masque/test/test_utils.py

@@ -5,17 +5,9 @@ from numpy.testing import assert_equal, assert_allclose
 from numpy import pi
 import pytest
 
-from ..utils import (
+from ..utils import remove_duplicate_vertices, remove_colinear_vertices, poly_contains_points, rotation_matrix_2d, apply_transforms, normalize_mirror, DeferredDict
-    DeferredDict,
-    apply_transforms,
-    normalize_mirror,
-    poly_contains_points,
-    remove_colinear_vertices,
-    remove_duplicate_vertices,
-    rotation_matrix_2d,
-)
 from ..file.utils import tmpfile
-from ..utils.curves import bezier, circular_arc, euler_bend, euler_spiral
+from ..utils.curves import bezier
 from ..error import PatternError
 
 
@@ -31,23 +23,6 @@ def test_remove_duplicate_vertices() -> None:
     assert_equal(v_clean_open, [[0, 0], [1, 1], [2, 2], [0, 0]])
 
 
-def test_remove_duplicate_vertices_tolerance_defaults_to_exact_match() -> None:
-    v = [[0, 0], [1, 1], [1 + 1e-13, 1], [2, 2], [1e-13, 0]]
-
-    assert_allclose(remove_duplicate_vertices(v, closed_path=True), v, atol=0, rtol=0)
-    assert_allclose(
-        remove_duplicate_vertices(v, closed_path=True, tolerance=1e-12),
-        [[0, 0], [1 + 1e-13, 1], [2, 2]],
-        atol=0,
-        rtol=0,
-        )
-
-
-def test_remove_duplicate_vertices_rejects_negative_tolerance() -> None:
-    with pytest.raises(ValueError, match='non-negative'):
-        remove_duplicate_vertices([[0, 0]], tolerance=-1)
-
-
 def test_remove_colinear_vertices() -> None:
     v = [[0, 0], [1, 0], [2, 0], [2, 1], [2, 2], [1, 1], [0, 0]]
     v_clean = remove_colinear_vertices(v, closed_path=True)
@@ -148,53 +123,6 @@ def test_bezier_accepts_exact_weight_count() -> None:
     assert_allclose(samples, [[0, 0], [2 / 3, 2 / 3], [1, 1]], atol=1e-10)
 
 
-def _endpoint_tangent(xy: numpy.ndarray) -> float:
-    dxy = xy[-1] - xy[-2]
-    return numpy.arctan2(dxy[1], dxy[0])
-
-
-@pytest.mark.parametrize(
-    ('switchover_angle', 'total_angle'),
-    [
-        (pi / 8, pi / 4),
-        (pi / 8, pi / 2),
-        (pi / 4, pi),
-    ],
-    )
-def test_euler_bend_supports_total_angle(switchover_angle: float, total_angle: float) -> None:
-    xy = euler_bend(switchover_angle, num_points=2000, total_angle=total_angle)
-
-    assert_allclose(xy[0], [0, 0], atol=1e-12)
-    assert_allclose(_endpoint_tangent(xy), -total_angle, atol=1e-3)
-
-
-def test_euler_bend_180_degrees_with_90_degree_circular_middle() -> None:
-    xy = euler_bend(pi / 4, num_points=2000, total_angle=pi)
-
-    assert_allclose(_endpoint_tangent(xy), -pi, atol=1e-3)
-    assert abs(xy[-1][0]) < 1e-3
-    assert xy[-1][1] < 0
-
-
-def test_euler_bend_rejects_too_large_switchover_angle() -> None:
-    with pytest.raises(PatternError, match='total_angle / 2'):
-        euler_bend(pi / 2, total_angle=pi / 2)
-
-
-def test_euler_spiral_and_circular_arc_helpers_match_endpoint_tangent() -> None:
-    xy_spiral = euler_spiral(pi / 4, num_points=1000)
-    assert_allclose(_endpoint_tangent(xy_spiral), -pi / 4, atol=1e-3)
-
-    xy_arc = circular_arc(
-        10,
-        pi / 2,
-        num_points=1000,
-        start_angle=_endpoint_tangent(xy_spiral),
-        start=xy_spiral[-1],
-        )
-    assert_allclose(_endpoint_tangent(xy_arc), -3 * pi / 4, atol=2e-3)
-
-
 def test_deferred_dict_accessors_resolve_values_once() -> None:
     calls = 0
 

