#  Copyright (c) 2020-2022, Manfred Moitzi
#  License: MIT License
import pytest
import math
from ezdxf.layouts import VirtualLayout
from ezdxf.math import Matrix44, OCS, Vec3, close_vectors
from ezdxf.path import (
    Path,
    bbox,
    precise_bbox,
    fit_paths_into_box,
    transform_paths,
    transform_paths_to_ocs,
    to_polylines3d,
    to_lines,
    to_lwpolylines,
    to_polylines2d,
    to_hatches,
    to_mpolygons,
    to_bsplines_and_vertices,
    to_splines_and_polylines,
    from_vertices,
    to_multi_path,
    single_paths,
    lines_to_curve3,
    lines_to_curve4,
    is_rectangular,
)
from ezdxf.path import make_path, Command
from ezdxf.entities import BoundaryPathType, EdgeType
from ezdxf.render import forms


class TestTransformPaths:
    def test_empty_paths(self):
        result = transform_paths([], Matrix44())
        assert len(result) == 0

    def test_start_point_only_paths(self):
        result = transform_paths([Path((1, 2, 3))], Matrix44())
        assert len(result) == 1
        assert len(result[0]) == 0
        assert result[0].start == (1, 2, 3)

    def test_transformation_is_executed(self):
        # Real transformation is just tested once, because Matrix44
        # transformation is tested in 605:
        result = transform_paths([Path((1, 2, 3))], Matrix44.translate(1, 1, 1))
        assert result[0].start == (2, 3, 4)

    def test_one_path_line_to(self):
        path = Path()
        path.line_to((1, 0))
        result = transform_paths([path], Matrix44())
        path0 = result[0]
        assert path0[0].type == Command.LINE_TO
        assert path0.start == (0, 0)
        assert path0.end == (1, 0)

    def test_one_path_curve3_to(self):
        path = Path()
        path.curve3_to((2, 0), (1, 1))
        result = transform_paths([path], Matrix44())
        path0 = result[0]
        assert path0[0].type == Command.CURVE3_TO
        assert len(path0[0]) == 2
        assert path0.start == (0, 0)
        assert path0.end == (2, 0)

    def test_one_path_curve4_to(self):
        path = Path()
        path.curve4_to((2, 0), (0, 1), (2, 1))
        result = transform_paths([path], Matrix44())
        path0 = result[0]
        assert path0[0].type == Command.CURVE4_TO
        assert len(path0[0]) == 3
        assert path0.start == (0, 0)
        assert path0.end == (2, 0)

    def test_one_path_multiple_command(self):
        path = Path()
        path.line_to((1, 0))
        path.curve3_to((2, 0), (2.5, 1))
        path.curve4_to((3, 0), (2, 1), (3, 1))
        result = transform_paths([path], Matrix44())

        path0 = result[0]
        assert path0[0].type == Command.LINE_TO
        assert path0[1].type == Command.CURVE3_TO
        assert path0[2].type == Command.CURVE4_TO
        assert path0.start == (0, 0)
        assert path0.end == (3, 0)

    def test_two_paths_one_command(self):
        path_a = Path()
        path_a.line_to((1, 0))
        path_b = Path((2, 0))
        path_b.line_to((3, 0))
        result = transform_paths([path_a, path_b], Matrix44())

        path0 = result[0]
        assert path0[0].type == Command.LINE_TO
        assert path0.start == (0, 0)
        assert path0.end == (1, 0)

        path1 = result[1]
        assert path1[0].type == Command.LINE_TO
        assert path1.start == (2, 0)
        assert path1.end == (3, 0)

    def test_two_paths_multiple_commands(self):
        path_a = Path()
        path_a.line_to((1, 0))
        path_a.curve3_to((2, 0), (2.5, 1))
        path_a.curve4_to((3, 0), (2, 1), (3, 1))

        path_b = path_a.transform(Matrix44.translate(4, 0, 0))
        result = transform_paths([path_a, path_b], Matrix44())

        path0 = result[0]
        assert path0[0].type == Command.LINE_TO
        assert path0[1].type == Command.CURVE3_TO
        assert path0[2].type == Command.CURVE4_TO
        assert path0.start == (0, 0)
        assert path0.end == (3, 0)

