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Manual merge of the TriangleMesh.cpp from the stable branch.

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This commit is contained in:
bubnikv 2018-12-12 10:02:01 +01:00
parent e1ca861ee6
commit 5ea8df0ca0
3 changed files with 413 additions and 217 deletions
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1
src/libslic3r/SLAPrint.hpp
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@ -185,6 +185,7 @@ public:
bool empty() const override { return m_objects.empty(); } bool empty() const override { return m_objects.empty(); }
ApplyStatus apply(const Model &model, const DynamicPrintConfig &config) override; ApplyStatus apply(const Model &model, const DynamicPrintConfig &config) override;
void process() override; void process() override;
// Returns true if an object step is done on all objects and there's at least one object.
bool is_step_done(SLAPrintObjectStep step) const; bool is_step_done(SLAPrintObjectStep step) const;
// Returns true if the last step was finished with success. // Returns true if the last step was finished with success.
bool finished() const override { return this->is_step_done(slaposIndexSlices); } bool finished() const override { return this->is_step_done(slaposIndexSlices); }

379
src/libslic3r/TriangleMesh.cpp
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@ -1212,21 +1212,11 @@ static inline void remove_tangent_edges(std::vector<IntersectionLine> &lines)
} }
} }
void TriangleMeshSlicer::make_loops(std::vector<IntersectionLine> &lines, Polygons* loops) const
{
#if 0
//FIXME slice_facet() may create zero length edges due to rounding of doubles into coord_t.
//#ifdef _DEBUG
for (const Line &l : lines)
assert(l.a != l.b);
#endif /* _DEBUG */
remove_tangent_edges(lines); struct OpenPolyline {
struct OpenPolyline {
OpenPolyline() {}; OpenPolyline() {};
OpenPolyline(const IntersectionReference &start, const IntersectionReference &end, Points &&points) : OpenPolyline(const IntersectionReference &start, const IntersectionReference &end, Points &&points) :
start(start), end(end), points(std::move(points)), consumed(false) {} start(start), end(end), points(std::move(points)), consumed(false) { this->length = Slic3r::length(this->points); }
void reverse() { void reverse() {
std::swap(start, end); std::swap(start, end);
std::reverse(points.begin(), points.end()); std::reverse(points.begin(), points.end());
@ -1234,10 +1224,14 @@ void TriangleMeshSlicer::make_loops(std::vector<IntersectionLine> &lines, Polygo
IntersectionReference start; IntersectionReference start;
IntersectionReference end; IntersectionReference end;
Points points; Points points;
double length;
bool consumed; bool consumed;
}; };
std::vector<OpenPolyline> open_polylines;
{ // called by TriangleMeshSlicer::make_loops() to connect sliced triangles into closed loops and open polylines by the triangle connectivity.
// Only connects segments crossing triangles of the same orientation.
static void chain_lines_by_triangle_connectivity(std::vector<IntersectionLine> &lines, Polygons &loops, std::vector<OpenPolyline> &open_polylines)
{
// Build a map of lines by edge_a_id and a_id. // Build a map of lines by edge_a_id and a_id.
std::vector<IntersectionLine*> by_edge_a_id; std::vector<IntersectionLine*> by_edge_a_id;
std::vector<IntersectionLine*> by_a_id; std::vector<IntersectionLine*> by_a_id;
@ -1312,7 +1306,7 @@ void TriangleMeshSlicer::make_loops(std::vector<IntersectionLine> &lines, Polygo
if ((first_line->edge_a_id != -1 && first_line->edge_a_id == last_line->edge_b_id) || if ((first_line->edge_a_id != -1 && first_line->edge_a_id == last_line->edge_b_id) ||
(first_line->a_id != -1 && first_line->a_id == last_line->b_id)) { (first_line->a_id != -1 && first_line->a_id == last_line->b_id)) {
// The current loop is complete. Add it to the output. // The current loop is complete. Add it to the output.
