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Reworked algorithm for Voronoi Offset curve extraction.

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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
View File

@ -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_

549
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,
@ -131,54 +222,199 @@ 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());
Polygons voronoi_offset(
const Geometry::VoronoiDiagram &vd,
const Lines &lines,
double offset_distance,
double discretization_error)
{
#ifndef NDEBUG
// 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
// Calculate minimum distance of input polygons to voronoi vertices and voronoi edges.
for (const VD::edge_type &edge : vd.edges()) {
// 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()];
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);
// Direction vector of this unconstrained Voronoi edge.
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;
pt2 = Vec2d(v0->x(), v0->y()) + dir.normalized() * scale_(10.);
} 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;
// 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;
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 {
// 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;
@ -189,22 +425,44 @@ Polygons voronoi_offset(const VD &vd, const Lines &lines, double offset_distance
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);
assert((Vec2d(v0->x(), v0->y()) - ipt.cast<double>()).norm() < SCALED_EPSILON);
#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;
// 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;
}
// 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);
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 {
assert((Point(v1->x(), v1->y()) - pt).cast<double>().norm() < SCALED_EPSILON);
d1 = dmin = 0.;
vertex_dist[v1 - &vd.vertices().front()] = d1;
}
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>());
@ -213,11 +471,35 @@ Polygons voronoi_offset(const VD &vd, const Lines &lines, double offset_distance
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);
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);
@ -225,80 +507,99 @@ Polygons voronoi_offset(const VD &vd, const Lines &lines, double offset_distance
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;
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);
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]);
}
vertex_dist[v0 - &vd.vertices().front()] = d0;
vertex_dist[v1 - &vd.vertices().front()] = d1;
}
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;
// Remove points outside of the line range.
if (t0 < 0. || t0 > l2) {
if (t1 < 0. || t1 > l2)
intersections.count = 0;
else {
assert(false);
return false;
-- 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;
}
}
}
}
}
};
/// \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);
#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
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
}