        path1 = result[1]
        assert path1[0].type == Command.LINE_TO
        assert path1[1].type == Command.CURVE3_TO
        assert path1[2].type == Command.CURVE4_TO
        assert path1.start == (4, 0)
        assert path1.end == (7, 0)

    def test_multi_path_objects(self):
        path = Path()
        path.line_to((1, 0, 0))
        path.move_to((2, 0, 0))
        paths = transform_paths([path], Matrix44.translate(0, 1, 0))
        assert len(paths) == 1
        path2 = paths[0]
        assert path2.start.isclose((0, 1, 0))
        assert len(path2) == 2
        assert path2.end.isclose((2, 1, 0))
        assert path2.has_sub_paths is True

    def test_to_ocs(self):
        p = Path((0, 1, 1))
        p.line_to((0, 1, 3))
        ocs = OCS((1, 0, 0))  # x-Axis
        result = list(transform_paths_to_ocs([p], ocs))
        p0 = result[0]
        assert ocs.from_wcs((0, 1, 1)) == p0.start
        assert ocs.from_wcs((0, 1, 3)) == p0[0].end


class TestPreciseBoundingBox:
    def test_empty_path(self):
        result = precise_bbox(Path())
        assert result.has_data is False

    def test_line_to(self):
        p = Path()
        p.line_to((1, 2, 3))
        result = precise_bbox(p)
        assert result.size == (1, 2, 3)

    def test_curve3_to(self):
        p = Path()
        p.curve3_to((2, 0), (1, 1))  # end, ctrl
        result = precise_bbox(p)
        assert result.extmax.y == pytest.approx(0.5)  # parabola

    def test_curve4_to(self):
        p = Path()
        p.curve4_to((2, 0), (0, 1), (2, 1))  # end, ctrl1, ctrl2
        result = precise_bbox(p)
        assert result.extmax.y == pytest.approx(0.75)

    def test_move_to(self):
        p = Path()
        p.line_to((1, 0, 0))
        p.move_to((1, 2, 3))
        p.line_to((1, 0, 0))
        result = precise_bbox(p)
        assert result.size == (1, 2, 3)


class TestBoundingBox:
    def test_empty_paths(self):
        result = bbox([])
        assert result.has_data is False

    def test_one_path(self):
        p = Path()
        p.line_to((1, 2, 3))
        assert bbox([p]).size == (1, 2, 3)

    def test_two_path(self):
        p1 = Path()
        p1.line_to((1, 2, 3))
        p2 = Path()
        p2.line_to((-3, -2, -1))
        assert bbox([p1, p2]).size == (4, 4, 4)

    @pytest.fixture(scope="class")
    def quadratic(self):
        p = Path()
        p.curve3_to((2, 0), (1, 1))
        return p

    def test_not_precise_box(self, quadratic):
        result = bbox([quadratic], fast=True)
        assert result.extmax.y == pytest.approx(1)  # control point

    def test_precise_box(self, quadratic):
        result = bbox([quadratic], fast=False)
        assert result.extmax.y == pytest.approx(0.5)  # parabola


class TestFitPathsIntoBoxUniformScaling:
    @pytest.fixture(scope="class")
    def spath(self):
        p = Path()
        p.line_to((1, 2, 3))
        return p

    def test_empty_paths(self):
        assert fit_paths_into_box([], (0, 0, 0)) == []

    def test_uniform_stretch_paths_limited_by_z(self, spath):
        result = fit_paths_into_box([spath], (6, 6, 6))
        box = bbox(result)
        assert box.size == (2, 4, 6)

    def test_uniform_stretch_paths_limited_by_y(self, spath):
        result = fit_paths_into_box([spath], (6, 3, 6))
        box = bbox(result)
        # stretch factor: 1.5
        assert box.size == (1.5, 3, 4.5)

    def test_uniform_stretch_paths_limited_by_x(self, spath):
        result = fit_paths_into_box([spath], (1.2, 6, 6))
        box = bbox(result)
        # stretch factor: 1.2
        assert box.size.isclose((1.2, 2.4, 3.6))

