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https://github.com/OrcaSlicer/OrcaSlicer.git
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Fix scale and mirror of rotated mirrored objects (#16131)
* Fix decomposition of mirrored transformations computeRotationScaling() may place the mirror on any axis, giving unstable rotation/scale for mirrored matrices. Decompose them by flipping each local axis and choosing the one needing the least rotation (lowest axis on ties). Merge the extract helpers into a single extract_rotation_scale() and simplify contains_skew() to check that the scale is diagonal. set_scaling_factor() now preserves the mirror sign on the scaled axis. Selection::scale_and_translate() uses Transformation's rotation and scale instead of calling computeRotationScaling() directly, so scaling a mirrored instance adds no skew. Add tests for mirrored decomposition, scaling, and skew detection. * Use Eigen polar decomposition for instance scaling Selection::scale_and_translate now splits the instance matrix with computeRotationScaling instead of get_rotation_matrix(). Adds a Model test checking that an instance created from another's offset, scale, rotation and mirror reproduces its matrix (as Add instance and Fill bed do). * tidy
This commit is contained in:
Ian Bassi
+31
-41
@@ -428,55 +428,44 @@ Transform3d Transformation::get_offset_matrix() const
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return translation_transform(get_offset());
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}
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static Transform3d extract_rotation_matrix(const Transform3d& trafo)
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{
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Matrix3d rotation;
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Matrix3d scale;
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trafo.computeRotationScaling(&rotation, &scale);
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return Transform3d(rotation);
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}
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static Transform3d extract_scale(const Transform3d& trafo)
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{
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Matrix3d rotation;
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Matrix3d scale;
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trafo.computeRotationScaling(&rotation, &scale);
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return Transform3d(scale);
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}
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// computeRotationScaling() may put a mirror on any axis; use the local axis needing the least rotation.
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static std::pair<Transform3d, Transform3d> extract_rotation_scale(const Transform3d& trafo)
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{
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Matrix3d rotation;
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Matrix3d scale;
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trafo.computeRotationScaling(&rotation, &scale);
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if (trafo.linear().determinant() >= 0.0) {
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trafo.computeRotationScaling(&rotation, &scale);
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return { Transform3d(rotation), Transform3d(scale) };
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}
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for (int axis = 0; axis < 3; ++axis) {
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Transform3d flipped = trafo;
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flipped.linear().col(axis) *= -1.0;
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Matrix3d r;
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Matrix3d s;
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flipped.computeRotationScaling(&r, &s);
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// EPSILON keeps the lowest axis on ties, e.g. a mirror rotated by 90 degrees.
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if (axis == 0 || r.trace() > rotation.trace() + EPSILON) {
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rotation = r;
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scale = s;
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scale.col(axis) *= -1.0;
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}
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}
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return { Transform3d(rotation), Transform3d(scale) };
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}
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static Transform3d extract_rotation_matrix(const Transform3d& trafo)
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{
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return extract_rotation_scale(trafo).first;
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}
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static Transform3d extract_scale(const Transform3d& trafo)
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{
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return extract_rotation_scale(trafo).second;
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}
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static bool contains_skew(const Transform3d& trafo)
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{
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Matrix3d rotation;
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Matrix3d scale;
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trafo.computeRotationScaling(&rotation, &scale);
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if (scale.isDiagonal())
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return false;
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if (scale.determinant() >= 0.0)
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return true;
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// the matrix contains mirror
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const Matrix3d ratio = scale.cwiseQuotient(trafo.matrix().block<3,3>(0,0));
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auto check_skew = [&ratio](int i, int j, bool& skew) {
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if (!std::isnan(ratio(i, j)) && !std::isnan(ratio(j, i)))
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skew |= std::abs(ratio(i, j) * ratio(j, i) - 1.0) > EPSILON;
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};
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bool has_skew = false;
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check_skew(0, 1, has_skew);
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check_skew(0, 2, has_skew);
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check_skew(1, 2, has_skew);
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return has_skew;
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return !extract_scale(trafo).linear().isDiagonal();
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}
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Vec3d Transformation::get_rotation() const
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@@ -550,7 +539,8 @@ void Transformation::set_scaling_factor(Axis axis, double scaling_factor)
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assert(scaling_factor > 0.0);
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auto [rotation, scale] = extract_rotation_scale(m_matrix);
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scale(axis, axis) = scaling_factor;
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// Keep a mirror that sits on this axis.