masque/utils/curves.py

@@ -3,7 +3,11 @@ from numpy.typing import ArrayLike, NDArray
 from numpy import pi
 
 from ..error import PatternError
-from .vertices import remove_duplicate_vertices
+
+try:
+    from numpy import trapezoid
+except ImportError:
+    from numpy import trapz as trapezoid        # type:ignore
 
 
 def bezier(
@@ -49,196 +53,70 @@ def bezier(
     return qq
 
 
-def _integrate_tangent(
-        qq: NDArray[numpy.float64],
-        theta: NDArray[numpy.float64],
-        num_points: int,
-        ) -> NDArray[numpy.float64]:
-    dx = numpy.cos(theta)
-    dy = numpy.sin(theta)
-
-    dq = qq[-1] / (qq.size - 1)
-    ix = numpy.zeros(qq.size)
-    iy = numpy.zeros(qq.size)
-    ix[1:] = numpy.cumsum((dx[:-1] + dx[1:]) / 2) * dq
-    iy[1:] = numpy.cumsum((dy[:-1] + dy[1:]) / 2) * dq
-
-    qq_target = numpy.linspace(0, qq[-1], num_points)
-    x_target = numpy.interp(qq_target, qq, ix)
-    y_target = numpy.interp(qq_target, qq, iy)
-
-    return numpy.stack((x_target, y_target), axis=1)
-
-
-def euler_spiral(
-        switchover_angle: float,
-        num_points: int = 200,
-        *,
-        start_angle: float = 0.0,
-        start: ArrayLike = (0.0, 0.0),
-        reverse: bool = False,
-        ) -> NDArray[numpy.float64]:
-    """
-    Generate one Euler bend transition segment.
-
-    Positive angles bend clockwise, matching `euler_bend()`. When `reverse` is
-    `False`, curvature ramps from zero to the switchover curvature. When
-    `reverse` is `True`, curvature ramps from the switchover curvature to zero.
-
-    Args:
-        switchover_angle: Tangent angle change across the Euler segment, in radians.
-        num_points: Number of points in the curve.
-        start_angle: Tangent angle at the first point.
-        start: First point of the segment.
-        reverse: If `True`, generate the exit segment of an Euler bend.
-
-    Returns:
-        `[[x0, y0], ...]` for the curve.
-    """
-    if num_points < 0:
-        raise PatternError(f'num_points must be non-negative, got {num_points}')
-    if switchover_angle < 0:
-        raise PatternError(f'switchover_angle must be non-negative, got {switchover_angle}')
-    if num_points == 0:
-        return numpy.empty((0, 2))
-
-    start = numpy.asarray(start, dtype=float)
-    if start.shape != (2,):
-        raise PatternError(f'start must be a 2D point; got shape {start.shape}')
-
-    if switchover_angle == 0:
-        return numpy.tile(start, (num_points, 1))
-
-    resolution = 100000
-    ll_max = numpy.sqrt(2 * switchover_angle)
-    qq = numpy.linspace(0, ll_max, resolution)
-    if reverse:
-        theta = start_angle - (ll_max * qq - qq * qq / 2)
-    else:
-        theta = start_angle - qq * qq / 2
-
-    return _integrate_tangent(qq, theta, num_points) + start
-
-
-def circular_arc(
-        radius: float,
-        arc_angle: float,
-        num_points: int = 200,
-        *,
-        start_angle: float = 0.0,
-        start: ArrayLike = (0.0, 0.0),
-        ) -> NDArray[numpy.float64]:
-    """
-    Generate a clockwise circular arc.
-
-    Args:
-        radius: Arc radius.
-        arc_angle: Clockwise tangent angle change across the arc, in radians.
-        num_points: Number of points in the curve, excluding the start point.
-        start_angle: Tangent angle at the start point.
-        start: Point where the arc starts.
-
-    Returns:
-        `[[x0, y0], ...]` for the arc, excluding `start`.
-    """
-    if num_points < 0:
-        raise PatternError(f'num_points must be non-negative, got {num_points}')
-    if radius <= 0:
-        raise PatternError(f'radius must be positive, got {radius}')
-    if arc_angle < 0:
-        raise PatternError(f'arc_angle must be non-negative, got {arc_angle}')
-    if num_points == 0:
-        return numpy.empty((0, 2))
-
-    start = numpy.asarray(start, dtype=float)
-    if start.shape != (2,):
-        raise PatternError(f'start must be a 2D point; got shape {start.shape}')
-
-    if arc_angle == 0:
-        return numpy.tile(start, (num_points, 1))
-
-    angles = numpy.linspace(0, arc_angle, num_points + 1)[1:]
-    right_normal = numpy.array([numpy.sin(start_angle), -numpy.cos(start_angle)])
-    center = start + radius * right_normal
-    radial = start - center
-
-    cos_t = numpy.cos(-angles)
-    sin_t = numpy.sin(-angles)
-    xx = center[0] + cos_t * radial[0] - sin_t * radial[1]
-    yy = center[1] + sin_t * radial[0] + cos_t * radial[1]
-    return numpy.stack((xx, yy), axis=1)
-
 