    def test_uniform_shrink_paths(self, spath):
        result = fit_paths_into_box([spath], (1.5, 1.5, 1.5))
        box = bbox(result)
        assert box.size.isclose((0.5, 1, 1.5))

    def test_project_into_xy(self, spath):
        result = fit_paths_into_box([spath], (6, 6, 0))
        box = bbox(result)
        # Note: z-axis is also ignored by extent detection:
        # scaling factor = 3x
        assert box.size.isclose((3, 6, 0)), "z-axis should be ignored"

    def test_project_into_xz(self, spath):
        result = fit_paths_into_box([spath], (6, 0, 6))
        box = bbox(result)
        assert box.size.isclose((2, 0, 6)), "y-axis should be ignored"

    def test_project_into_yz(self, spath):
        result = fit_paths_into_box([spath], (0, 6, 6))
        box = bbox(result)
        assert box.size.isclose((0, 4, 6)), "x-axis should be ignored"

    def test_invalid_target_size(self, spath):
        with pytest.raises(ValueError):
            fit_paths_into_box([spath], (0, 0, 0))


class TestFitPathsIntoBoxNonUniformScaling:
    @pytest.fixture(scope="class")
    def spath(self):
        p = Path()
        p.line_to((1, 2, 3))
        return p

    def test_non_uniform_stretch_paths(self, spath):
        result = fit_paths_into_box([spath], (8, 7, 6), uniform=False)
        box = bbox(result)
        assert box.size == (8, 7, 6)

    def test_non_uniform_shrink_paths(self, spath):
        result = fit_paths_into_box([spath], (1.5, 1.5, 1.5), uniform=False)
        box = bbox(result)
        assert box.size == (1.5, 1.5, 1.5)

    def test_project_into_xy(self, spath):
        result = fit_paths_into_box([spath], (6, 6, 0), uniform=False)
        box = bbox(result)
        assert box.size == (6, 6, 0), "z-axis should be ignored"

    def test_project_into_xz(self, spath):
        result = fit_paths_into_box([spath], (6, 0, 6), uniform=False)
        box = bbox(result)
        assert box.size == (6, 0, 6), "y-axis should be ignored"

    def test_project_into_yz(self, spath):
        result = fit_paths_into_box([spath], (0, 6, 6), uniform=False)
        box = bbox(result)
        assert box.size == (0, 6, 6), "x-axis should be ignored"


class TestPathToBsplineAndVertices:
    def test_empty_path(self):
        result = list(to_bsplines_and_vertices(Path()))
        assert result == []

    def test_only_vertices(self):
        p = from_vertices([(1, 0), (2, 0), (3, 1)])
        result = list(to_bsplines_and_vertices(p))
        assert len(result) == 1, "expected one list of vertices"
        assert len(result[0]) == 3, "expected 3 vertices"

    def test_one_quadratic_bezier(self):
        p = Path()
        p.curve3_to((4, 0), (2, 2))
        result = list(to_bsplines_and_vertices(p))
        assert len(result) == 1, "expected one B-spline"
        cpnts = result[0].control_points
        # A quadratic bezier should be converted to cubic bezier curve, which
        # has a precise cubic B-spline representation.
        assert len(cpnts) == 4, "expected 4 control vertices"
        assert cpnts[0] == (0, 0)
        assert cpnts[3] == (4, 0)

    def test_one_cubic_bezier(self):
        p = Path()
        p.curve4_to((4, 0), (1, 2), (3, 2))
        result = list(to_bsplines_and_vertices(p))
        assert len(result) == 1, "expected one B-spline"
        # cubic bezier curve maps 1:1 to cubic B-spline curve
        # see tests: 630b for the bezier_to_bspline() function

    def test_adjacent_cubic_beziers_with_G1_continuity(self):
        p = Path()
        p.curve4_to((4, 0), (1, 2), (3, 2))
        p.curve4_to((8, 0), (5, -2), (7, -2))
        result = list(to_bsplines_and_vertices(p))
        assert len(result) == 1, "expected one B-spline"
        # cubic bezier curve maps 1:1 to cubic B-spline curve
        # see tests: 630b for the bezier_to_bspline() function