loops->emplace_back(std::move(loop_pts)); loops.emplace_back(std::move(loop_pts));
#ifdef SLIC3R_TRIANGLEMESH_DEBUG #ifdef SLIC3R_TRIANGLEMESH_DEBUG
printf(" Discovered %s polygon of %d points\n", (p.is_counter_clockwise() ? "ccw" : "cw"), (int)p.points.size()); printf(" Discovered %s polygon of %d points\n", (p.is_counter_clockwise() ? "ccw" : "cw"), (int)p.points.size());
#endif #endif
@ -1335,10 +1329,26 @@ void TriangleMeshSlicer::make_loops(std::vector<IntersectionLine> &lines, Polygo
next_line->set_skip(); next_line->set_skip();
} }
} }
} }
// Now process the open polylines. std::vector<OpenPolyline*> open_polylines_sorted(std::vector<OpenPolyline> &open_polylines, bool update_lengths)
if (! open_polylines.empty()) { {
std::vector<OpenPolyline*> out;
out.reserve(open_polylines.size());
for (OpenPolyline &opl : open_polylines)
if (! opl.consumed) {
if (update_lengths)
opl.length = Slic3r::length(opl.points);
out.emplace_back(&opl);
}
std::sort(out.begin(), out.end(), [](const OpenPolyline *lhs, const OpenPolyline *rhs){ return lhs->length > rhs->length; });
return out;
}
// called by TriangleMeshSlicer::make_loops() to connect remaining open polylines across shared triangle edges and vertices.
// Depending on "try_connect_reversed", it may or may not connect segments crossing triangles of opposite orientation.
static void chain_open_polylines_exact(std::vector<OpenPolyline> &open_polylines, Polygons &loops, bool try_connect_reversed)
{
// Store the end points of open_polylines into vectors sorted // Store the end points of open_polylines into vectors sorted
struct OpenPolylineEnd { struct OpenPolylineEnd {
OpenPolylineEnd(OpenPolyline *polyline, bool start) : polyline(polyline), start(start) {} OpenPolylineEnd(OpenPolyline *polyline, bool start) : polyline(polyline), start(start) {}
@ -1346,106 +1356,287 @@ void TriangleMeshSlicer::make_loops(std::vector<IntersectionLine> &lines, Polygo
// Is it the start or end point? // Is it the start or end point?
bool start; bool start;
const IntersectionReference& ipref() const { return start ? polyline->start : polyline->end; } const IntersectionReference& ipref() const { return start ? polyline->start : polyline->end; }
int point_id() const { return ipref().point_id; } // Return a unique ID for the intersection point.
int edge_id () const { return ipref().edge_id; } // Return a positive id for a point, or a negative id for an edge.
int id() const { const IntersectionReference &r = ipref(); return (r.point_id >= 0) ? r.point_id : - r.edge_id; }
bool operator==(const OpenPolylineEnd &rhs) const { return this->polyline == rhs.polyline && this->start == rhs.start; }
}; };
auto by_edge_lower = [](const OpenPolylineEnd &ope1, const OpenPolylineEnd &ope2) { return ope1.edge_id() < ope2.edge_id(); }; auto by_id_lower = [](const OpenPolylineEnd &ope1, const OpenPolylineEnd &ope2) { return ope1.id() < ope2.id(); };
auto by_point_lower = [](const OpenPolylineEnd &ope1, const OpenPolylineEnd &ope2) { return ope1.point_id() < ope2.point_id(); }; std::vector<OpenPolylineEnd> by_id;
std::vector<OpenPolylineEnd> by_edge_id; by_id.reserve(2 * open_polylines.size());
std::vector<OpenPolylineEnd> by_point_id;
by_edge_id.reserve(2 * open_polylines.size());
by_point_id.reserve(2 * open_polylines.size());
for (OpenPolyline &opl : open_polylines) { for (OpenPolyline &opl : open_polylines) {
if (opl.start.edge_id != -1) if (opl.start.point_id != -1 || opl.start.edge_id != -1)
by_edge_id .emplace_back(OpenPolylineEnd(&opl, true)); by_id.emplace_back(OpenPolylineEnd(&opl, true));
if (opl.end.edge_id != -1) if (try_connect_reversed && (opl.end.point_id != -1 || opl.end.edge_id != -1))
by_edge_id .emplace_back(OpenPolylineEnd(&opl, false)); by_id.emplace_back(OpenPolylineEnd(&opl, false));
if (opl.start.point_id != -1)
by_point_id.emplace_back(OpenPolylineEnd(&opl, true));
if (opl.end.point_id != -1)
by_point_id.emplace_back(OpenPolylineEnd(&opl, false));
} }
std::sort(by_edge_id .begin(), by_edge_id .end(), by_edge_lower); std::sort(by_id.begin(), by_id.end(), by_id_lower);
std::sort(by_point_id.begin(), by_point_id.end(), by_point_lower); // Find an iterator to by_id_lower for the particular end of OpenPolyline (by comparing the OpenPolyline pointer and the start attribute).
