Implement 2D minkowski() as a boundary sweep

pyproject.toml

@@ -4,7 +4,7 @@ build-backend = "scikit_build_core.build"
 
 [project]
 name = "openscad_cpp_evaluator"
-version = "0.29.0"
+version = "0.29.1"
 description = "C++ OpenSCAD evaluator with Python bindings"
 readme = "README.md"
 requires-python = ">=3.12"

src/builtins/topology.cpp

@@ -3,6 +3,8 @@
 #include "openscad_cpp_evaluator/call_args.hpp"
 #include "openscad_cpp_evaluator/evaluator.hpp"
 
+#include <manifold/polygon.h>
+
 namespace oscadeval {
 
 // hull()/minkowski() -- like union/difference/intersection, these splice
@@ -72,18 +74,128 @@ CSGParams resolveMinkowski(Evaluator& ev, const oscad::ModularCall& node, EvalCo
     return CSGParams{};
 }
 
-// minkowski() only operates on 3D bodies -- 2D sections among the
-// foreground children are silently ignored, matching _generate_minkowski
-// exactly (it filters `c.body is not None`, never falls back to sections
-// the way hull does).
+
+namespace {
+
+// The convex pieces of a 2D shape, as point lists.
+//
+// A Minkowski sum only has a closed form for convex operands -- there it
+// is the convex hull of every pairwise sum -- so a shape that is not
+// convex has to be cut into pieces that are. A convex outline with no
+// holes is already one piece, which is the common case (a circle being
+// swept over something) and much cheaper than triangulating it.
+std::vector<manifold::SimplePolygon> convexPieces(const manifold::CrossSection& section) {
+    const manifold::Polygons polys = section.ToPolygons();
+    std::vector<manifold::SimplePolygon> out;
+
+    if (polys.size() == 1) {
+        const manifold::SimplePolygon& ring = polys[0];
+        bool convex = ring.size() >= 3;
+        int sign = 0;
+        for (size_t i = 0; convex && i < ring.size(); ++i) {
+            const manifold::vec2& a = ring[i];
+            const manifold::vec2& b = ring[(i + 1) % ring.size()];
+            const manifold::vec2& c = ring[(i + 2) % ring.size()];
+            const double cross = (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x);
+            if (std::abs(cross) < 1e-12) continue;      // collinear, no turn
+            const int s = cross > 0 ? 1 : -1;
+            if (sign == 0) sign = s;
+            else if (s != sign) convex = false;
+        }
+        if (convex) {
+            out.push_back(ring);
+            return out;
+        }
+    }
+
+    for (const manifold::ivec3& tri : manifold::Triangulate(polys)) {
+        // Triangulate indexes the contours end to end.
+        std::vector<manifold::vec2> flat;
+        for (const manifold::SimplePolygon& ring : polys)
+            flat.insert(flat.end(), ring.begin(), ring.end());
+        if (static_cast<size_t>(tri.x) >= flat.size() || static_cast<size_t>(tri.y) >= flat.size() ||
+            static_cast<size_t>(tri.z) >= flat.size()) {
+            continue;
+        }
+        out.push_back({flat[tri.x], flat[tri.y], flat[tri.z]});
+    }
+    return out;
+}
+
+// The 2D Minkowski sum of two shapes.
+//
+// Manifold has no 2D Minkowski, so this is the boundary-sweep identity:
+// for B convex and containing the origin,
+//
+//     A (+) B  =  A  union  (boundary of A (+) B)
+//
+// and the boundary is a chain of segments, each of which sums with a
+// convex B to the hull of B at its two ends. So sweeping B along every
+// edge of A and unioning A itself is the whole answer -- A is never cut
+// up, however concave it is or however many holes it has. Only B is,
+// and only because the per-segment hull needs it convex.
+//
+// The two conditions on B are met rather than assumed: it is decomposed
+// into convex pieces (Minkowski distributes over union, so the pieces'
+// sums are unioned), and each piece is shifted onto the origin with the
+// shift undone afterwards, since A (+) B = ((A (+) (B - c)) + c).
+//
+// ponytail: one hull per edge of A per convex piece of B. A piece count
+// of one is the case that turns up -- a circle swept over something --
+// and then it is simply one hull per edge.
+manifold::CrossSection minkowski2d(const manifold::CrossSection& a, const manifold::CrossSection& b) {
+    const manifold::Polygons outline = a.ToPolygons();
+    std::vector<manifold::CrossSection> parts;
+
+    for (const manifold::SimplePolygon& piece : convexPieces(b)) {
+        if (piece.size() < 3) continue;
+        // Bring the piece onto the origin; the sum is shifted back after.
+        manifold::vec2 shift = piece[0];
+        manifold::SimplePolygon centred;
+        centred.reserve(piece.size());
+        for (const manifold::vec2& q : piece) centred.push_back({q.x - shift.x, q.y - shift.y});
+
+        std::vector<manifold::CrossSection> swept;
+        // A itself: only sound because `centred` contains the origin.
+        swept.push_back(a);
+        for (const manifold::SimplePolygon& ring : outline) {
+            for (size_t i = 0; i < ring.size(); ++i) {
+                const manifold::vec2& v0 = ring[i];
+                const manifold::vec2& v1 = ring[(i + 1) % ring.size()];
+                manifold::SimplePolygon ends;
+                ends.reserve(centred.size() * 2);
+                for (const manifold::vec2& q : centred) {
+                    ends.push_back({v0.x + q.x, v0.y + q.y});
+                    ends.push_back({v1.x + q.x, v1.y + q.y});
+                }
+                swept.push_back(manifold::CrossSection::Hull(ends));
+            }
+        }
+        manifold::CrossSection sum =
+            manifold::CrossSection::BatchBoolean(swept, manifold::OpType::Add);
+        parts.push_back(sum.Translate(shift));
+    }
+
+    if (parts.empty()) return manifold::CrossSection();
+    return manifold::CrossSection::BatchBoolean(parts, manifold::OpType::Add);
+}
+
+} // namespace
+
+// minkowski() over 3D bodies, or over 2D sections when that is what it
+// was given. 2D used to be dropped on the floor -- silently, so
+// `linear_extrude() minkowski() { square(); circle(); }` produced nothing
+// at all where the reference produces the rounded square you asked for.
 std::vector<ColoredBody> generateMinkowski(Evaluator& ev, const CSGParams&, const std::vector<std::unique_ptr<CSGNode>>& children,
                                             const oscad::ASTNode& node) {
     const std::vector<ColoredBody> bodies = flattenCsgTree(children);
     const RoleSplit split = splitByRole(bodies);
 