    def test_adjacent_cubic_beziers_without_G1_continuity(self):
        p = Path()
        p.curve4_to((4, 0), (1, 2), (3, 2))
        p.curve4_to((8, 0), (5, 2), (7, 2))
        result = list(to_bsplines_and_vertices(p))
        assert len(result) == 2, "expected two B-splines"

    def test_multiple_segments(self):
        p = Path()
        p.curve4_to((4, 0), (1, 2), (3, 2))
        p.line_to((6, 0))
        p.curve3_to((8, 0), (7, 1))
        result = list(to_bsplines_and_vertices(p))
        assert len(result) == 3, "expected three segments"


class TestToEntityConverter:
    @pytest.fixture
    def path(self):
        p = Path()
        p.line_to((4, 0, 0))
        p.curve4_to((0, 0, 0), (3, 1, 1), (1, 1, 1))
        return p

    @pytest.fixture
    def path1(self):
        p = Path((0, 0, 1))
        p.curve4_to((4, 0, 1), (1, 1, 1), (3, 1, 1))
        return p

    def test_empty_to_polylines3d(self):
        assert list(to_polylines3d([])) == []

    def test_to_polylines3d(self, path):
        polylines = list(to_polylines3d(path))
        assert len(polylines) == 1
        p0 = polylines[0]
        assert p0.dxftype() == "POLYLINE"
        assert p0.is_3d_polyline is True
        assert len(p0) == 18
        assert p0.vertices[0].dxf.location == (0, 0, 0)
        assert p0.vertices[-1].dxf.location == (0, 0, 0)

    def test_empty_to_lines(self):
        assert list(to_lines([])) == []

    def test_to_lines(self, path):
        lines = list(to_lines(path))
        assert len(lines) == 17
        l0 = lines[0]
        assert l0.dxftype() == "LINE"
        assert l0.dxf.start == (0, 0, 0)
        assert l0.dxf.end == (4, 0, 0)

    def test_empty_to_lwpolyline(self):
        assert list(to_lwpolylines([])) == []

    def test_empty_path_to_lwpolyline(self):
        assert list(to_lwpolylines([Path()])) == []

    def test_to_lwpolylines(self, path):
        polylines = list(to_lwpolylines(path))
        assert len(polylines) == 1
        p0 = polylines[0]
        assert p0.dxftype() == "LWPOLYLINE"
        assert p0[0] == (0, 0, 0, 0, 0)  # x, y, swidth, ewidth, bulge
        assert p0[-1] == (0, 0, 0, 0, 0)

    def test_to_lwpolylines_with_wcs_elevation(self, path1):
        polylines = list(to_lwpolylines(path1))
        p0 = polylines[0]
        assert p0.dxf.elevation == 1

    def test_to_lwpolylines_with_ocs(self, path1):
        m = Matrix44.x_rotate(math.pi / 4)
        path = path1.transform(m)
        extrusion = m.transform((0, 0, 1))
        polylines = list(to_lwpolylines(path, extrusion=extrusion))
        p0 = polylines[0]
        assert p0.dxf.elevation == pytest.approx(1)
        assert p0.dxf.extrusion.isclose(extrusion)
        assert (
            all(
                math.isclose(a, b, abs_tol=1e-12)
                for a, b in zip(p0[0], (0, 0, 0, 0, 0))
            )
            is True
        )
        assert (
            all(
                math.isclose(a, b, abs_tol=1e-12)
                for a, b in zip(p0[-1], (4, 0, 0, 0, 0))
            )
            is True
        )

    def test_multi_path_to_lwpolylines(self):
        path = Path()
        path.line_to((1, 0, 0))
        path.move_to((2, 0, 0))
        path.line_to((3, 0, 0))
        polylines = list(to_lwpolylines(path))
        assert len(polylines) == 2
        assert len(polylines[0]) == 2
        assert len(polylines[1]) == 2

    def test_empty_to_polylines2d(self):
        assert list(to_polylines2d([])) == []

