Make Tree-Support Deterministic (#15565)

* Make tree support deterministic without giving up its parallelism

* Break equal-distance ties in the tree support MST by coordinates

* test: cover the determinism this PR fixes

The MST unit tests here cover the tie-break, but the drop_nodes rework
has no test.

Adds two cases to the tree support suite. The thread-scheduling one
slices five configs twice each and compares the support point sequence,
which is what the node ordering moves. The MST tie one pins the branch
diameter and line width that carry Prim's equal-distance ties into the
toolpaths.

slice_with_tree_support takes an optional config list so the second case
can add the tree parameters it needs, and the double-slice comparison is
shared rather than written twice.

Both fail on main without this PR. The first passes from 60d1ceb580, the
second from e148865dd6.

---------

Co-authored-by: raistlin7447 <kris.austin@gmail.com>

tests/libslic3r/CMakeLists.txt

@@ -29,6 +29,7 @@ add_executable(${_TEST_NAME}_tests
     test_polygon.cpp
     test_mutable_polygon.cpp
     test_mutable_priority_queue.cpp
+    test_minimum_spanning_tree.cpp
     test_nozzle_volume_type.cpp
     test_step.cpp
     test_stl.cpp

tests/libslic3r/test_minimum_spanning_tree.cpp

@@ -0,0 +1,66 @@
+#include <catch2/catch_all.hpp>
+
+#include <algorithm>
+
+#include "libslic3r/MinimumSpanningTree.hpp"
+#include "libslic3r/Point.hpp"
+
+using namespace Slic3r;
+
+// A 5x5 lattice: at every step of Prim's algorithm several candidates sit at the same
+// distance from the tree, so the tie-break decides the tree's shape.
+static std::vector<Point> lattice()
+{
+    std::vector<Point> vertices;
+    for (int y = 0; y < 5; ++y)
+        for (int x = 0; x < 5; ++x)
+            vertices.emplace_back(Point::new_scale(x, y));
+    return vertices;
+}
+
+static std::vector<Point> sorted_neighbours(const MinimumSpanningTree &mst, const Point &vertex)
+{
+    std::vector<Point> neighbours = mst.adjacent_nodes(vertex);
+    std::sort(neighbours.begin(), neighbours.end());
+    return neighbours;
+}
+
+TEST_CASE("Minimum spanning tree connects every vertex", "[MinimumSpanningTree]")
+{
+    const std::vector<Point> vertices = lattice();
+    const MinimumSpanningTree mst(vertices);
+
+    REQUIRE(mst.vertices().size() == vertices.size());
+    size_t adjacency_entries = 0;
+    for (const Point &vertex : vertices) {
+        const std::vector<Point> neighbours = mst.adjacent_nodes(vertex);
+        REQUIRE(! neighbours.empty());
+        adjacency_entries += neighbours.size();
+    }
+    // A tree on n vertices has n - 1 edges, each listed from both ends.
+    REQUIRE(adjacency_entries == 2 * (vertices.size() - 1));
+}
+
+TEST_CASE("Minimum spanning tree does not depend on the order of the non-root vertices", "[MinimumSpanningTree][Regression]")
+{
+    const std::vector<Point> vertices = lattice();
+    const MinimumSpanningTree reference(vertices);
+
+    // The root stays first: Prim's tree legitimately depends on where it starts.
+    // Every other order of the remaining vertices must give the same tree.
+    std::vector<std::vector<Point>> orders;
+    orders.emplace_back(vertices);
+    std::reverse(orders.back().begin() + 1, orders.back().end());
+    for (size_t shift = 1; shift + 1 < vertices.size(); ++shift) {
+        orders.emplace_back(vertices);
+        std::rotate(orders.back().begin() + 1, orders.back().begin() + 1 + shift, orders.back().end());
+    }
+
+    for (const std::vector<Point> &order : orders) {
+        const MinimumSpanningTree mst(order);
+        for (const Point &vertex : vertices) {
+            INFO("vertex " << vertex.x() << "," << vertex.y());
+            REQUIRE(sorted_neighbours(mst, vertex) == sorted_neighbours(reference, vertex));
+        }
+    }
+}