 def euler_bend(
         switchover_angle: float,
         num_points: int = 200,
-        *,
-        total_angle: float = pi / 2,
         ) -> NDArray[numpy.float64]:
     """
-    Generate an Euler bend (AKA Clothoid bend or Cornu spiral).
+    Generate a 90 degree Euler bend (AKA Clothoid bend or Cornu spiral).
-
-    Positive angles bend clockwise. By default, this generates the historical
-    90 degree bend.
 
     Args:
         switchover_angle: After this angle, the bend will transition into a circular arc
             (and transition back to an Euler spiral on the far side). If this is set to
-            `total_angle / 2`, no circular arc will be added.
+            `>= pi / 4`, no circular arc will be added.
-        num_points: Number of points in the curve.
+        num_points: Number of points in the curve
-        total_angle: Total tangent angle change across the bend, in radians.
 
     Returns:
         `[[x0, y0], ...]` for the curve
     """
-    if switchover_angle <= 0:
-        raise PatternError(f'switchover_angle must be positive, got {switchover_angle}')
-    if total_angle <= 0:
-        raise PatternError(f'total_angle must be positive, got {total_angle}')
-    if switchover_angle > total_angle / 2:
-        raise PatternError(
-            f'switchover_angle must be <= total_angle / 2; '
-            f'got {switchover_angle} for total_angle {total_angle}'
-            )
-    if num_points < 2:
-        raise PatternError(f'num_points must be at least 2, got {num_points}')
-
-    arc_angle = total_angle - 2 * switchover_angle
     ll_max = numpy.sqrt(2 * switchover_angle)        # total length of (one) spiral portion
-    ll_tot = 2 * ll_max + arc_angle
+    ll_tot = 2 * ll_max + (pi / 2 - 2 * switchover_angle)
-    num_points_spiral = max(2, numpy.floor(ll_max / ll_tot * num_points).astype(int))
+    num_points_spiral = numpy.floor(ll_max / ll_tot * num_points).astype(int)
-    num_points_arc = max(0, num_points - 2 * num_points_spiral)
+    num_points_arc = num_points - 2 * num_points_spiral
-    if arc_angle > 0:
-        num_points_arc = max(1, num_points_arc)
 
