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BambuStudio/libslic3r/Geometry/MedialAxis.cpp

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#include "MedialAxis.hpp"
#include "clipper.hpp"
#include "VoronoiOffset.hpp"
#ifdef SLIC3R_DEBUG
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
#endif // SLIC3R_DEBUG
namespace Slic3r { namespace Geometry {
#ifdef SLIC3R_DEBUG
// 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 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);
return (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 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()) {
point_type p1 = retrieve_point(segments, cell1);
point_type p2 = retrieve_point(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(segments, cell2) : retrieve_point(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 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(segments, *edge.cell()) :
retrieve_point(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
void dump_voronoi_to_svg(const Lines &lines, /* const */ boost::polygon::voronoi_diagram<double> &vd, const ThickPolylines *polylines, const char *path)
{
const double scale = 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 bool internalEdgesOnly = false;
const bool primaryEdgesOnly = false;
BoundingBox bbox = BoundingBox(lines);
bbox.min(0) -= coord_t(1. / SCALING_FACTOR);
bbox.min(1) -= coord_t(1. / SCALING_FACTOR);
bbox.max(0) += coord_t(1. / SCALING_FACTOR);
bbox.max(1) += coord_t(1. / SCALING_FACTOR);
::Slic3r::SVG svg(path, bbox);
if (polylines != NULL)
svg.draw(*polylines, "lime", "lime", voronoiLineWidth);
// 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(bbox.max(0) - bbox.min(0)) + double(bbox.max(1) - bbox.min(1));
// For the discretization of the Voronoi parabolic segments.
const double discretization_step = 0.0005 * 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(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(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
if (polylines != NULL)
svg.draw(*polylines, "blue", voronoiLineWidth);
svg.Close();
}
#endif // SLIC3R_DEBUG
template<typename VD, typename SEGMENTS>
inline const typename VD::point_type retrieve_cell_point(const typename VD::cell_type& cell, const SEGMENTS &segments)
{
assert(cell.source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_START_POINT || cell.source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_END_POINT);
return (cell.source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_START_POINT) ? low(segments[cell.source_index()]) : high(segments[cell.source_index()]);
}
template<typename VD, typename SEGMENTS>
inline std::pair<typename VD::coord_type, typename VD::coord_type> measure_edge_thickness(const VD &vd, const typename VD::edge_type& edge, const SEGMENTS &segments)
{
typedef typename VD::coord_type T;
const typename VD::point_type pa(edge.vertex0()->x(), edge.vertex0()->y());
const typename VD::point_type pb(edge.vertex1()->x(), edge.vertex1()->y());
const typename VD::cell_type &cell1 = *edge.cell();
const typename VD::cell_type &cell2 = *edge.twin()->cell();
if (cell1.contains_segment()) {
if (cell2.contains_segment()) {
// Both cells contain a linear segment, the left / right cells are symmetric.
// Project pa, pb to the left segment.
const typename VD::segment_type segment1 = segments[cell1.source_index()];
const typename VD::point_type p1a = project_point_to_segment(segment1, pa);
const typename VD::point_type p1b = project_point_to_segment(segment1, pb);
return std::pair<T, T>(T(2.)*dist(pa, p1a), T(2.)*dist(pb, p1b));
} else {
// 1st cell contains a linear segment, 2nd cell contains a point.
// The medial axis between the cells is a parabolic arc.
// Project pa, pb to the left segment.
const typename VD::point_type p2 = retrieve_cell_point<VD>(cell2, segments);
return std::pair<T, T>(T(2.)*dist(pa, p2), T(2.)*dist(pb, p2));
}
} else if (cell2.contains_segment()) {
// 1st cell contains a point, 2nd cell contains a linear segment.
// The medial axis between the cells is a parabolic arc.
const typename VD::point_type p1 = retrieve_cell_point<VD>(cell1, segments);
return std::pair<T, T>(T(2.)*dist(pa, p1), T(2.)*dist(pb, p1));
} else {
// Both cells contain a point. The left / right regions are triangular and symmetric.
const typename VD::point_type p1 = retrieve_cell_point<VD>(cell1, segments);
return std::pair<T, T>(T(2.)*dist(pa, p1), T(2.)*dist(pb, p1));
}
}
// Converts the Line instances of Lines vector to VD::segment_type.
