initial space to the
// transformed one and vice versa. The assumption is made that projection of
// the point lies between the start-point and endpoint of the segment.
template <class InCT,
template<class> class Point,
template<class> class Segment>
static
typename enable_if<
typename gtl_and<
typename gtl_if<
typename is_point_concept<
typename geometry_concept< Point<int> >::type
>::type
>::type,
typename gtl_if<
typename is_segment_concept<
typename geometry_concept< Segment<long> >::type
>::type
>::type
>::type,
CT
>::type get_point_projection(
const Point<CT>& point, const Segment<InCT>& segment) {
CT segment_vec_x = cast(x(high(segment))) - cast(x(low(segment)));
CT segment_vec_y = cast(y(high(segment))) - cast(y(low(segment)));
CT point_vec_x = x(point) - cast(x(low(segment)));
CT point_vec_y = y(point) - cast(y(low(segment)));
CT sqr_segment_length =
segment_vec_x * segment_vec_x + segment_vec_y * segment_vec_y;
CT vec_dot = segment_vec_x * point_vec_x + segment_vec_y * point_vec_y;
return vec_dot / sqr_segment_length;
}
template <typename InCT>
static CT cast(const InCT& value) {
return static_cast<CT>(value);
}
};
} } // namespace boost::polygon
// The following code for the visualization of the boost Voronoi diagram is based on:
//
// Boost.Polygon library voronoi_visualizer.cpp file
// Copyright Andrii Sydorchuk 2010-2012.
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)
namespace Voronoi { namespace Internal {
typedef double coordinate_type;
typedef boost::polygon::point_data<coordinate_type> point_type;
typedef boost::polygon::segment_data<coordinate_type> segment_type;
typedef boost::polygon::rectangle_data<coordinate_type> rect_type;
typedef boost::polygon::voronoi_diagram<coordinate_type> VD;
typedef VD::cell_type cell_type;
typedef VD::cell_type::source_index_type source_index_type;
typedef VD::cell_type::source_category_type source_category_type;
typedef VD::edge_type edge_type;
typedef VD::cell_container_type cell_container_type;
typedef VD::cell_container_type vertex_container_type;
typedef VD::edge_container_type edge_container_type;
typedef VD::const_cell_iterator const_cell_iterator;
typedef VD::const_vertex_iterator const_vertex_iterator;
typedef VD::const_edge_iterator const_edge_iterator;
static const std::size_t EXTERNAL_COLOR = 1;
inline void color_exterior(const VD::edge_type* edge)
{
if (edge->color() == EXTERNAL_COLOR)
return;
edge->color(EXTERNAL_COLOR);
edge->twin()->color(EXTERNAL_COLOR);
const VD::vertex_type* v = edge->vertex1();
if (v == NULL || !edge->is_primary())
return;
v->color(EXTERNAL_COLOR);
const VD::edge_type* e = v->incident_edge();
do {
color_exterior(e);
e = e->rot_next();
} while (e != v->incident_edge());
}
inline point_type retrieve_point(const Points &points, const std::vector<segment_type> &segments, const cell_type& cell)
{
assert(cell.source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_START_POINT || cell.source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_END_POINT ||
cell.source_category() == boost::polygon::SOURCE_CATEGORY_SINGLE_POINT);
return cell.source_category() == boost::polygon::SOURCE_CATEGORY_SINGLE_POINT ?
Voronoi::Internal::point_type(double(points[cell.source_index()].x()), double(points[cell.source_index()].y())) :
(cell.source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_START_POINT) ?
low(segments[cell.source_index()]) : high(segments[cell.source_index()]);
}
inline void clip_infinite_edge(const Points &points, const std::vector<segment_type> &segments, const edge_type& edge, coordinate_type bbox_max_size, std::vector<point_type>* clipped_edge)
{
const cell_type& cell1 = *edge.cell();
const cell_type& cell2 = *edge.twin()->cell();
point_type origin, direction;
// Infinite edges could not be created by two segment sites.