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scale(axis, axis) = std::copysign(scaling_factor, scale(axis, axis));
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const Vec3d offset = get_offset();
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m_matrix = rotation * scale;
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@@ -3,6 +3,10 @@
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#include <catch2/catch_test_macros.hpp>
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#include <catch2/catch_message.hpp>
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#include <catch2/generators/catch_generators.hpp>
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#include <catch2/generators/catch_generators_range.hpp>
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#include <catch2/matchers/catch_matchers.hpp>
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#include <catch2/matchers/catch_matchers_floating_point.hpp>
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#include "libslic3r/Point.hpp"
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#include "libslic3r/BoundingBox.hpp"
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#include "libslic3r/Polygon.hpp"
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@@ -758,3 +762,118 @@ TEST_CASE("Convex polygon intersection test prusa polygons", "[Geometry][Rotcali
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REQUIRE(res == ref);
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}
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}
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namespace {
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// Scale on the local axes, with a mirror on `mirror_axis`, then rotation.
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Transform3d mirrored_transform(const Matrix3d &rotation, const Vec3d &scale, int mirror_axis)
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{
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Vec3d signed_scale = scale;
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signed_scale[mirror_axis] = -signed_scale[mirror_axis];
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Transform3d trafo = Transform3d::Identity();
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trafo.linear() = rotation * signed_scale.asDiagonal();
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return trafo;
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}
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const std::vector<Matrix3d> &test_rotations()
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{
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static const std::vector<Matrix3d> rotations = {
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Matrix3d::Identity(),
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Eigen::AngleAxisd(0.5 * PI, Vec3d::UnitZ()).toRotationMatrix(),
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Eigen::AngleAxisd(0.7, Vec3d(1., 2., 3.).normalized()).toRotationMatrix(),
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Eigen::AngleAxisd(2.5, Vec3d(-1., 0.5, 2.).normalized()).toRotationMatrix(),
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};
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return rotations;
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}
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} // namespace
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TEST_CASE("Mirrored transformations decompose into a rotation and a diagonal scale", "[Geometry]")
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{
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const size_t rotation_idx = GENERATE(range(size_t(0), test_rotations().size()));
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const int mirror_axis = GENERATE(0, 1, 2);
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const Vec3d scale = GENERATE(Vec3d(1., 1., 1.), Vec3d(2., 2., 2.), Vec3d(1., 1., 3.), Vec3d(1., 2., 3.));
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CAPTURE(rotation_idx, mirror_axis, scale.transpose());
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const Geometry::Transformation trafo(mirrored_transform(test_rotations()[rotation_idx], scale, mirror_axis));
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const Vec3d scaling = trafo.get_scaling_factor();
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const Vec3d mirror = trafo.get_mirror();
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for (int i = 0; i < 3; ++i) {
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CHECK_THAT(scaling[i], Catch::Matchers::WithinAbs(scale[i], 1e-9));
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CHECK_THAT(std::abs(mirror[i]), Catch::Matchers::WithinAbs(1., 1e-12));
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}
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CHECK_THAT(mirror.prod(), Catch::Matchers::WithinAbs(-1., 1e-12));
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CHECK_FALSE(trafo.has_skew());
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const bool uniform = scale.x() == scale.y() && scale.y() == scale.z();
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CHECK(trafo.is_scaling_uniform() == uniform);
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const Matrix3d rotation = trafo.get_rotation_matrix().linear();
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CHECK_THAT(rotation.determinant(), Catch::Matchers::WithinAbs(1., 1e-9));
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const Matrix3d rebuilt = rotation * trafo.get_scaling_factor_matrix().linear() * trafo.get_mirror_matrix().linear();
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CHECK(rebuilt.isApprox(trafo.get_matrix().linear(), 1e-9));
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}
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TEST_CASE("An unrotated mirror keeps its axis and needs no rotation", "[Geometry]")
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{
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const int mirror_axis = GENERATE(0, 1, 2);
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const Vec3d scale = GENERATE(Vec3d(1., 1., 1.), Vec3d(1., 2., 3.));
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CAPTURE(mirror_axis, scale.transpose());
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const Geometry::Transformation trafo(mirrored_transform(Matrix3d::Identity(), scale, mirror_axis));
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const Vec3d mirror = trafo.get_mirror();
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for (int i = 0; i < 3; ++i)
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CHECK_THAT(mirror[i], Catch::Matchers::WithinAbs(i == mirror_axis ? -1. : 1., 1e-12));
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CHECK(trafo.get_rotation().isZero(1e-9));
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}
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TEST_CASE("A mirrored and rotated transformation at unit scale reports unit scales", "[Geometry]")
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{
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// Valid mirrored instance transform as stored in a 3MF project.