    def test_to_polylines2d(self, path):
        polylines = list(to_polylines2d(path))
        assert len(polylines) == 1
        p0 = polylines[0]
        assert p0.dxftype() == "POLYLINE"
        assert p0.is_2d_polyline is True
        assert p0[0].dxf.location == (0, 0, 0)
        assert p0[-1].dxf.location == (0, 0, 0)

    def test_to_polylines2d_with_wcs_elevation(self, path1):
        polylines = list(to_polylines2d(path1))
        p0 = polylines[0]
        assert p0.dxf.elevation == (0, 0, 1)

    def test_to_polylines2d_with_ocs(self, path1):
        m = Matrix44.x_rotate(math.pi / 4)
        path = path1.transform(m)
        extrusion = m.transform((0, 0, 1))
        polylines = list(to_polylines2d(path, extrusion=extrusion))
        p0 = polylines[0]
        assert p0.dxf.elevation.isclose((0, 0, 1))
        assert p0.dxf.extrusion.isclose(extrusion)
        assert p0[0].dxf.location.isclose((0, 0, 1))
        assert p0[-1].dxf.location.isclose((4, 0, 1))

    def test_empty_to_hatches(self):
        assert list(to_hatches([])) == []

    def test_to_poly_path_hatches(self, path):
        hatches = list(to_hatches(path, edge_path=False))
        assert len(hatches) == 1
        h0 = hatches[0]
        assert h0.dxftype() == "HATCH"
        assert len(h0.paths) == 1

    def test_to_poly_path_hatches_with_wcs_elevation(self, path1):
        hatches = list(to_hatches(path1, edge_path=False))
        ho = hatches[0]
        assert ho.dxf.elevation.isclose((0, 0, 1))

    def test_to_poly_path_hatches_with_ocs(self, path1):
        m = Matrix44.x_rotate(math.pi / 4)
        path = path1.transform(m)
        extrusion = m.transform((0, 0, 1))
        hatches = list(to_hatches(path, edge_path=False, extrusion=extrusion))
        h0 = hatches[0]
        assert h0.dxf.elevation.isclose((0, 0, 1))
        assert h0.dxf.extrusion.isclose(extrusion)
        polypath0 = h0.paths[0]
        assert (
            all(abs(a) < 1e-12 for a in polypath0.vertices[0])
            is True  # ~(0, 0, 0)
        )  # x, y, bulge
        assert (
            all(abs(a) < 1e-12 for a in polypath0.vertices[-1])
            is True  # ~(0, 0, 0)
        ), "should be closed automatically"

    def test_to_edge_path_hatches(self, path):
        hatches = list(to_hatches(path, edge_path=True))
        assert len(hatches) == 1
        h0 = hatches[0]
        assert h0.dxftype() == "HATCH"
        assert len(h0.paths) == 1
        edge_path = h0.paths[0]
        assert edge_path.type == BoundaryPathType.EDGE
        line, spline = edge_path.edges
        assert line.type == EdgeType.LINE
        assert line.start == (0, 0)
        assert line.end == (4, 0)
        assert spline.type == EdgeType.SPLINE
        assert close_vectors(
            Vec3.generate(spline.control_points),
            [(4, 0), (3, 1), (1, 1), (0, 0)],
        )

    def test_to_splines_and_polylines(self, path):
        entities = list(to_splines_and_polylines([path]))
        assert len(entities) == 2
        polyline = entities[0]
        spline = entities[1]
        assert polyline.dxftype() == "POLYLINE"
        assert spline.dxftype() == "SPLINE"
        assert polyline.vertices[0].dxf.location.isclose((0, 0))
        assert polyline.vertices[1].dxf.location.isclose((4, 0))
        assert close_vectors(
            Vec3.generate(spline.control_points),
            [(4, 0, 0), (3, 1, 1), (1, 1, 1), (0, 0, 0)],
        )

    def test_to_mpolygons_returns_expected_dxf_type(self, path):
        # Works internally like to_hatches() but with polyline paths
        # as boundaries only.
        polygons = list(
            to_mpolygons(
                path,
                dxfattribs={
                    "color": 6,  # boundary line color
                    "fill_color": 1,
                },
            )
        )
        assert len(polygons) == 1
        mp = polygons[0]
        assert mp.dxftype() == "MPOLYGON"
        assert len(mp.paths) == 1
        assert mp.dxf.color == 6
        assert mp.dxf.fill_color == 1