     std::vector<const ColoredBody*> bodies3d;
+    std::vector<const ColoredBody*> sections2d;
     for (const ColoredBody& c : split.foreground) {
         if (c.body) bodies3d.push_back(&c);
+        else if (c.section) sections2d.push_back(&c);
     }
 
     std::vector<ColoredBody> passthrough;
@@ -92,6 +204,24 @@ std::vector<ColoredBody> generateMinkowski(Evaluator& ev, const CSGParams&, cons
     passthrough.insert(passthrough.end(), split.showOnly.begin(), split.showOnly.end());
     passthrough.insert(passthrough.end(), split.displayOnly.begin(), split.displayOnly.end());
 
+    // 2D only: sum the sections instead. A mix of 2D and 3D is the
+    // reference's error case, and the 3D bodies win here as they do there.
+    if (bodies3d.empty() && sections2d.size() >= 2) {
+        manifold::CrossSection acc = *sections2d.front()->section;
+        for (size_t i = 1; i < sections2d.size(); ++i)
+            acc = minkowski2d(acc, *sections2d[i]->section);
+        ColoredBody cb;
+        cb.section = std::move(acc);
+        cb.color = sections2d.front()->color;
+        std::vector<ColoredBody> out = {std::move(cb)};
+        out.insert(out.end(), passthrough.begin(), passthrough.end());
+        return out;
+    }
+    if (bodies3d.empty() && sections2d.size() == 1) {
+        std::vector<ColoredBody> out = {*sections2d.front()};
+        out.insert(out.end(), passthrough.begin(), passthrough.end());
+        return out;
+    }
     if (bodies3d.empty()) return passthrough;
     if (bodies3d.size() == 1) {
         std::vector<ColoredBody> result = {*bodies3d.front()};