auto find_polyline_end = [&by_id, by_id_lower](const OpenPolylineEnd &end) -> std::vector<OpenPolylineEnd>::iterator {
for (auto it = std::lower_bound(by_id.begin(), by_id.end(), end, by_id_lower);
it != by_id.end() && it->id() == end.id(); ++ it)
if (*it == end)
return it;
return by_id.end();
};
// Try to connect the loops. // Try to connect the loops.
for (OpenPolyline &opl : open_polylines) { std::vector<OpenPolyline*> sorted_by_length = open_polylines_sorted(open_polylines, false);
if (opl.consumed) for (OpenPolyline *opl : sorted_by_length) {
if (opl->consumed)
continue; continue;
opl.consumed = true; opl->consumed = true;
OpenPolylineEnd end(&opl, false); OpenPolylineEnd end(opl, false);
for (;;) { for (;;) {
// find a line starting where last one finishes // find a line starting where last one finishes
OpenPolylineEnd* next_start = nullptr; auto it_next_start = std::lower_bound(by_id.begin(), by_id.end(), end, by_id_lower);
if (end.edge_id() != -1) { for (; it_next_start != by_id.end() && it_next_start->id() == end.id(); ++ it_next_start)
auto it_begin = std::lower_bound(by_edge_id.begin(), by_edge_id.end(), end, by_edge_lower); if (! it_next_start->polyline->consumed)
if (it_begin != by_edge_id.end()) { goto found;
auto it_end = std::upper_bound(it_begin, by_edge_id.end(), end, by_edge_lower);
for (auto it_edge = it_begin; it_edge != it_end; ++ it_edge)
if (! it_edge->polyline->consumed) {
next_start = &(*it_edge);
break;
}
}
}
if (next_start == nullptr && end.point_id() != -1) {
auto it_begin = std::lower_bound(by_point_id.begin(), by_point_id.end(), end, by_point_lower);
if (it_begin != by_point_id.end()) {
auto it_end = std::upper_bound(it_begin, by_point_id.end(), end, by_point_lower);
for (auto it_point = it_begin; it_point != it_end; ++ it_point)
if (! it_point->polyline->consumed) {
next_start = &(*it_point);
break;
}
}
}
if (next_start == nullptr) {
// The current loop could not be closed. Unmark the segment. // The current loop could not be closed. Unmark the segment.
opl.consumed = false; opl->consumed = false;
break; break;
} found:
// Attach this polyline to the end of the initial polyline. // Attach this polyline to the end of the initial polyline.
if (next_start->start) { if (it_next_start->start) {
auto it = next_start->polyline->points.begin(); auto it = it_next_start->polyline->points.begin();
std::copy(++ it, next_start->polyline->points.end(), back_inserter(opl.points)); std::copy(++ it, it_next_start->polyline->points.end(), back_inserter(opl->points));
//opl.points.insert(opl.points.back(), ++ it, next_start->polyline->points.end());
} else { } else {
auto it = next_start->polyline->points.rbegin(); auto it = it_next_start->polyline->points.rbegin();
std::copy(++ it, next_start->polyline->points.rend(), back_inserter(opl.points)); std::copy(++ it, it_next_start->polyline->points.rend(), back_inserter(opl->points));
//opl.points.insert(opl.points.back(), ++ it, next_start->polyline->points.rend()); }
opl->length += it_next_start->polyline->length;
// Mark the next polyline as consumed.
it_next_start->polyline->points.clear();
it_next_start->polyline->length = 0.;
it_next_start->polyline->consumed = true;
if (try_connect_reversed) {
// Running in a mode, where the polylines may be connected by mixing their orientations.
