#include <stack>
#include <libslic3r/Geometry.hpp>
#include <libslic3r/Line.hpp>
#include <libslic3r/Polygon.hpp>
#include <libslic3r/SVG.hpp>
#include "VoronoiOffset.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);
assert(projection_start != projection_end);
// 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);
assert(mid_x != cur_x || mid_y != cur_y);
assert(mid_x != new_x || mid_y != new_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);
CT div = (new_y - cur_y) * (new_y - cur_y) + (new_x - cur_x) * (new_x - cur_x);
assert(div != 0);
dist = dist * dist / div;
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)
{
assert(edge.is_infinite());
assert((edge.vertex0() == nullptr) != (edge.vertex1() == nullptr));
const cell_type& cell1 = *edge.cell();
const cell_type& cell2 = *edge.twin()->cell();
// Infinite edges could not be created by two segment sites.
assert(cell1.contains_point() || cell2.contains_point());
if (! cell1.contains_point() && ! cell2.contains_point()) {
printf("Error! clip_infinite_edge - infinite edge separates two segment cells\n");
return;
}
point_type direction;
if (cell1.contains_point() && cell2.contains_point()) {
assert(! edge.is_secondary());
point_type p1 = retrieve_point(points, segments, cell1);
point_type p2 = retrieve_point(points, segments, cell2);
if (edge.vertex0() == nullptr)
std::swap(p1, p2);
direction.x(p1.y() - p2.y());
direction.y(p2.x() - p1.x());
} else {
assert(edge.is_secondary());
segment_type segment = cell1.contains_segment() ? segments[cell1.source_index()] : segments[cell2.source_index()];
direction.x(high(segment).y() - low(segment).y());
direction.y(low(segment).x() - high(segment).x());
}
coordinate_type koef = bbox_max_size / (std::max)(fabs(direction.x()), fabs(direction.y()));
if (edge.vertex0() == nullptr) {
clipped_edge->push_back(point_type(edge.vertex1()->x() + direction.x() * koef, edge.vertex1()->y() + direction.y() * koef));
clipped_edge->push_back(point_type(edge.vertex1()->x(), edge.vertex1()->y()));
} else {
clipped_edge->push_back(point_type(edge.vertex0()->x(), edge.vertex0()->y()));
clipped_edge->push_back(point_type(edge.vertex0()->x() + direction.x() * koef, edge.vertex0()->y() + direction.y() * koef));
}
}
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(),
double scale = 0)
{
const bool internalEdgesOnly = false;
BoundingBox bbox;
bbox.merge(get_extents(points));
bbox.merge(get_extents(lines));
bbox.merge(get_extents(offset_curves));
bbox.merge(get_extents(helper_lines));
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)
bbox.merge(Point(it->x(), it->y()));
bbox.min -= (0.01 * bbox.size().cast<double>()).cast<coord_t>();
bbox.max += (0.01 * bbox.size().cast<double>()).cast<coord_t>();
if (scale == 0)
scale =
// 0.1
0.01
* std::min(bbox.size().x(), bbox.size().y());
else
scale *= SCALING_FACTOR;
const std::string inputSegmentPointColor = "lightseagreen";
const coord_t inputSegmentPointRadius = std::max<coord_t>(1, coord_t(0.09 * scale));
const std::string inputSegmentColor = "lightseagreen";
const coord_t inputSegmentLineWidth = coord_t(0.03 * scale);
const std::string voronoiPointColor = "black";
const std::string voronoiPointColorOutside = "red";
const std::string voronoiPointColorInside = "blue";
const coord_t voronoiPointRadius = std::max<coord_t>(1, coord_t(0.06 * scale));
const std::string voronoiLineColorPrimary = "black";
const std::string voronoiLineColorSecondary = "green";
const std::string voronoiArcColor = "red";
const coord_t voronoiLineWidth = coord_t(0.02 * scale);
const std::string offsetCurveColor = "magenta";
const coord_t offsetCurveLineWidth = coord_t(0.02 * scale);
const std::string helperLineColor = "orange";
const coord_t helperLineWidth = coord_t(0.04 * scale);
const bool primaryEdgesOnly = false;
::Slic3r::SVG svg(path, bbox);
// 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 = 0.0002 * 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.
if (internalEdgesOnly) {
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) {
const std::string *color = nullptr;
switch (Voronoi::vertex_category(*it)) {
case Voronoi::VertexCategory::OnContour: color = &voronoiPointColor; break;
case Voronoi::VertexCategory::Outside: color = &voronoiPointColorOutside; break;
case Voronoi::VertexCategory::Inside: color = &voronoiPointColorInside; break;
default: color = &voronoiPointColor; // assert(false);
}
Point pt(coord_t(it->x()), coord_t(it->y()));
if (it->x() * pt.x() >= 0. && it->y() * pt.y() >= 0.)
// Conversion to coord_t is valid.
svg.draw(Point(coord_t(it->x()), coord_t(it->y())), *color, 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) {
Vec2d a(samples[i].x(), samples[i].y());
Vec2d b(samples[i+1].x(), samples[i+1].y());
// Convert to coord_t.
Point ia = a.cast<coord_t>();
Point ib = b.cast<coord_t>();
// Is the conversion possible? Do the resulting points fit into int32_t?
auto in_range = [](const Point &ip, const Vec2d &p) { return p.x() * ip.x() >= 0. && p.y() * ip.y() >= 0.; };
bool a_in_range = in_range(ia, a);
bool b_in_range = in_range(ib, b);
if (! a_in_range || ! b_in_range) {
if (! a_in_range && ! b_in_range)
// None fits, ignore.
continue;
// One fit, the other does not. Try to clip.
Vec2d v = b - a;
v.normalize();
v *= bbox.size().cast<double>().norm();
auto p = a_in_range ? Vec2d(a + v) : Vec2d(b - v);
Point ip = p.cast<coord_t>();
if (! in_range(ip, p))
continue;
(a_in_range ? ib : ia) = ip;
}
svg.draw(Line(ia, ib), color, voronoiLineWidth);
}
}
#endif
svg.draw_outline(offset_curves, offsetCurveColor, offsetCurveLineWidth);
svg.draw(helper_lines, helperLineColor, helperLineWidth);
svg.Close();
}
} // namespace Slic3r