tests/test_booleans.cpp

@@ -317,3 +317,126 @@ TEST(PolyhedronFaces, ADegenerateFaceDoesNotThrowOrHang) {
     )");
     EXPECT_EQ(e.bodies.size(), 1u);
 }
+
+// -- 2D minkowski ---------------------------------------------------------
+
+// minkowski() used to drop 2D sections on the floor, silently: this
+// produced no geometry at all where the reference produces the rounded
+// square asked for. Manifold has no 2D Minkowski, so it is built from
+// convex pieces and hulls -- see minkowski2d().
+TEST(Minkowski2D, RoundsAConvexOutline) {
+    Evaluated e = evaluateSrc(
+        "linear_extrude(6) minkowski() { square([30,20], center=true); circle(4, $fn=24); }");
+    ASSERT_EQ(e.bodies.size(), 1u);
+    ASSERT_TRUE(e.bodies[0].body.has_value());
+    // A 30x20 rectangle grown by 4: the rectangle, four 4-wide sides, and
+    // the corners adding up to one circle. Times 6 high.
+    const double expected = (30.0 * 20.0 + 2 * 4 * (30 + 20) + M_PI * 16.0) * 6.0;
+    EXPECT_NEAR(e.bodies[0].body->Volume(), expected, expected * 0.01);
+    const manifold::Box box = e.bodies[0].body->BoundingBox();
+    EXPECT_NEAR(box.max.x - box.min.x, 38.0, 0.01);
+    EXPECT_NEAR(box.max.y - box.min.y, 28.0, 0.01);
+}
+
+// The case a hull cannot fake: a concave outline has to stay concave.
+TEST(Minkowski2D, KeepsAConcaveOutlineConcave) {
+    Evaluated e = evaluateSrc(R"(
+        linear_extrude(4) minkowski() {
+            polygon([[0,0],[40,0],[40,25],[22,25],[22,12],[0,12]]);
+            circle(3, $fn=16);
+        }
+    )");
+    ASSERT_EQ(e.bodies.size(), 1u);
+    const manifold::Box box = e.bodies[0].body->BoundingBox();
+    EXPECT_NEAR(box.max.x - box.min.x, 46.0, 0.2);
+    EXPECT_NEAR(box.max.y - box.min.y, 31.0, 0.2);
+    // The notch has to still be a notch. A volume bound is too blunt to
+    // say so -- hulling the pieces rather than unioning them lands within
+    // 1% of the right answer here -- so probe the hole itself: the L is
+    // missing the region x 0..22, y 12..25, and rounding by 3 does not
+    // reach anywhere near the middle of it.
+    // The probe has to sit inside what a hull WOULD cover and outside the
+    // real shape, or it proves nothing: the hull runs from (0,12) to
+    // (22,25), and the rounded L stops at y=15 for any x below 22.
+    const manifold::Manifold probe =
+        manifold::Manifold::Cube({1.0, 1.0, 8.0}).Translate({17.0, 17.0, -2.0});
+    EXPECT_TRUE((*e.bodies[0].body ^ probe).IsEmpty()) << "the notch was filled in";
+    // ...while somewhere solid is genuinely solid.
+    const manifold::Manifold inside =
+        manifold::Manifold::Cube({2.0, 2.0, 8.0}).Translate({30.0, 5.0, -2.0});
+    EXPECT_FALSE((*e.bodies[0].body ^ inside).IsEmpty());
+}
+
+TEST(Minkowski2D, OneSectionIsHandedBackUnchanged) {
+    Evaluated e = evaluateSrc("linear_extrude(3) minkowski() { square([10,10]); }");
+    ASSERT_EQ(e.bodies.size(), 1u);
+    EXPECT_NEAR(e.bodies[0].body->Volume(), 300.0, 1e-6);
+}
+
+TEST(Minkowski2D, ThreeDStillWorksAndStillWins) {