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Transform3d matrix = Transform3d::Identity();
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matrix.linear() << 4.4408921e-16, 0.819152044, 0.573576436,
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1.0, -4.4408921e-16, -1.11022302e-16,
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-5.55111512e-17, -0.573576436, 0.819152044;
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const Geometry::Transformation trafo(matrix);
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CHECK(trafo.get_scaling_factor().isApprox(Vec3d::Ones(), 1e-8));
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CHECK(trafo.get_mirror().allFinite());
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CHECK(trafo.is_scaling_uniform());
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}
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TEST_CASE("Scaling one axis of a mirrored transformation keeps the mirror and adds no skew", "[Geometry]")
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{
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const size_t rotation_idx = GENERATE(range(size_t(0), test_rotations().size()));
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const int mirror_axis = GENERATE(0, 1, 2);
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const int scaled_axis = GENERATE(0, 1, 2);
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CAPTURE(rotation_idx, mirror_axis, scaled_axis);
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const Matrix3d &rotation = test_rotations()[rotation_idx];
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Geometry::Transformation trafo(mirrored_transform(rotation, Vec3d::Ones(), mirror_axis));
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trafo.set_scaling_factor(Axis(scaled_axis), 2.);
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Vec3d expected_scale = Vec3d::Ones();
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expected_scale[scaled_axis] = 2.;
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CHECK(trafo.get_matrix().linear().isApprox(mirrored_transform(rotation, expected_scale, mirror_axis).linear(), 1e-9));
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CHECK(trafo.is_left_handed());
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CHECK_FALSE(trafo.has_skew());
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}
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TEST_CASE("Transformations without a mirror decompose as computeRotationScaling() does", "[Geometry]")
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{
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Transform3d skewed = Transform3d::Identity();
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skewed.linear() << 1., 0.3, 0.,
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0., 1., 0.,
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0., 0., 2.;
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const Transform3d matrix = GENERATE_COPY(Transform3d(test_rotations()[2]) * Geometry::scale_transform(Vec3d(1., 2., 3.)),
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Transform3d(test_rotations()[3]) * skewed);
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Matrix3d rotation;
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Matrix3d scale;
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matrix.computeRotationScaling(&rotation, &scale);
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const Geometry::Transformation trafo(matrix);
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CHECK(trafo.get_rotation_matrix().linear() == rotation);
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CHECK(trafo.has_skew() == !scale.isDiagonal());
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}
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TEST_CASE("Skew is detected with and without a mirror", "[Geometry]")
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{
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Transform3d skewed = Transform3d::Identity();
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skewed.linear() << 1., 0.3, 0.,
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0., 1., 0.,
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0., 0., 1.;
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const bool mirrored = GENERATE(false, true);
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const Transform3d matrix = Transform3d(test_rotations()[2]) * skewed * Geometry::scale_transform(Vec3d(mirrored ? -1. : 1., 1., 1.));
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CHECK(Geometry::Transformation(matrix).has_skew());
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}
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@@ -8,10 +8,13 @@
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#include "libslic3r/Point.hpp"
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#include <catch2/catch_test_macros.hpp>
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#include <catch2/catch_message.hpp>
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#include <catch2/generators/catch_generators.hpp>
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#include <catch2/matchers/catch_matchers.hpp>
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#include <catch2/matchers/catch_matchers_floating_point.hpp>
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#include "libslic3r/Model.hpp"
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#include "libslic3r/Geometry.hpp"
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#include "libslic3r/libslic3r.h"
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using namespace Slic3r;
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@@ -71,3 +74,26 @@ TEST_CASE("An object's raw mesh keeps the triangles of each part on its own vert
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CHECK_THAT(min_x.front(), Catch::Matchers::WithinAbs(0., 1e-4));
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CHECK_THAT(min_x.back(), Catch::Matchers::WithinAbs(30., 1e-4));
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}
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TEST_CASE("An instance added from another's scale, rotation and mirror matches it", "[Model]")
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{
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// Add instance and Fill bed copy an instance this way.
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const int case_idx = GENERATE(0, 1);
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Transform3d trafo = Transform3d::Identity();
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if (case_idx == 0)
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trafo.linear() = Eigen::AngleAxisd(0.5 * PI, Vec3d::UnitZ()).toRotationMatrix() * Vec3d(-1., 1., 1.).asDiagonal();
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else
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trafo.linear() << 4.4408921e-16, 0.819152044, 0.573576436,
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1.0, -4.4408921e-16, -1.11022302e-16,
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-5.55111512e-17, -0.573576436, 0.819152044;
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CAPTURE(case_idx);
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Model model;
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ModelObject *object = model.add_object();
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object->add_volume(make_cube(10, 20, 30));
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ModelInstance *original = object->add_instance();
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original->set_transformation(Geometry::Transformation(trafo));
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const ModelInstance *copy = object->add_instance(original->get_offset(), original->get_scaling_factor(),
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original->get_rotation(), original->get_mirror());
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CHECK(copy->get_matrix().linear().isApprox(original->get_matrix().linear(), 1e-9));
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}
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