// Update the end point lookup structure after the end point of the current polyline was extended.
auto it_end = find_polyline_end(end);
auto it_next_end = find_polyline_end(OpenPolylineEnd(it_next_start->polyline, !it_next_start->start));
// Swap the end points of the current and next polyline, but keep the polyline ptr and the start flag.
std::swap(opl->end, it_next_end->start ? it_next_end->polyline->start : it_next_end->polyline->end);
// Swap the positions of OpenPolylineEnd structures in the sorted array to match their respective end point positions.
std::swap(*it_end, *it_next_end);
} }
end = *next_start;
end.start = !end.start;
next_start->polyline->points.clear();
next_start->polyline->consumed = true;
// Check whether we closed this loop. // Check whether we closed this loop.
const IntersectionReference &ip1 = opl.start; if ((opl->start.edge_id != -1 && opl->start.edge_id == opl->end.edge_id) ||
const IntersectionReference &ip2 = end.ipref(); (opl->start.point_id != -1 && opl->start.point_id == opl->end.point_id)) {
if ((ip1.edge_id != -1 && ip1.edge_id == ip2.edge_id) ||
(ip1.point_id != -1 && ip1.point_id == ip2.point_id)) {
// The current loop is complete. Add it to the output. // The current loop is complete. Add it to the output.
//assert(opl.points.front().point_id == opl.points.back().point_id); //assert(opl->points.front().point_id == opl->points.back().point_id);
//assert(opl.points.front().edge_id == opl.points.back().edge_id); //assert(opl->points.front().edge_id == opl->points.back().edge_id);
// Remove the duplicate last point. // Remove the duplicate last point.
opl.points.pop_back(); opl->points.pop_back();
if (opl.points.size() >= 3) { if (opl->points.size() >= 3) {
if (try_connect_reversed && area(opl->points) < 0)
// The closed polygon is patched from pieces with messed up orientation, therefore // The closed polygon is patched from pieces with messed up orientation, therefore
// the orientation of the patched up polygon is not known. // the orientation of the patched up polygon is not known.
// Orient the patched up polygons CCW. This heuristic may close some holes and cavities. // Orient the patched up polygons CCW. This heuristic may close some holes and cavities.
double area = 0.; std::reverse(opl->points.begin(), opl->points.end());
for (size_t i = 0, j = opl.points.size() - 1; i < opl.points.size(); j = i ++) loops.emplace_back(std::move(opl->points));
area += double(opl.points[j](0) + opl.points[i](0)) * double(opl.points[i](1) - opl.points[j](1));
if (area < 0)
std::reverse(opl.points.begin(), opl.points.end());
loops->emplace_back(std::move(opl.points));
} }
opl.points.clear(); opl->points.clear();
break; break;
} }
// Continue with the current loop. // Continue with the current loop.
} }
} }
}
// called by TriangleMeshSlicer::make_loops() to connect remaining open polylines across shared triangle edges and vertices,
// possibly closing small gaps.
// Depending on "try_connect_reversed", it may or may not connect segments crossing triangles of opposite orientation.
static void chain_open_polylines_close_gaps(std::vector<OpenPolyline> &open_polylines, Polygons &loops, double max_gap, bool try_connect_reversed)
{
const coord_t max_gap_scaled = (coord_t)scale_(max_gap);
// Sort the open polylines by their length, so the new loops will be seeded from longer chains.
// Update the polyline lengths, return only not yet consumed polylines.
std::vector<OpenPolyline*> sorted_by_length = open_polylines_sorted(open_polylines, true);
// Store the end points of open_polylines into ClosestPointInRadiusLookup<OpenPolylineEnd>.
struct OpenPolylineEnd {
OpenPolylineEnd(OpenPolyline *polyline, bool start) : polyline(polyline), start(start) {}
OpenPolyline *polyline;
// Is it the start or end point?
bool start;
const Point& point() const { return start ? polyline->points.front() : polyline->points.back(); }
bool operator==(const OpenPolylineEnd &rhs) const { return this->polyline == rhs.polyline && this->start == rhs.start; }
};
struct OpenPolylineEndAccessor {
const Point* operator()(const OpenPolylineEnd &pt) const { return pt.polyline->consumed ? nullptr : &pt.point(); }
};
typedef ClosestPointInRadiusLookup<OpenPolylineEnd, OpenPolylineEndAccessor> ClosestPointLookupType;
ClosestPointLookupType closest_end_point_lookup(max_gap_scaled);
for (OpenPolyline *opl : sorted_by_length) {
closest_end_point_lookup.insert(OpenPolylineEnd(opl, true));
if (try_connect_reversed)
closest_end_point_lookup.insert(OpenPolylineEnd(opl, false));
} }
// Try to connect the loops.
for (OpenPolyline *opl : sorted_by_length) {
if (opl->consumed)
continue;
OpenPolylineEnd end(opl, false);
if (try_connect_reversed)
// The end point of this polyline will be modified, thus the following entry will become invalid. Remove it.