if (! cell1.contains_point() && ! cell2.contains_point()) {
printf("Error! clip_infinite_edge - infinite edge separates two segment cells\n");
return;
}
if (cell1.contains_point() && cell2.contains_point()) {
point_type p1 = retrieve_point(points, segments, cell1);
point_type p2 = retrieve_point(points, segments, cell2);
origin.x((p1.x() + p2.x()) * 0.5);
origin.y((p1.y() + p2.y()) * 0.5);
direction.x(p1.y() - p2.y());
direction.y(p2.x() - p1.x());
} else {
origin = cell1.contains_segment() ? retrieve_point(points, segments, cell2) : retrieve_point(points, segments, cell1);
segment_type segment = cell1.contains_segment() ? segments[cell1.source_index()] : segments[cell2.source_index()];
coordinate_type dx = high(segment).x() - low(segment).x();
coordinate_type dy = high(segment).y() - low(segment).y();
if ((low(segment) == origin) ^ cell1.contains_point()) {
direction.x(dy);
direction.y(-dx);
} else {
direction.x(-dy);
direction.y(dx);
}
}
coordinate_type koef = bbox_max_size / (std::max)(fabs(direction.x()), fabs(direction.y()));
if (edge.vertex0() == NULL) {
clipped_edge->push_back(point_type(
origin.x() - direction.x() * koef,
origin.y() - direction.y() * koef));
} else {
clipped_edge->push_back(
point_type(edge.vertex0()->x(), edge.vertex0()->y()));
}
if (edge.vertex1() == NULL) {
clipped_edge->push_back(point_type(
origin.x() + direction.x() * koef,
origin.y() + direction.y() * koef));
} else {
clipped_edge->push_back(
point_type(edge.vertex1()->x(), edge.vertex1()->y()));
}
}
inline void sample_curved_edge(const Points &points, const std::vector<segment_type> &segments, const edge_type& edge, std::vector<point_type> &sampled_edge, coordinate_type max_dist)
{
point_type point = edge.cell()->contains_point() ?
retrieve_point(points, segments, *edge.cell()) :
retrieve_point(points, segments, *edge.twin()->cell());
segment_type segment = edge.cell()->contains_point() ?
segments[edge.twin()->cell()->source_index()] :
segments[edge.cell()->source_index()];
::boost::polygon::voronoi_visual_utils<coordinate_type>::discretize(point, segment, max_dist, &sampled_edge);
}
} /* namespace Internal */ } // namespace Voronoi
static inline void dump_voronoi_to_svg(
const char *path,
/* const */ VD &vd,
const Points &points,
const Lines &lines,
const Polygons &offset_curves = Polygons(),
const double scale = 0.7) // 0.2?
{
const std::string inputSegmentPointColor = "lightseagreen";
const coord_t inputSegmentPointRadius = coord_t(0.09 * scale / SCALING_FACTOR);
const std::string inputSegmentColor = "lightseagreen";
const coord_t inputSegmentLineWidth = coord_t(0.03 * scale / SCALING_FACTOR);
const std::string voronoiPointColor = "black";
const coord_t voronoiPointRadius = coord_t(0.06 * scale / SCALING_FACTOR);
const std::string voronoiLineColorPrimary = "black";
const std::string voronoiLineColorSecondary = "green";
const std::string voronoiArcColor = "red";
const coord_t voronoiLineWidth = coord_t(0.02 * scale / SCALING_FACTOR);
const std::string offsetCurveColor = "magenta";
const coord_t offsetCurveLineWidth = coord_t(0.09 * scale / SCALING_FACTOR);
const bool internalEdgesOnly = false;
const bool primaryEdgesOnly = false;
BoundingBox bbox;
bbox.merge(get_extents(points));
bbox.merge(get_extents(lines));
bbox.min -= (0.01 * bbox.size().cast<double>()).cast<coord_t>();
bbox.max += (0.01 * bbox.size().cast<double>()).cast<coord_t>();
::Slic3r::SVG svg(path, bbox);
// bbox.scale(1.2);
// For clipping of half-lines to some reasonable value.
// The line will then be clipped by the SVG viewer anyway.
const double bbox_dim_max = double(std::max(bbox.size().x(), bbox.size().y()));
// For the discretization of the Voronoi parabolic segments.
const double discretization_step = 0.05 * bbox_dim_max;
// Make a copy of the input segments with the double type.
std::vector<Voronoi::Internal::segment_type> segments;
for (Lines::const_iterator it = lines.begin(); it != lines.end(); ++ it)
segments.push_back(Voronoi::Internal::segment_type(
Voronoi::Internal::point_type(double(it->a(0)), double(it->a(1))),
Voronoi::Internal::point_type(double(it->b(0)), double(it->b(1)))));
// Color exterior edges.
for (boost::polygon::voronoi_diagram<double>::const_edge_iterator it = vd.edges().begin(); it != vd.edges().end(); ++it)
if (!it->is_finite())
Voronoi::Internal::color_exterior(&(*it));
// Draw the end points of the input polygon.