template<typename VD>
class Lines2VDSegments
{
public:
Lines2VDSegments(const Lines &alines) : lines(alines) {}
typename VD::segment_type operator[](size_t idx) const {
return typename VD::segment_type(
typename VD::point_type(typename VD::coord_type(lines[idx].a(0)), typename VD::coord_type(lines[idx].a(1))),
typename VD::point_type(typename VD::coord_type(lines[idx].b(0)), typename VD::coord_type(lines[idx].b(1))));
}
private:
const Lines &lines;
};
MedialAxis::MedialAxis(double min_width, double max_width, const ExPolygon &expolygon) :
m_expolygon(expolygon), m_lines(expolygon.lines()), m_min_width(min_width), m_max_width(max_width)
{}
void MedialAxis::build(ThickPolylines* polylines)
{
m_vd.construct_voronoi(m_lines.begin(), m_lines.end());
Slic3r::Voronoi::annotate_inside_outside(m_vd, m_lines);
// static constexpr double threshold_alpha = M_PI / 12.; // 30 degrees
// std::vector<Vec2d> skeleton_edges = Slic3r::Voronoi::skeleton_edges_rough(vd, lines, threshold_alpha);
/*
// DEBUG: dump all Voronoi edges
{
for (VD::const_edge_iterator edge = m_vd.edges().begin(); edge != m_vd.edges().end(); ++edge) {
if (edge->is_infinite()) continue;
ThickPolyline polyline;
polyline.points.push_back(Point( edge->vertex0()->x(), edge->vertex0()->y() ));
polyline.points.push_back(Point( edge->vertex1()->x(), edge->vertex1()->y() ));
polylines->push_back(polyline);
}
return;
}
*/
// collect valid edges (i.e. prune those not belonging to MAT)
// note: this keeps twins, so it inserts twice the number of the valid edges
m_edge_data.assign(m_vd.edges().size() / 2, EdgeData{});
for (VD::const_edge_iterator edge = m_vd.edges().begin(); edge != m_vd.edges().end(); edge += 2)
if (edge->is_primary() && edge->is_finite() &&
(Voronoi::vertex_category(edge->vertex0()) == Voronoi::VertexCategory::Inside ||
Voronoi::vertex_category(edge->vertex1()) == Voronoi::VertexCategory::Inside) &&
this->validate_edge(&*edge)) {
// Valid skeleton edge.
this->edge_data(*edge).first.active = true;
}
// iterate through the valid edges to build polylines
ThickPolyline reverse_polyline;
for (VD::const_edge_iterator seed_edge = m_vd.edges().begin(); seed_edge != m_vd.edges().end(); seed_edge += 2)
if (EdgeData &seed_edge_data = this->edge_data(*seed_edge).first; seed_edge_data.active) {
// Mark this edge as visited.
seed_edge_data.active = false;
// Start a polyline.
ThickPolyline polyline;
polyline.points.emplace_back(seed_edge->vertex0()->x(), seed_edge->vertex0()->y());
polyline.points.emplace_back(seed_edge->vertex1()->x(), seed_edge->vertex1()->y());
polyline.width.emplace_back(seed_edge_data.width_start);
polyline.width.emplace_back(seed_edge_data.width_end);
// Grow the polyline in a forward direction.
this->process_edge_neighbors(&*seed_edge, &polyline);
assert(polyline.width.size() == polyline.points.size() * 2 - 2);
// Grow the polyline in a backward direction.
reverse_polyline.clear();
this->process_edge_neighbors(seed_edge->twin(), &reverse_polyline);
polyline.points.insert(polyline.points.begin(), reverse_polyline.points.rbegin(), reverse_polyline.points.rend());
polyline.width.insert(polyline.width.begin(), reverse_polyline.width.rbegin(), reverse_polyline.width.rend());
polyline.endpoints.first = reverse_polyline.endpoints.second;
assert(polyline.width.size() == polyline.points.size() * 2 - 2);
// Prevent loop endpoints from being extended.
if (polyline.first_point() == polyline.last_point()) {
polyline.endpoints.first = false;
polyline.endpoints.second = false;
}
// Append polyline to result.
polylines->emplace_back(std::move(polyline));
}
#ifdef SLIC3R_DEBUG
{
static int iRun = 0;
dump_voronoi_to_svg(m_lines, m_vd, polylines, debug_out_path("MedialAxis-%d.svg", iRun ++).c_str());
printf("Thick lines: ");
for (ThickPolylines::const_iterator it = polylines->begin(); it != polylines->end(); ++ it) {
ThickLines lines = it->thicklines();
for (ThickLines::const_iterator it2 = lines.begin(); it2 != lines.end(); ++ it2) {
printf("%f,%f ", it2->a_width, it2->b_width);
}
}
printf("\n");
}
#endif /* SLIC3R_DEBUG */
}
void MedialAxis::build(Polylines* polylines)
{
ThickPolylines tp;
this->build(&tp);
polylines->reserve(polylines->size() + tp.size());
for (auto &pl : tp)
polylines->emplace_back(pl.points);
}
void MedialAxis::process_edge_neighbors(const VD::edge_type *edge, ThickPolyline* polyline)
{
for (;;) {
// Since rot_next() works on the edge starting point but we want
// to find neighbors on the ending point, we just swap edge with
// its twin.