closest_end_point_lookup.erase(end);
opl->consumed = true;
size_t n_segments_joined = 1;
for (;;) {
// Find a line starting where last one finishes, only return non-consumed open polylines (OpenPolylineEndAccessor returns null for consumed).
std::pair<const OpenPolylineEnd*, double> next_start_and_dist = closest_end_point_lookup.find(end.point());
const OpenPolylineEnd *next_start = next_start_and_dist.first;
// Check whether we closed this loop.
double current_loop_closing_distance2 = (opl->points.back() - opl->points.front()).cast<double>().squaredNorm();
bool loop_closed = current_loop_closing_distance2 < coordf_t(max_gap_scaled) * coordf_t(max_gap_scaled);
if (next_start != nullptr && loop_closed && current_loop_closing_distance2 < next_start_and_dist.second) {
// Heuristics to decide, whether to close the loop, or connect another polyline.
// One should avoid closing loops shorter than max_gap_scaled.
loop_closed = sqrt(current_loop_closing_distance2) < 0.3 * length(opl->points);
}
if (loop_closed) {
// Remove the start point of the current polyline from the lookup.
// Mark the current segment as not consumed, otherwise the closest_end_point_lookup.erase() would fail.
opl->consumed = false;
closest_end_point_lookup.erase(OpenPolylineEnd(opl, true));
if (current_loop_closing_distance2 == 0.) {
// Remove the duplicate last point.
opl->points.pop_back();
} else {
// The end points are different, keep both of them.
}
if (opl->points.size() >= 3) {
if (try_connect_reversed && n_segments_joined > 1 && area(opl->points) < 0)
// The closed polygon is patched from pieces with messed up orientation, therefore
// the orientation of the patched up polygon is not known.
// Orient the patched up polygons CCW. This heuristic may close some holes and cavities.
std::reverse(opl->points.begin(), opl->points.end());
loops.emplace_back(std::move(opl->points));
}
opl->points.clear();
opl->consumed = true;
break;
}
if (next_start == nullptr) {
// The current loop could not be closed. Unmark the segment.
opl->consumed = false;
if (try_connect_reversed)
// Re-insert the end point.
closest_end_point_lookup.insert(OpenPolylineEnd(opl, false));
break;
}
// Attach this polyline to the end of the initial polyline.
if (next_start->start) {
auto it = next_start->polyline->points.begin();
if (*it == opl->points.back())
++ it;
std::copy(it, next_start->polyline->points.end(), back_inserter(opl->points));
} else {
auto it = next_start->polyline->points.rbegin();
if (*it == opl->points.back())
++ it;
std::copy(it, next_start->polyline->points.rend(), back_inserter(opl->points));
}
++ n_segments_joined;
// Remove the end points of the consumed polyline segment from the lookup.
OpenPolyline *opl2 = next_start->polyline;
closest_end_point_lookup.erase(OpenPolylineEnd(opl2, true));
if (try_connect_reversed)
closest_end_point_lookup.erase(OpenPolylineEnd(opl2, false));
opl2->points.clear();
opl2->consumed = true;
// Continue with the current loop.
}
}
}
void TriangleMeshSlicer::make_loops(std::vector<IntersectionLine> &lines, Polygons* loops) const
{
#if 0
//FIXME slice_facet() may create zero length edges due to rounding of doubles into coord_t.
//#ifdef _DEBUG
for (const Line &l : lines)
assert(l.a != l.b);
#endif /* _DEBUG */
// There should be no tangent edges, as the horizontal triangles are ignored and if two triangles touch at a cutting plane,
// only the bottom triangle is considered to be cutting the plane.
// remove_tangent_edges(lines);
#ifdef SLIC3R_DEBUG_SLICE_PROCESSING
BoundingBox bbox_svg;
{
static int iRun = 0;
for (const Line &line : lines) {
bbox_svg.merge(line.a);
bbox_svg.merge(line.b);
}
SVG svg(debug_out_path("TriangleMeshSlicer_make_loops-raw_lines-%d.svg", iRun ++).c_str(), bbox_svg);
for (const Line &line : lines)
svg.draw(line);
svg.Close();
}
#endif /* SLIC3R_DEBUG_SLICE_PROCESSING */
std::vector<OpenPolyline> open_polylines;
chain_lines_by_triangle_connectivity(lines, *loops, open_polylines);
#ifdef SLIC3R_DEBUG_SLICE_PROCESSING
{
static int iRun = 0;
SVG svg(debug_out_path("TriangleMeshSlicer_make_loops-polylines-%d.svg", iRun ++).c_str(), bbox_svg);
svg.draw(union_ex(*loops));
for (const OpenPolyline &pl : open_polylines)
svg.draw(Polyline(pl.points), "red");
svg.Close();
}
#endif /* SLIC3R_DEBUG_SLICE_PROCESSING */
// Now process the open polylines.