+    Evaluated a = evaluateSrc("minkowski() { cube([30,20,6], center=true); sphere(3, $fn=12); }");
+    ASSERT_EQ(a.bodies.size(), 1u);
+    EXPECT_GT(a.bodies[0].body->Volume(), 30.0 * 20.0 * 6.0);
+}
+
+// The edge sweep is only valid when the shape being swept is convex and
+// contains the origin, and when a third operand is folded rather than
+// unioned in. Each of these fails, by a measurable amount, if the
+// corresponding step is skipped -- so each is here on its own.
+
+TEST(Minkowski2D, SweepsAConcaveSweeperByItsConvexPieces) {
+    // Hulling the sweeper instead of decomposing it computes A (+) hull(B)
+    // and comes out at 5092 against the reference's 4992.
+    Evaluated e = evaluateSrc(R"(
+        linear_extrude(4) minkowski() {
+            polygon([[0,0],[40,0],[40,25],[22,25],[22,12],[0,12]]);
+            polygon([[0,0],[8,0],[8,8],[5,8],[5,3],[0,3]]);
+        }
+    )");
+    ASSERT_EQ(e.bodies.size(), 1u);
+    EXPECT_NEAR(e.bodies[0].body->Volume(), 4992.0, 5.0);
+}
+
+TEST(Minkowski2D, ASweeperAwayFromTheOriginStillLandsInTheRightPlace) {
+    // The identity unions A itself, which only holds when the sweeper
+    // contains the origin. Without shifting it there and back, the result
+    // keeps an untranslated copy of A and starts at x=0 instead of x=16.
+    Evaluated e = evaluateSrc(R"(
+        linear_extrude(4) minkowski() {
+            polygon([[0,0],[40,0],[40,25],[22,25],[22,12],[0,12]]);
+            translate([20,0]) circle(4, $fn=24);
+        }
+    )");
+    ASSERT_EQ(e.bodies.size(), 1u);
+    const manifold::Box box = e.bodies[0].body->BoundingBox();
+    EXPECT_NEAR(box.min.x, 16.0, 0.2);
+    EXPECT_NEAR(e.bodies[0].body->Volume(), 5120.47, 5.0);
+}
+
+TEST(Minkowski2D, ThreeOperandsAreSummedInTurnNotUnioned) {
+    // A (+) B (+) C, not A (+) (B union C) -- which would give 3711.
+    Evaluated e = evaluateSrc(
+        "linear_extrude(4) minkowski() { square([30,20], center=true);"
+        " circle(3, $fn=16); square([6,2], center=true); }");
+    ASSERT_EQ(e.bodies.size(), 1u);
+    EXPECT_NEAR(e.bodies[0].body->Volume(), 4670.21, 5.0);
+    const manifold::Box box = e.bodies[0].body->BoundingBox();
+    EXPECT_NEAR(box.max.x - box.min.x, 42.0, 0.2);
+}
+
+TEST(Minkowski2D, AShapeWithAHoleHasBothItsContoursSwept) {
+    // Only the boundary of the shape being swept along is walked, so a
+    // hole is not a special case -- it is another contour.
+    Evaluated e = evaluateSrc(R"(
+        linear_extrude(3) minkowski() {
+            difference() { square([40,30], center=true); circle(8, $fn=24); }
+            circle(2, $fn=16);
+        }
+    )");
+    ASSERT_EQ(e.bodies.size(), 1u);
+    EXPECT_NEAR(e.bodies[0].body->Volume(), 4141.98, 5.0);
+    // The hole shrinks by the sweep rather than filling in.
+    const manifold::Manifold probe =
+        manifold::Manifold::Cube({1.0, 1.0, 6.0}).Translate({-0.5, -0.5, -1.0});
+    EXPECT_TRUE((*e.bodies[0].body ^ probe).IsEmpty()) << "the hole was filled in";
+}