-    xy_spiral = euler_spiral(switchover_angle, num_points_spiral)
+    def gen_spiral(ll_max: float) -> NDArray[numpy.float64]:
+        if ll_max == 0:
+            return numpy.zeros((num_points_spiral, 2))
+
+        resolution = 100000
+        qq = numpy.linspace(0, ll_max, resolution)
+        dx = numpy.cos(qq * qq / 2)
+        dy = -numpy.sin(qq * qq / 2)
+
+        dq = ll_max / (resolution - 1)
+        ix = numpy.zeros(resolution)
+        iy = numpy.zeros(resolution)
+        ix[1:] = numpy.cumsum((dx[:-1] + dx[1:]) / 2) * dq
+        iy[1:] = numpy.cumsum((dy[:-1] + dy[1:]) / 2) * dq
+
+        ll_target = numpy.linspace(0, ll_max, num_points_spiral)
+        x_target = numpy.interp(ll_target, qq, ix)
+        y_target = numpy.interp(ll_target, qq, iy)
+
+        return numpy.stack((x_target, y_target), axis=1)
+
+    xy_spiral = gen_spiral(ll_max)
     xy_parts = [xy_spiral]
 
-    if arc_angle > 0:
+    if switchover_angle < pi / 4:
         # Build a circular segment to join the two euler portions
         rmin = 1.0 / ll_max
-        xy_arc = circular_arc(
+        half_angle = pi / 4 - switchover_angle
-            rmin,
+        qq = numpy.linspace(half_angle * 2, 0, num_points_arc + 1) + switchover_angle
-            arc_angle,
+        xc = rmin * numpy.cos(qq)
-            num_points_arc,
+        yc = rmin * numpy.sin(qq) + xy_spiral[-1, 1]
-            start_angle=-switchover_angle,
+        xc += xy_spiral[-1, 0] - xc[0]
-            start=xy_spiral[-1],
+        yc += xy_spiral[-1, 1] - yc[0]
-            )
+        xy_parts.append(numpy.stack((xc[1:], yc[1:]), axis=1))
-        xy_parts.append(xy_arc)
 
     endpoint_xy = xy_parts[-1][-1, :]
-    second_spiral = euler_spiral(
+    second_spiral = xy_spiral[::-1, ::-1] + endpoint_xy - xy_spiral[-1, ::-1]
-        switchover_angle,
-        num_points_spiral,
-        start_angle=-(total_angle - switchover_angle),
-        start=endpoint_xy,
-        reverse=True,
-        )
 
-    xy_parts.append(second_spiral[1:])
+    xy_parts.append(second_spiral)
     xy = numpy.concatenate(xy_parts)
 
     # Remove any 2x-duplicate points
-    xy = remove_duplicate_vertices(xy, closed_path=False, tolerance=1e-12)
+    xy = xy[(numpy.roll(xy, 1, axis=0) - xy  > 1e-12).any(axis=1)]
 
     return xy

masque/utils/vertices.py

@@ -5,11 +5,7 @@ import numpy
 from numpy.typing import NDArray, ArrayLike
 
 
-def remove_duplicate_vertices(
+def remove_duplicate_vertices(vertices: ArrayLike, closed_path: bool = True) -> NDArray[numpy.float64]:
-        vertices: ArrayLike,
-        closed_path: bool = True,
-        tolerance: float = 0.0,
-        ) -> NDArray[numpy.float64]:
     """
     Given a list of vertices, remove any consecutive duplicates.
 
@@ -17,22 +13,14 @@ def remove_duplicate_vertices(
         vertices: `[[x0, y0], [x1, y1], ...]`
         closed_path: If True, `vertices` is interpreted as an implicity-closed path
             (i.e. the last vertex will be removed if it is the same as the first)
-        tolerance: Maximum coordinate-wise absolute difference for two vertices to
-            be considered duplicates. Default `0` requires exact equality.
 
     Returns:
         `vertices` with no consecutive duplicates. This may be a view into the original array.
     """
-    if tolerance < 0:
-        raise ValueError(f'tolerance must be non-negative, got {tolerance}')
-
     vertices = numpy.asarray(vertices)
     if vertices.shape[0] <= 1:
         return vertices
-    if tolerance == 0:
+    duplicates = (vertices == numpy.roll(vertices, -1, axis=0)).all(axis=1)
-        duplicates = (vertices == numpy.roll(vertices, -1, axis=0)).all(axis=1)
-    else:
-        duplicates = (numpy.abs(vertices - numpy.roll(vertices, -1, axis=0)) <= tolerance).all(axis=1)
     if not closed_path:
         duplicates[-1] = False