const VD::edge_type *twin = edge->twin();
// count neighbors for this edge
size_t num_neighbors = 0;
const VD::edge_type *first_neighbor = nullptr;
for (const VD::edge_type *neighbor = twin->rot_next(); neighbor != twin; neighbor = neighbor->rot_next())
if (this->edge_data(*neighbor).first.active) {
if (num_neighbors == 0)
first_neighbor = neighbor;
++ num_neighbors;
}
// if we have a single neighbor then we can continue recursively
if (num_neighbors == 1) {
if (std::pair<EdgeData&, bool> neighbor_data = this->edge_data(*first_neighbor);
neighbor_data.first.active) {
neighbor_data.first.active = false;
polyline->points.emplace_back(first_neighbor->vertex1()->x(), first_neighbor->vertex1()->y());
if (neighbor_data.second) {
polyline->width.push_back(neighbor_data.first.width_end);
polyline->width.push_back(neighbor_data.first.width_start);
} else {
polyline->width.push_back(neighbor_data.first.width_start);
polyline->width.push_back(neighbor_data.first.width_end);
}
edge = first_neighbor;
// Continue chaining.
continue;
}
} else if (num_neighbors == 0) {
polyline->endpoints.second = true;
} else {
// T-shaped or star-shaped joint
}
// Stop chaining.
break;
}
}
bool MedialAxis::validate_edge(const VD::edge_type* edge)
{
auto retrieve_segment = [this](const VD::cell_type* cell) -> const Line& { return m_lines[cell->source_index()]; };
auto retrieve_endpoint = [retrieve_segment](const VD::cell_type* cell) -> const Point& {
const Line &line = retrieve_segment(cell);
return cell->source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_START_POINT ? line.a : line.b;
};
// prevent overflows and detect almost-infinite edges
#ifndef CLIPPERLIB_INT32
if (std::abs(edge->vertex0()->x()) > double(CLIPPER_MAX_COORD_UNSCALED) ||
std::abs(edge->vertex0()->y()) > double(CLIPPER_MAX_COORD_UNSCALED) ||
std::abs(edge->vertex1()->x()) > double(CLIPPER_MAX_COORD_UNSCALED) ||
std::abs(edge->vertex1()->y()) > double(CLIPPER_MAX_COORD_UNSCALED))
return false;
#endif // CLIPPERLIB_INT32
// construct the line representing this edge of the Voronoi diagram
const Line line({ edge->vertex0()->x(), edge->vertex0()->y() },
{ edge->vertex1()->x(), edge->vertex1()->y() });
// retrieve the original line segments which generated the edge we're checking
const VD::cell_type* cell_l = edge->cell();
const VD::cell_type* cell_r = edge->twin()->cell();
const Line &segment_l = retrieve_segment(cell_l);
const Line &segment_r = retrieve_segment(cell_r);
/*
SVG svg("edge.svg");
svg.draw(m_expolygon);
svg.draw(line);
svg.draw(segment_l, "red");
svg.draw(segment_r, "blue");
svg.Close();
*/
/* Calculate thickness of the cross-section at both the endpoints of this edge.
Our Voronoi edge is part of a CCW sequence going around its Voronoi cell
located on the left side. (segment_l).
This edge's twin goes around segment_r. Thus, segment_r is
oriented in the same direction as our main edge, and segment_l is oriented
in the same direction as our twin edge.
We used to only consider the (half-)distances to segment_r, and that works
whenever segment_l and segment_r are almost specular and facing. However,
at curves they are staggered and they only face for a very little length
(our very short edge represents such visibility).
Both w0 and w1 can be calculated either towards cell_l or cell_r with equal
results by Voronoi definition.
When cell_l or cell_r don't refer to the segment but only to an endpoint, we
calculate the distance to that endpoint instead. */
coordf_t w0 = cell_r->contains_segment()
? segment_r.distance_to(line.a)*2
: (retrieve_endpoint(cell_r) - line.a).cast<double>().norm()*2;
coordf_t w1 = cell_l->contains_segment()
? segment_l.distance_to(line.b)*2
: (retrieve_endpoint(cell_l) - line.b).cast<double>().norm()*2;
if (cell_l->contains_segment() && cell_r->contains_segment()) {
// calculate the relative angle between the two boundary segments
double angle = fabs(segment_r.orientation() - segment_l.orientation());
if (angle > PI)
angle = 2. * PI - angle;
assert(angle >= 0 && angle <= PI);
// fabs(angle) ranges from 0 (collinear, same direction) to PI (collinear, opposite direction)
// we're interested only in segments close to the second case (facing segments)
// so we allow some tolerance.
// this filter ensures that we're dealing with a narrow/oriented area (longer than thick)
// we don't run it on edges not generated by two segments (thus generated by one segment
// and the endpoint of another segment), since their orientation would not be meaningful
if (PI - angle > PI / 8.) {
// angle is not narrow enough
// only apply this filter to segments that are not too short otherwise their
// angle could possibly be not meaningful
if (w0 < SCALED_EPSILON || w1 < SCALED_EPSILON || line.length() >= m_min_width)
return false;
}
} else {
if (w0 < SCALED_EPSILON || w1 < SCALED_EPSILON)
return false;
}
if ((w0 >= m_min_width || w1 >= m_min_width) &&
(w0 <= m_max_width || w1 <= m_max_width)) {
std::pair<EdgeData&, bool> ed = this->edge_data(*edge);
if (ed.second)
std::swap(w0, w1);
ed.first.width_start = w0;
ed.first.width_end = w1;
return true;
}
return false;
}
} } // namespace Slicer::Geometry
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