# Issue #224 regression test
@pytest.fixture
def ellipse():
    layout = VirtualLayout()
    return layout.add_ellipse(
        center=(1999.488177113287, -1598.02265357955, 0.0),
        major_axis=(629.968069297, 0.0, 0.0),
        ratio=0.495263197,
        start_param=-1.261396328799999,
        end_param=-0.2505454928,
        dxfattribs={
            "layer": "0",
            "linetype": "Continuous",
            "color": 3,
            "extrusion": (0.0, 0.0, -1.0),
        },
    )


def test_to_multi_path():
    p0 = Path((1, 0, 0))
    p0.line_to((2, 0, 0))
    p0.move_to((3, 0, 0))  # will be replaced by move_to(4, 0, 0)
    p1 = Path((4, 0, 0))
    p1.line_to((5, 0, 0))
    p1.move_to((6, 0, 0))
    path = to_multi_path([p0, p1])
    assert path.has_sub_paths is True
    assert path.start == (1, 0, 0)
    assert path.end == (6, 0, 0)
    assert path[1].type == Command.MOVE_TO
    assert path[1].end == (4, 0, 0)


def test_to_multi_path_ignores_empty_paths():
    p0 = Path((1, 0, 0))
    p0.line_to((2, 0, 0))
    empty = Path((100, 0, 0))
    path = to_multi_path([p0, empty])
    assert len(path) == 1
    assert path.has_sub_paths is False
    assert path.end.isclose((2, 0, 0))


def test_single_paths_from_a_single_path_object():
    p = Path((1, 0, 0))
    assert len(list(single_paths([p]))) == 1


def test_single_paths_from_a_multi_path_object():
    p = Path((1, 0, 0))
    p.line_to((2, 0, 0))  # 1st sub-path
    p.move_to((3, 0, 0))  # 2nd sub-path
    p.line_to((4, 0, 0))
    p.move_to((5, 0, 0))  # 3rd sub-path
    paths = list(single_paths([p]))
    assert len(paths) == 3


def test_issue_224_end_points(ellipse):
    p = make_path(ellipse)

    assert ellipse.start_point.isclose(p.start)
    assert ellipse.end_point.isclose(p.end)

    # end point locations measured in BricsCAD:
    assert ellipse.start_point.isclose((2191.3054, -1300.8375), abs_tol=1e-4)
    assert ellipse.end_point.isclose((2609.7870, -1520.6677), abs_tol=1e-4)


def test_issue_494_make_path_from_spline_defined_by_fit_points_and_tangents():
    from ezdxf.entities import Spline

    spline = Spline.new(
        dxfattribs={
            "degree": 3,
            "start_tangent": (0.9920663924871818, 0.1257150464243202, 0.0),
            "end_tangent": (0.9999448476387669, -0.0105024606965807, 0.0),
        },
    )
    spline.fit_points = [
        (209.5080107190219, 206.963463282597, 0.0),
        (209.55254921431026, 206.96662062623636, 0.0),
    ]
    p = make_path(spline)
    assert len(p) > 0


class TestAllLinesToCurveConverter:
    def test_create_a_curve3_command(self):
        path = Path()
        path.line_to((1, 0))
        path = lines_to_curve3(path)
        assert path[0].type == Command.CURVE3_TO

    def test_create_a_curve4_command(self):
        path = Path()
        path.line_to((1, 0))
        path = lines_to_curve4(path)
        assert path[0].type == Command.CURVE4_TO