for (Lines::const_iterator it = lines.begin(); it != lines.end(); ++it) {
svg.draw(it->a, inputSegmentPointColor, inputSegmentPointRadius);
svg.draw(it->b, inputSegmentPointColor, inputSegmentPointRadius);
}
// Draw the input polygon.
for (Lines::const_iterator it = lines.begin(); it != lines.end(); ++it)
svg.draw(Line(Point(coord_t(it->a(0)), coord_t(it->a(1))), Point(coord_t(it->b(0)), coord_t(it->b(1)))), inputSegmentColor, inputSegmentLineWidth);
#if 1
// Draw voronoi vertices.
for (boost::polygon::voronoi_diagram<double>::const_vertex_iterator it = vd.vertices().begin(); it != vd.vertices().end(); ++it)
if (! internalEdgesOnly || it->color() != Voronoi::Internal::EXTERNAL_COLOR)
svg.draw(Point(coord_t(it->x()), coord_t(it->y())), voronoiPointColor, voronoiPointRadius);
for (boost::polygon::voronoi_diagram<double>::const_edge_iterator it = vd.edges().begin(); it != vd.edges().end(); ++it) {
if (primaryEdgesOnly && !it->is_primary())
continue;
if (internalEdgesOnly && (it->color() == Voronoi::Internal::EXTERNAL_COLOR))
continue;
std::vector<Voronoi::Internal::point_type> samples;
std::string color = voronoiLineColorPrimary;
if (!it->is_finite()) {
Voronoi::Internal::clip_infinite_edge(points, segments, *it, bbox_dim_max, &samples);
if (! it->is_primary())
color = voronoiLineColorSecondary;
} else {
// Store both points of the segment into samples. sample_curved_edge will split the initial line
// until the discretization_step is reached.
samples.push_back(Voronoi::Internal::point_type(it->vertex0()->x(), it->vertex0()->y()));
samples.push_back(Voronoi::Internal::point_type(it->vertex1()->x(), it->vertex1()->y()));
if (it->is_curved()) {
Voronoi::Internal::sample_curved_edge(points, segments, *it, samples, discretization_step);
color = voronoiArcColor;
} else if (! it->is_primary())
color = voronoiLineColorSecondary;
}
for (std::size_t i = 0; i + 1 < samples.size(); ++i)
svg.draw(Line(Point(coord_t(samples[i].x()), coord_t(samples[i].y())), Point(coord_t(samples[i+1].x()), coord_t(samples[i+1].y()))), color, voronoiLineWidth);
}
#endif
svg.draw_outline(offset_curves, offsetCurveColor, offsetCurveLineWidth);
svg.Close();
}
#endif
// https://svn.boost.org/trac10/ticket/12067
// This bug seems to be confirmed.
// Vojtech supposes that there may be no Voronoi edges produced for
@ -1586,7 +1194,7 @@ TEST_CASE("Voronoi NaN coordinates 12139", "[Voronoi][!hide][!mayfail]")
#ifdef VORONOI_DEBUG_OUT
dump_voronoi_to_svg(debug_out_path("voronoi-NaNs.svg").c_str(),
vd, Points(), lines, Polygons(), 0.015);
vd, Points(), lines, Polygons(), Lines(), 0.015);
#endif
}
@ -1606,12 +1214,19 @@ TEST_CASE("Voronoi offset", "[VoronoiOffset]")
Lines lines = to_lines(poly_with_hole);
construct_voronoi(lines.begin(), lines.end(), &vd);
Polygons offsetted_polygons = voronoi_offset(vd, lines, scale_(0.2), scale_(0.005));
Polygons offsetted_polygons_out = voronoi_offset(vd, lines, scale_(0.2), scale_(0.005));
REQUIRE(offsetted_polygons_out.size() == 1);
#ifdef VORONOI_DEBUG_OUT
dump_voronoi_to_svg(debug_out_path("voronoi-offset.svg").c_str(),
vd, Points(), lines, offsetted_polygons);
dump_voronoi_to_svg(debug_out_path("voronoi-offset-out.svg").c_str(),
vd, Points(), lines, offsetted_polygons_out);
#endif
REQUIRE(offsetted_polygons.size() == 2);
Polygons offsetted_polygons_in = voronoi_offset(vd, lines, - scale_(0.2), scale_(0.005));
REQUIRE(offsetted_polygons_in.size() == 1);
#ifdef VORONOI_DEBUG_OUT
dump_voronoi_to_svg(debug_out_path("voronoi-offset-in.svg").c_str(),
vd, Points(), lines, offsetted_polygons_in);
#endif
}