// Do it in two rounds, first try to connect in the same direction only,
// then try to connect the open polylines in reversed order as well.
chain_open_polylines_exact(open_polylines, *loops, false);
chain_open_polylines_exact(open_polylines, *loops, true);
#ifdef SLIC3R_DEBUG_SLICE_PROCESSING
{
static int iRun = 0;
SVG svg(debug_out_path("TriangleMeshSlicer_make_loops-polylines2-%d.svg", iRun++).c_str(), bbox_svg);
svg.draw(union_ex(*loops));
for (const OpenPolyline &pl : open_polylines) {
if (pl.points.empty())
continue;
svg.draw(Polyline(pl.points), "red");
svg.draw(pl.points.front(), "blue");
svg.draw(pl.points.back(), "blue");
}
svg.Close();
}
#endif /* SLIC3R_DEBUG_SLICE_PROCESSING */
// Try to close gaps.
// Do it in two rounds, first try to connect in the same direction only,
// then try to connect the open polylines in reversed order as well.
const double max_gap = 2.; //mm
chain_open_polylines_close_gaps(open_polylines, *loops, max_gap, false);
chain_open_polylines_close_gaps(open_polylines, *loops, max_gap, true);
#ifdef SLIC3R_DEBUG_SLICE_PROCESSING
{
static int iRun = 0;
SVG svg(debug_out_path("TriangleMeshSlicer_make_loops-polylines-final-%d.svg", iRun++).c_str(), bbox_svg);
svg.draw(union_ex(*loops));
for (const OpenPolyline &pl : open_polylines) {
if (pl.points.empty())
continue;
svg.draw(Polyline(pl.points), "red");
svg.draw(pl.points.front(), "blue");
svg.draw(pl.points.back(), "blue");
}
svg.Close();
}
#endif /* SLIC3R_DEBUG_SLICE_PROCESSING */
} }
// Only used to cut the mesh into two halves. // Only used to cut the mesh into two halves.

8
xs/t/01_trianglemesh.t
View File

@ -79,7 +79,9 @@ my $cube = {
my $m = Slic3r::TriangleMesh->new; my $m = Slic3r::TriangleMesh->new;
$m->ReadFromPerl($cube->{vertices}, $cube->{facets}); $m->ReadFromPerl($cube->{vertices}, $cube->{facets});
$m->repair; $m->repair;
my @z = (0,2,4,8,6,8,10,12,14,16,18,20); # The slice at zero height does not belong to the mesh, the slicing considers the vertical structures to be
# open intervals at the bottom end, closed at the top end.
my @z = (0.0001,2,4,8,6,8,10,12,14,16,18,20);
my $result = $m->slice(\@z); my $result = $m->slice(\@z);
my $SCALING_FACTOR = 0.000001; my $SCALING_FACTOR = 0.000001;
for my $i (0..$#z) { for my $i (0..$#z) {
@ -105,7 +107,9 @@ my $cube = {
# this second test also checks that performing a second slice on a mesh after # this second test also checks that performing a second slice on a mesh after
# a transformation works properly (shared_vertices is correctly invalidated); # a transformation works properly (shared_vertices is correctly invalidated);
# at Z = -10 we have a bottom horizontal surface # at Z = -10 we have a bottom horizontal surface
my $slices = $m->slice([ -5, -10 ]); # (The slice at zero height does not belong to the mesh, the slicing considers the vertical structures to be
# open intervals at the bottom end, closed at the top end, so the Z = -10 is shifted a bit up to get a valid slice).
my $slices = $m->slice([ -5, -10+0.00001 ]);
is $slices->[0][0]->area, $slices->[1][0]->area, 'slicing a bottom tangent plane includes its area'; is $slices->[0][0]->area, $slices->[1][0]->area, 'slicing a bottom tangent plane includes its area';
} }
} }