    @pytest.mark.parametrize(
        "func",
        [
            lines_to_curve3,
            lines_to_curve4,
        ],
    )
    def test_line_to_curve_creates_a_linear_segment(self, func):
        v1, v2 = 1, 2
        path = Path(start=(v1, v1, v1))
        path.line_to((v2, v2, v2))
        path = func(path)
        vertices = list(path.flattening(1))
        assert len(vertices) > 2
        assert all(
            [
                math.isclose(v.x, v.y) and math.isclose(v.x, v.z)
                for v in vertices
            ]
        ), "all vertices have to be located along a line (x == y == z)"

    def test_remove_line_segments_of_zero_length_at_the_start(self):
        # CURVE3_TO and CURVE4_TO can not process zero length segments
        path = Path()
        path.line_to((0, 0))  # line segment of length==0 should be removed
        path.line_to((1, 0))
        path = lines_to_curve4(path)
        assert len(path) == 1
        assert path.start == (0, 0)
        assert path[0].type == Command.CURVE4_TO
        assert path[0].end == (1, 0)

    def test_remove_line_segments_of_zero_length_between_commands(self):
        # CURVE3_TO and CURVE4_TO can not process zero length segments
        path = Path()
        path.line_to((1, 0))
        path.line_to((1, 0))  # line segment of length==0 should be removed
        path.line_to((2, 0))
        path = lines_to_curve4(path)
        assert len(path) == 2
        assert path.start == (0, 0)
        assert path[0].type == Command.CURVE4_TO
        assert path[0].end == (1, 0)
        assert path[1].type == Command.CURVE4_TO
        assert path[1].end == (2, 0)

    def test_remove_line_segments_of_zero_length_at_the_end(self):
        # CURVE3_TO and CURVE4_TO can not process zero length segments
        path = Path()
        path.line_to((1, 0))
        path.line_to((1, 0))  # line segment of length==0 should be removed
        path = lines_to_curve4(path)
        assert len(path) == 1
        assert path.start == (0, 0)
        assert path[0].type == Command.CURVE4_TO
        assert path[0].end == (1, 0)

    def test_does_not_remove_a_line_representing_a_single_point(self):
        path = Path((1, 0))
        path.line_to((1, 0))  # represents the point (1, 0)
        path = lines_to_curve4(path)
        assert len(path) == 1
        assert path[0].type == Command.LINE_TO

    @pytest.mark.parametrize(
        "start,delta",
        [
            (0, 1e-11),  # uses absolute tolerance of 1e-12 near zero!
            (10, 1e-8),  # uses relative tolerance of 1e-9 away from zero!
        ],
    )
    def test_for_very_short_line_segments(self, start, delta):
        path = Path((start, 0, 0))
        path.line_to((start + delta, 0, 0))
        path = lines_to_curve4(path)
        assert len(path) == 1
        assert path[0].type == Command.CURVE4_TO
        assert len(list(path.flattening(1))) > 3

    @pytest.mark.parametrize(
        "start,delta",
        [
            (0, 1e-12),  # uses absolute tolerance of 1e-12 near zero!
            (10, 1e-9),  # uses relative tolerance of 1e-9 away from zero!
        ],
    )
    def test_which_length_is_too_short_to_create_a_curve(self, start, delta):
        path = Path((start, 0, 0))
        path.line_to((start + delta, 0, 0))
        path = lines_to_curve4(path)
        assert len(path) == 1
        assert (
            path[0].type == Command.LINE_TO
        ), "should not remove a single line segment representing a point"
        assert len(list(path.flattening(1))) == 2


class TestIsRectangular:
    def test_empty_path(self):
        assert is_rectangular(Path()) is False

    def test_less_than_four_corners(self):
        p = from_vertices([(0, 0), (1, 0), (1, 1)])
        assert is_rectangular(p) is False

    def test_open_square(self):
        p = from_vertices([(0, 0), (1, 0), (1, 1), (0, 1)])
        assert is_rectangular(p) is True

    def test_closed_square(self):
        p = from_vertices([(0, 0), (1, 0), (1, 1), (0, 1), (0, 0)])
        assert is_rectangular(p) is True

    def test_rectangle(self):
        p = from_vertices([(0, 0), (2, 0), (2, 1), (0, 1)])
        assert is_rectangular(p) is True

    def test_parallelogram(self):
        p = from_vertices([(0, 0), (2, 0), (3, 1), (1, 1)])
        assert is_rectangular(p) is False

    def test_non_aligned_square(self):
        p = from_vertices(forms.rotate(forms.square(2), 30))
        assert is_rectangular(p, aligned=False) is True
